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In systems engineering, software engineering, and computer science, a function model or functional model is a structured representation of the functions (activities, actions, processes, operations) within the modeled system or subject area.
A function model, similar with the activity model or process model, is a graphical representation of an enterprise's function within a defined scope. The purposes of the function model are to describe the functions and processes, assist with discovery of information needs, help identify opportunities, and establish a basis for determining product and service costs.
== History ==
The function model in the field of systems engineering and software engineering originates in the 1950s and 1960s, but the origin of functional modelling of organizational activity goes back to the late 19th century.
In the late 19th century the first diagrams appeared that pictured business activities, actions, processes, or operations, and in the first half of the 20th century the first structured methods for documenting business process activities emerged. One of those methods was the flow process chart, introduced by Frank Gilbreth to members of American Society of Mechanical Engineers (ASME) in 1921 with the presentation, entitled “Process Charts—First Steps in Finding the One Best Way”. Gilbreth's tools quickly found their way into industrial engineering curricula.
The emergence of the field of systems engineering can be traced back to Bell Telephone Laboratories in the 1940s. The need to identify and manipulate the properties of a system as a whole, which in complex engineering projects may greatly differ from the sum of the parts' properties, motivated various industries to apply the discipline. One of the first to define the function model in this field was the British engineer William Gosling. In his book The design of engineering systems (1962, p. 25) he stated:
A functional model must thus achieve two aims in order to be of use. It must furnish a throughput description mechanics capable of completely defining the first and last throughput states, and perhaps some of the intervening states. It must also offer some means by which any input, correctly described in terms of this mechanics, can be used to generate an output which is an equally correct description of the output which the actual system would have given for the input concerned. It may also be noted that there are two other things which a functional model may do, but which are not necessary to all functional models. Thus such a system may, but need not, describe the system throughputs other than at the input and output, and it may also contain a description of the operation which each element carries out on the throughput, but once again this is not.
One of the first well defined function models, was the functional flow block diagram (FFBD) developed by the defense-related TRW Incorporated in the 1950s. In the 1960s it was exploited by the NASA to visualize the time sequence of events in a space systems and flight missions. It is further widely used in classical systems engineering to show the order of execution of system functions.
== Functional modeling topics ==
=== Functional perspective ===
In systems engineering and software engineering a function model is created with a functional modeling perspective. The functional perspective is one of the perspectives possible in business process modelling, other perspectives are for example behavioural, organisational or informational.
A functional modeling perspective concentrates on describing the dynamic process. The main concept in this modeling perspective is the process, this could be a function, transformation, activity, action, task etc. A well-known example of a modeling language employing this perspective is data flow diagrams.
The perspective uses four symbols to describe a process, these being:
Process: Illustrates transformation from input to output.
Store: Data-collection or some sort of material.
Flow: Movement of data or material in the process.
External Entity: External to the modeled system, but interacts with it.
Now, with these symbols, a process can be represented as a network of these symbols. This decomposed process is a DFD, data flow diagram.
In Dynamic Enterprise Modeling a division is made in the Control model, Function Model, Process model and Organizational model.
=== Functional decomposition ===
Functional decomposition refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed from those parts by function composition. In general, this process of decomposition is undertaken either for the purpose of gaining insight into the identity of the constituent components, or for the purpose of obtaining a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of modularity.
Functional decomposition has a prominent role in computer programming, where a major goal is to modularize processes to the greatest extent possible. For example, a library management system may be broken up into an inventory module, a patron information module, and a fee assessment module. In the early decades of computer programming, this was manifested as the "art of subroutining," as it was called by some prominent practitioners.
Functional decomposition of engineering systems is a method for analyzing engineered systems. The basic idea is to try to divide a system in such a way that each block of the block diagram can be described without an "and" or "or" in the description.
This exercise forces each part of the system to have a pure function. When a system is composed of pure functions, they can be reused, or replaced. A usual side effect is that the interfaces between blocks become simple and generic. Since the interfaces usually become simple, it is easier to replace a pure function with a related, similar function.
== Functional modeling methods ==
The functional approach is extended in multiple diagrammic techniques and modeling notations. This section gives an overview of the important techniques in chronological order.
=== Function block diagram ===
A functional block diagram is a block diagram, that describes the functions and interrelationships of a system. The functional block diagram can picture:
Functions of a system pictured by blocks
Input of a block pictured with lines, and
Relationships between 9 functions
Functional sequences and paths for matter and or signals
The block diagram can use additional schematic symbols to show particular properties.
Specific function block diagram are the classic functional flow block diagram, and the Function Block Diagram (FBD) used in the design of programmable logic controllers.
=== Functional flow block diagram ===
The functional flow block diagram (FFBD) is a multi-tier, time-sequenced, step-by-step flow diagram of the system's functional flow.
The diagram is developed in the 1950s and widely used in classical systems engineering. The functional flow block diagram is also referred to as Functional Flow Diagram, functional block diagram, and functional flow.
Functional flow block diagrams (FFBD) usually define the detailed, step-by-step operational and support sequences for systems, but they are also used effectively to define processes in developing and producing systems. The software development processes also use FFBDs extensively. In the system context, the functional flow steps may include combinations of hardware, software, personnel, facilities, and/or procedures.
In the FFBD method, the functions are organized and depicted by their logical order of execution. Each function is shown with respect to its logical relationship to the execution and completion of other functions. A node labeled with the function name depicts each function. Arrows from left to right show the order of execution of the functions. Logic symbols represent sequential or parallel execution of functions.
=== HIPO and oPO ===
HIPO for hierarchical input process output is a popular 1970s systems analysis design aid and documentation technique for representing the modules of a system as a hierarchy and for documenting each module.
It was used to develop requirements, construct the design, and support implementation of an expert system to demonstrate automated rendezvous. Verification was then conducted systematically because of the method of design and implementation.
The overall design of the system is documented using HIPO charts or structure charts. The structure chart is similar in appearance to an organizational chart, but has been modified to show additional detail. Structure charts can be used to display several types of information, but are used most commonly to diagram either data structures or code structures.
=== N2 Chart ===
The N2 Chart is a diagram in the shape of a matrix, representing functional or physical interfaces between system elements. It is used to systematically identify, define, tabulate, design, and analyze functional and physical interfaces. It applies to system interfaces and hardware and/or software interfaces.
The N2 diagram has been used extensively to develop data interfaces, primarily in the software areas. However, it can also be used to develop hardware interfaces. The basic N2 chart is shown in Figure 2. The system functions are placed on the diagonal; the remainder of the squares in the N × N matrix represent the interface inputs and outputs.
=== Structured Analysis and Design Technique ===
Structured Analysis and Design Technique (SADT) is a software engineering methodology for describing systems as a hierarchy of functions, a diagrammatic notation for constructing a sketch for a software application. It offers building blocks to represent entities and activities, and a variety of arrows to relate boxes. These boxes and arrows have an associated informal semantics. SADT can be used as a functional analysis tool of a given process, using successive levels of details. The SADT method allows to define user needs for IT developments, which is used in industrial Information Systems, but also to explain and to present an activity's manufacturing processes, procedures.
The SADT supplies a specific functional view of any enterprise by describing the functions and their relationships in a company. These functions fulfill the objectives of a company, such as sales, order planning, product design, part manufacturing, and human resource management. The SADT can depict simple functional relationships and can reflect data and control flow relationships between different functions. The IDEF0 formalism is based on SADT, developed by Douglas T. Ross in 1985.
=== IDEF0 ===
IDEF0 is a function modeling methodology for describing manufacturing functions, which offers a functional modeling language for the analysis, development, re-engineering, and integration of information systems; business processes; or software engineering analysis. It is part of the IDEF family of modeling languages in the field of software engineering, and is built on the functional modeling language building SADT.
The IDEF0 Functional Modeling method is designed to model the decisions, actions, and activities of an organization or system. It was derived from the established graphic modeling language structured analysis and design technique (SADT) developed by Douglas T. Ross and SofTech, Inc. In its original form, IDEF0 includes both a definition of a graphical modeling language (syntax and semantics) and a description of a comprehensive methodology for developing models. The US Air Force commissioned the SADT developers to develop a function model method for analyzing and communicating the functional perspective of a system. IDEF0 should assist in organizing system analysis and promote effective communication between the analyst and the customer through simplified graphical devices.
=== Axiomatic design ===
Axiomatic design is a top down hierarchical functional decomposition process used as a solution synthesis framework for the analysis, development, re-engineering, and integration of products, information systems, business processes or software engineering solutions. Its structure is suited mathematically to analyze coupling between functions in order to optimize the architectural robustness of potential functional solution models.
== Related types of models ==
In the field of systems and software engineering numerous specific function and functional models and close related models have been defined. Here only a few general types will be explained.
=== Business function model ===
A Business Function Model (BFM) is a general description or category of operations performed routinely to carry out an organization's mission. They "provide a conceptual structure for the identification of general business functions". It can show the critical business processes in the context of the business area functions. The processes in the business function model must be consistent with the processes in the value chain models. Processes are a group of related business activities performed to produce an end product or to provide a service. Unlike business functions that are performed on a continual basis, processes are characterized by the fact that they have a specific beginning and an end point marked by the delivery of a desired output. The figure on the right depicts the relationship between the business processes, business functions, and the business area's business reference model.
=== Business Process Model and Notation ===
Business Process Model and Notation (BPMN) is a graphical representation for specifying business processes in a workflow. BPMN was developed by Business Process Management Initiative (BPMI), and is currently maintained by the Object Management Group since the two organizations merged in 2005. The current version of BPMN is 2.0.
The Business Process Model and Notation (BPMN) specification provides a graphical notation for specifying business processes in a Business Process Diagram (BPD). The objective of BPMN is to support business process management for both technical users and business users by providing a notation that is intuitive to business users yet able to represent complex process semantics. The BPMN specification also provides a mapping between the graphics of the notation to the underlying constructs of execution languages, particularly BPEL4WS.
=== Business reference model ===
A Business reference model is a reference model, concentrating on the functional and organizational aspects of the core business of an enterprise, service organization or government agency. In enterprise engineering a business reference model is part of an Enterprise Architecture Framework or Architecture Framework, which defines how to organize the structure and views associated with an Enterprise Architecture.
A reference model in general is a model of something that embodies the basic goal or idea of something and can then be looked at as a reference for various purposes. A business reference model is a means to describe the business operations of an organization, independent of the organizational structure that perform them. Other types of business reference model can also depict the relationship between the business processes, business functions, and the business area's business reference model. These reference model can be constructed in layers, and offer a foundation for the analysis of service components, technology, data, and performance.
=== Operator function model ===
The Operator Function Model (OFM) is proposed as an alternative to traditional task analysis techniques used by human factors engineers. An operator function model attempts to represent in mathematical form how an operator might decompose a complex system into simpler parts and coordinate control actions and system configurations so that acceptable overall system performance is achieved. The model represents basic issues of knowledge representation, information flow, and decision making in complex systems. Miller (1985) suggests that the network structure can be thought of as a possible representation of an operator's internal model of the system plus a control structure which specifies how the model is used to solve the decision problems that comprise operator control functions.
== See also ==
Bus Functional Model
Business process modeling
Data and information visualization
Data model
Enterprise modeling
Functional Software Architecture
Multilevel Flow Modeling
Polynomial function model
Rational function model
Scientific modeling
Unified Modeling Language
View model
== References ==
This article incorporates public domain material from the National Institute of Standards and Technology
This article incorporates public domain material from Operator Function Model (OFM). Federal Aviation Administration. | Wikipedia/Function_modeling |
A bus functional model (BFM), also known as a transaction verification model (TVM) is a non-synthesizable software model of an integrated circuit component having one or more external buses. The emphasis of the model is on simulating system bus transactions prior to building and testing the actual hardware. BFMs are usually defined as tasks in Hardware description languages (HDLs), which apply stimuli to the design under verification via complex waveforms and protocols. A BFM is typically implemented using hardware description languages such as Verilog, VHDL, SystemC, or SystemVerilog.
Typically, BFMs offer a two-sided interface: One interface side drives and samples low-level signals according to the bus protocol. On its other side, tasks are available to create and respond to bus transactions. BFMs are often used as reusable building blocks to create simulation test benches, in which the bus interface ports of a design under test are connected to appropriate BFMs.
Another common application of BFMs is the provision of substitute models for IP components: Instead of a netlist or RTL design of an IP component, a 3rd party IP supplier might provide only a BFM suitable for verification purposes. The actual IP component in the form of a gate-level netlist can be directly provided to the foundry by the IP provider.
In the past, BFM were treated as a non-synthesizable entity, however recently BFMs are becoming available as synthesizable models as well.
== Transaction verification models ==
BFMs are sometimes referred to as TVMs or Transaction Verification Models. This is to emphasize that bus operations of the model have been bundled into atomic bus transactions to make it easier to issue and view bus transactions. Visualizations of the bus transactions modeled by TVMs are similar to the output of a protocol analyzer or bus sniffer.
== References ==
Mitchel, Donna (2001). "Manual and Automatic VHDL/Verilog Test Bench Coding Techniques" (PDF). Dedicated Systems Magazine. 9 (2). Archived from the original (PDF) on 22 January 2004. Retrieved 8 April 2013. | Wikipedia/Bus_Functional_Model |
A reference model—in systems, enterprise, and software engineering—is an abstract framework or domain-specific ontology consisting of an interlinked set of clearly defined concepts produced by an expert or body of experts to encourage clear communication. A reference model can represent the component parts of any consistent idea, from business functions to system components, as long as it represents a complete set. This frame of reference can then be used to communicate ideas clearly among members of the same community.
Reference models are often illustrated as a set of concepts with some indication of the relationships between the concepts.
== Overview ==
According to OASIS (Organization for the Advancement of Structured Information Standards) a reference model is "an abstract framework for understanding significant relationships among the entities of some environment, and for the development of consistent standards or specifications supporting that environment. A reference model is based on a small number of unifying concepts and may be used as a basis for education and explaining standards to a non-specialist. A reference model is not directly tied to any standards, technologies or other concrete implementation details, but it does seek to provide a common semantics that can be used unambiguously across and between different implementations."
There are a number of concepts rolled up into that of a 'reference model.' Each of these concepts is important:
Abstract: a reference model is abstract. It provides information about environments of a certain kind. A reference model describes the type or kind of entities that may occur in such an environment, not the particular entities that actually do occur in a specific environment. For example, when describing the architecture of a particular house (which is a specific environment of a certain kind), an actual exterior wall may have dimensions and materials, but the concept of a wall (type of entity) is part of the reference model. One must understand the concept of a wall in order to build a house that has walls.
Entities and relationships: A reference model describes both types of entities (things that exist) and their relationships (how they connect, interact with one another, and exhibit joint properties). A list of entity types, by itself, doesn't provide enough information to serve as a reference model.
Within an environment: A reference model does not attempt to describe "all things." A reference model is used to clarify "things within an environment" or a problem space. To be useful, a reference model should include a clear description of the problem that it solves, and the concerns of the stakeholders who need to see the problem get solved.
Technology agnostic: A reference model's usefulness is limited if it makes assumptions about the technology or platforms in place in a particular computing environment. A reference model typically is intended to promote understanding a class of problems, not specific solutions for those problems. As such, it must assist the practitioner by aiding the process of imagining and evaluating a variety of potential solutions. That does not preclude the development of a reference model that describes a set of software applications, because the problem space may be "how to manage a set of software applications."
== The uses of a reference model ==
There are many uses for a reference model. One use is to create standards for both the objects that inhabit the model and their relationships to one another. By creating standards, the work of engineers and developers who need to create objects that behave according to the standard is made easier. Software can be written that meets a standard. When done well, a standard can make use of design patterns that support key qualities of software, such as the ability to extend the software in an inexpensive way.
Another use of a reference model is to educate. Using a reference model, leaders in software development can help break down a large problem space into smaller problems that can be understood, tackled, and refined. Developers who are new to a particular set of problems can quickly learn what the different problems are, and can focus on the problems that they are being asked to solve, while trusting that other areas are well understood and rigorously constructed. The level of trust is important to allow software developers to efficiently focus on their work.
A third use of a reference model is to improve communication between people. A reference model breaks up a problem into entities, or "things that exist all by themselves." This is often an explicit recognition of concepts that many people already share, but when created in an explicit manner, a reference model is useful by defining how these concepts differ from, and relate to, one another. This improves communication between individuals involved in using these concepts.
A fourth use of a reference model is to create clear roles and responsibilities. By creating a model of entities and their relationships, an organization can dedicate specific individuals or teams, making them responsible for solving a problem that concerns a specific set of entities. For example, if a reference model describes a set of business measurements needed to create a balanced scorecard, then each measurement can be assigned to a specific business leader. That allows a senior manager to hold each of their team members responsible for producing high quality results.
A fifth use of a reference model is to allow the comparison of different things. By breaking up a problem space into basic concepts, a reference model can be used to examine two different solutions to that problem. In doing so, the component parts of a solution can be discussed in relation to one another. For example, if a reference model describes computer systems that help track contacts between a business and their customers, then a reference model can be used by a business to decide which of five different software products to purchase, based on their needs. A reference model, in this example, could be used to compare how well each of the candidate solutions can be configured to meet the needs of a particular business process.
== Examples ==
Instances of reference models include, among others:
Agent Systems Reference Model,
Core Architecture Data Model reference model of DoDAF
Federal Enterprise Architecture Framework reference model of the FEA
HP Information Security Service Management (ISSM) - Reference Model (RM)
IBM Information Framework, a reference model for financial services
NIST Enterprise Architecture Model reference models from several Federal Enterprise Architectures
OGC Reference Model (Open Geospatial Consortium),
OpenReference, an open reference model for business performance, processes and practices
Open Systems Interconnection Basic Reference Model
IEEE 802 reference model
Purdue Enterprise Reference Architecture
Real-time Control System for real-time control problem domains
Reference Model of Open Distributed Processing,
TAFIM was the 1990 reference model of the earlier version of the DoDAF, and
Von Neumann architecture as a reference model for sequential computing
Digital Library Reference Model
ENVRI (Environmental Research Infrastructures) Reference Model
== See also ==
Business reference model
Open System Environment Reference Model
Reference architecture
== References == | Wikipedia/Reference_model |
A functional software architecture (FSA) is an architectural model that identifies enterprise functions, interactions and corresponding IT needs. These functions can be used as a reference by different domain experts to develop IT-systems as part of a co-operative information-driven enterprise. In this way, both software engineers and enterprise architects can create an information-driven, integrated organizational environment.
== Overview ==
When an integrated software system needs to be developed and implemented several tasks and corresponding responsibilities can normally be divided:
Strategic management and business consultants set objectives in relation to a more efficient/effective business process.
Enterprise engineers come up with a design of a more efficient business process and a request for a certain information system in the form of an Enterprise Architecture.
Software engineers come up with the design of this information system, which describes the components and structural features of the system by use of a certain architecture description language (ADL).
Computer programmers code the different modules and actually implement the system.
The described work division is in reality much more complex and also involves more actors but it outlines the involvement of people with different backgrounds in creating a software system that enables the organization to reach business objectives. A wide variety of material produced by different actors within this system development process needs to be exchanged between, and understood by, multiple actors.
Especially in the field of software engineering many tools (A4 Tool, CAME, ARIS), languages (ACME, Rapide, UML) and methods (DSDM, RUP, ISPL) are developed and extensively used. Also, the transition between the software engineers (step 3) and computer programmers (step 4) is already highly formalized by, for instance, object-oriented development.
Setting strategic objectives (step 1) and the corresponding search for business opportunities and weaknesses is a subject extensively discussed and investigated for more than a hundred years. Concepts like business process reengineering, product software market analysis, and requirements analysis are commonly known and extensively used in this context. These strategic inputs must be used for the development of a good enterprise design (step 2), which can then be used for software design and implementation respectively.
Recent studies have shown that these enterprise architectures can be developed by several different methods and techniques. Before these methods and techniques are discussed in detail a definition of an enterprise architecture is given:
An Enterprise Architecture is a strategic information asset base, which defines the mission, the information necessary to perform the mission and the technologies necessary to perform the mission, and the transitional processes for implementing new technologies in response to the changing mission needs.
This definition emphasizes the use of the architecture as a rich strategic information source for the improvement of business processes and development of needed information systems. If defined, maintained, and implemented effectively, these institutional blueprints assist in optimizing the interdependencies and interrelationships among an organization's business operations and the underlying IT that support operations.
Having read the definition of functional software architecture at the beginning of this entry we can see a functional software architecture as a type of enterprise architecture that can be used as a rich reference for the development of an integrated information system. Naming it a functional software architecture encourages practitioners to use it as a strategic input for a technical architecture. A formal mapping between functional software architecture and a type of ADL is therefore needed. In this way, the formal use and reuse of enterprise architectures as strategic input for software architectures can be realized.
== Development ==
As the boundary of an enterprise is extended, it becomes increasingly important that a common "big picture" of needed business, people and IT system activities is developed and shared by all the parties involved. A functional software architecture does this by breaking down the organization in business functions and corresponding IT needs. In this way, the enterprise engineer provides a rich schematic reference that can be used by the software engineer in the development of these IT-systems.
The development of a functional software architecture can be done by a number of (combined) methods and techniques. Filling in the "gap" between the enterprise engineers and software engineers through the use of different combinations of methods and techniques will be the main objective. However, this objective can only be reached when combined methods result in clear and rich functional software architectures that are developed and used by both parties.
Optimizing the internal and external business processes through process reengineering is one of the main objectives an enterprise can have in times of high external pressure. A business process involves value-creating activities with certain inputs and outputs, which are interconnected and thereby jointly contribute to the outcome (product or service) of the process. Process reengineering covers a variety of perspectives on how to change the organization. It is concerned with the redesign of strategic, value-adding processes, systems, policies and organizational structures to optimize the processes of an organization.
== Modeling the business ==
Within the area of enterprise engineering formal methodologies, methods and techniques are designed, tested and extensively used in order to offer organizations reusable business process solutions:
Computer-integrated manufacturing open systems architecture (CIMOSA) methodology
Integrated definition (IDEF) methodology
Petri Nets
Unified modeling language (UML) or unified enterprise modeling language (UEML)
Enterprise Function Diagrams (EFD)
These methodologies/techniques and methods are all more or less suited in modeling the enterprise and its underlying processes. So, which of them are suited for the further development of information technology systems that are needed for effective and efficient (re)designed processes? More important, why using a time-consuming enterprise methodology when information and software engineers can’t or won’t use the unclear results in the development of efficiency enabling IT systems? Before we can give the answers to these questions some short descriptions of the listed methods above are given.
=== Computer-integrated manufacturing open systems architecture ===
CIMOSA provides templates and interconnected modeling constructs to encode business, people and IT aspects of enterprise requirements. This is done from multiple perspectives: information view, function view, resource view, and organization view. These constructs can further be used to structure and facilitate the design and implementation of detailed IT systems.
The division in different views makes it a clarifying reference for enterprise and software engineers. It shows information needs for different enterprise functionalities (activities, processes, operations) and corresponding resources. In this way, it can easily be determined which IT-system will fulfill the information needs in a certain activity and process.
=== Integrated definition (IDEF) ===
IDEF is a structured modeling technique, which was first developed for the modeling of manufacturing systems. It was already being used by the U.S. Airforce in 1981. Initially, it had 4 different notations to model an enterprise from a certain viewpoint. These were IDEF0, IDEF1, IDEF2 and IDEF3 for functional, data, dynamic and process analysis respectively. In the past decades, several tools and techniques for the integration of the notations are developed incrementally.
IDEF clearly shows how a business process flows through a variety of decomposed business functions with corresponding information inputs, outputs, and actors. Like CIMOSA, it also uses different enterprise views. Moreover, IDEF can be easily transformed into UML-diagrams for the further development of its systems. these positive characteristics make it a powerful method for the development of functional software architectures.
=== Petri Nets ===
Petri nets are known tools to model manufacturing systems. They are highly expressive and provide good formalisms for the modeling of concurrent systems. The most advantageous properties are that of simple representation of states, concurrent system transitions, and capabilities to model the duration of transitions.
Petri nets, therefore, can be used to model certain business processes with corresponding state and transitions or activities within and outputs. Moreover, Petri Nets can be used to model different software systems and transitions between these systems. In this way, programmers use it as a schematic coding reference.
In recent years several attempts have shown that Petri nets can contribute to the development of business process integration. One of these is the Model Blue methodology, which is developed by IBM Chinese Research Laboratory and outlines the importance of model-driven business integration as an emerging approach for building integrated platforms. A mapping between their Model Blue business view and an equivalent Petri Net is also shown, which indicates that their research closes the gap between business and IT. However, instead of Petri Nets they rather use their own Model Blue IT view, which can be derived from their business view through a transformation engine.
=== Unified modeling language ===
UML is a broadly accepted modeling language for the development of software systems and applications. The object-oriented community also tries to use UML for enterprise modeling purposes. They emphasize the use of enterprise objects or business objects from which complex enterprise systems are made. A collection of these objects and corresponding interactions between them can represent a complex business system or process. Where Petri Nets focus on the interaction and states of objects, UML focuses more on the business objects themselves. Sometimes these are called the "enterprise building blocks", which includes resources, processes, goals, rules, and metamodels. Although UML in this way can be used to model an integrated software system it has been argued that the reality of business can be modeled with a software modeling language. In reaction, the object-oriented community makes business extensions for UML and adapts the language. UEML is derived from UML and is proposed as a business modeling language. The question remains if this business transformation is the right thing to do. It was earlier said that UML in combination with other "pure’ business methods can be a better alternative.
=== Enterprise function diagrams ===
EFD is a used modeling technique for the representation of enterprise functions and corresponding interactions. Different business processes can be modeled in these representations through the use of "function modules" and triggers. A starting business process delivers different inputs to different functions. A process flowing through all the functions and sub-functions creates multiple outputs. Enterprise function diagrams hereby give a very easy-to-use and detailed representation of a business process and corresponding functions, inputs, outputs, and triggers.
In this way, EFD has many similarities with IDEF0 diagrams, which also represent in a hierarchical way business processes as a combination of functions and triggers. The difference is that an EFD places the business functions in an organization's hierarchical perspective, which outlines the downstream of certain processes in the organization. On the contrary, IDEF0 diagrams show the responsibilities of certain business functions through the use of arrows. Also, IDEF0 has a clear representation of inputs and outputs of every (sub)function.
EFD possibly could be used as a business front-end to a software modeling language like UML. The major resemblance with IDEF as a modeling tool indicates that it can be done. However, more research is needed to improve the EFD technique in such a way that formal mappings to UML can be made. about the complementary use of IDEF and UML has contributed to the acceptance of IDEF as business-front end. A similar study should be done with EFD and UML.
== References == | Wikipedia/Functional_Software_Architecture |
A business process, business method, or business function is a collection of related, structured activities or tasks performed by people or equipment in which a specific sequence produces a service or product (that serves a particular business goal) for a particular customer or customers. Business processes occur at all organizational levels and may or may not be visible to the customers. A business process may often be visualized (modeled) as a flowchart of a sequence of activities with interleaving decision points or as a process matrix of a sequence of activities with relevance rules based on data in the process. The benefits of using business processes include improved customer satisfaction and improved agility for reacting to rapid market change. Process-oriented organizations break down the barriers of structural departments and try to avoid functional silos.
== Overview ==
A business process begins with a mission objective (an external event) and ends with achievement of the business objective of providing a result that provides customer value. Additionally, a process may be divided into subprocesses (process decomposition), the particular inner functions of the process. Business processes may also have a process owner, a responsible party for ensuring the process runs smoothly from start to finish.
Broadly speaking, business processes can be organized into three types, according to von Rosing et al.:
Operational processes, which constitute the core business and create the primary value stream, e.g., taking orders from customers, opening an account, and manufacturing a component
Management processes, the processes that oversee operational processes, including corporate governance, budgetary oversight, and employee oversight
Supporting processes, which support the core operational processes, e.g., accounting, recruitment, call center, technical support, and safety training
There are other definitions of the classification of processes proposed by
Strategic processes, which are managerial, directive or steering processes. Management has an important role in each of these. This type of process is related to strategic planning, partnerships, etc.
Operational processes, which are business processes, are of a productive or "missional" nature. These processes generate a product or service to be delivered to customers. These are considered to be unique or specific to each organisation.
Support processes, which are auxiliary in nature, support for operational and strategic processes. These are responsible for providing resources and are presented in most organizations.
A business made up of many process may be decomposed into various subprocesses, each of which have their own peculiar aspects but also contribute to achieving the objectives of the business. The business review analyzes processes, that usually include the mapping or modeling of processes and sub-processes down to a group of activities at different levels. Processes can be modeled using a large number of methods and techniques. For instance, the Business Process Modeling Notation is a business process modeling technique that can be used for drawing business processes in a visualized workflow. While decomposing processes into process classifications, categories can be helpful, but care must be taken in doing so as there may be crossover. At last, all processes are part of a largely unified customer-focused result, one of "customer value creation." This goal is expedited with business process management, which aims to analyze, improve, and enact business processes.
== History ==
=== Adam Smith ===
An important early (1776) description of processes was that of economist Adam Smith in his famous example of a pin factory. Inspired by an article in Diderot's Encyclopédie, Smith described the production of a pin in the following way:
One man draws out the wire; another straights it; a third cuts it; a fourth points it; a fifth grinds it at the top for receiving the head; to make the head requires two or three distinct operations; to put it on is a peculiar business; to whiten the pins is another ... and the important business of making a pin is, in this manner, divided into about eighteen distinct operations, which, in some manufactories, are all performed by distinct hands, though in others the same man will sometimes perform two or three of them.
Smith also first recognized how output could be increased through the use of labor division. Previously, in a society where production was dominated by handcrafted goods, one man would perform all the activities required during the production process, while Smith described how the work was divided into a set of simple tasks which would be performed by specialized workers. The result of labor division in Smith's example resulted in productivity increasing by 24,000 percent (sic), i.e. that the same number of workers made 240 times as many pins as they had been producing before the introduction of labor division.
Smith did not advocate labor division at any price or per se. The appropriate level of task division was defined through experimental design of the production process. In contrast to Smith's view which was limited to the same functional domain and comprised activities that are in direct sequence in the manufacturing process, today's process concept includes cross-functionality as an important characteristic. Following his ideas, the division of labor was adopted widely, while the integration of tasks into a functional, or cross-functional, process was not considered as an alternative option until much later.
=== Frederick Winslow Taylor ===
American engineer Frederick Winslow Taylor greatly influenced and improved the quality of industrial processes in the early twentieth century. His Principles of Scientific Management focused on standardization of processes, systematic training and clearly defining the roles of management and employees. His methods were widely adopted in the United States, Russia and parts of Europe and led to further developments such as "time and motion study" and visual task optimization techniques, such as Gantt charts.
=== Peter Drucker ===
In the latter part of the twentieth century, management guru Peter Drucker focused much of his work on the simplification and decentralization of processes, which led to the concept of outsourcing. He also coined the concept of the "knowledge worker," as differentiated from manual workers – and how knowledge management would become part of an entity's processes.
=== Other definitions ===
Davenport (1993) defines a (business) process as:
a structured, measured set of activities designed to produce a specific output for a particular customer or market. It implies a strong emphasis on how work is done within an organization, in contrast to a product focus's emphasis on what. A process is thus a specific ordering of work activities across time and space, with a beginning and an end, and clearly defined inputs and outputs: a structure for action. ... Taking a process approach implies adopting the customer's point of view. Processes are the structure by which an organization does what is necessary to produce value for its customers.
This definition contains certain characteristics that a process must possess. These characteristics are achieved by focusing on the business logic of the process (how work is done) instead of taking a product perspective (what is done). Following Davenport's definition of a process, we can conclude that a process must have clearly defined boundaries, input and output, consist of smaller parts and activities which are ordered in time and space, that there must be a receiver of the process outcome—a customer – and that the transformation taking place within the process must add customer value.
Hammer & Champy's (1993) definition can be considered as a subset of Davenport's. They define a process as:
a collection of activities that takes one or more kinds of input and creates an output that is of value to the customer.
As we can note, Hammer & Champy have a more transformation-oriented perception and put less emphasis on the structural component – process boundaries and the order of activities in time and space.
Rummler & Brache (1995) use a definition that clearly encompasses a focus on the organization's external customers, when stating that
a business process is a series of steps designed to produce a product or service. Most processes (...) are cross-functional, spanning the 'white space' between the boxes on the organization chart. Some processes result in a product or service that is received by an organization's external customer. We call these primary processes. Other processes produce products that are invisible to the external customer but essential to the effective management of the business. We call these support processes.
The above definition distinguishes two types of processes, primary and support processes, depending on whether a process is directly involved in the creation of customer value or concerned with the organization's internal activities. In this sense, Rummler and Brache's definition follows Porter's value chain model, which also builds on a division of primary and secondary activities. According to Rummler and Brache, a typical characteristic of a successful process-based organization is the absence of secondary activities in the primary value flow that is created in the customer oriented primary processes. The characteristic of processes as spanning the white space on the organization chart indicates that processes are embedded in some form of organizational structure. Also, a process can be cross-functional, i.e. it ranges over several business functions.
Johansson et al. (1993). define a process as:
a set of linked activities that take an input and transform it to create an output. Ideally, the transformation that occurs in the process should add value to the input and create an output that is more useful and effective to the recipient either upstream or downstream.
This definition also emphasizes the constitution of links between activities and the transformation that takes place within the process. Johansson et al. also include the upstream part of the value chain as a possible recipient of the process output. Summarizing the four definitions above, we can compile the following list of characteristics for a business process:
Definability: It must have clearly defined boundaries, input and output.
Order: It must consist of activities that are ordered according to their position in time and space (a sequence).
Customer: There must be a recipient of the process' outcome, a customer.
Value-adding: The transformation taking place within the process must add value to the recipient, either upstream or downstream.
Embeddedness: A process cannot exist in itself, it must be embedded in an organizational structure.
Cross-functionality: A process regularly can, but not necessarily must, span several functions.
Frequently, identifying a process owner (i.e., the person responsible for the continuous improvement of the process) is considered as a prerequisite. Sometimes the process owner is the same person who is performing the process.
== Related concepts ==
=== Workflow ===
Workflow is the procedural movement of information, material, and tasks from one participant to another. Workflow includes the procedures, people and tools involved in each step of a business process. A single workflow may either be sequential, with each step contingent upon completion of the previous one, or parallel, with multiple steps occurring simultaneously. Multiple combinations of single workflows may be connected to achieve a resulting overall process.
=== Business process re-engineering ===
Business process re-engineering (BPR) was originally conceptualized by Hammer and Davenport as a means to improve organizational effectiveness and productivity. It can involve starting from a "blank slate" and completely recreating major business processes, or it can involve comparing the "as-is" process and the "to-be" process and mapping the path for change from one to the other. Often BPR will involve the use of information technology to secure significant performance improvement. The term unfortunately became associated with corporate "downsizing" in the mid-1990s.
=== Business process management (BPM) ===
Though the term has been used contextually to mixed effect, "business process management" (BPM) can generally be defined as a discipline involving a combination of a wide variety of business activity flows (e.g., business process automation, modeling, and optimization) that strives to support the goals of an enterprise within and beyond multiple boundaries, involving many people, from employees to customers and external partners. A major part of BPM's enterprise support involves the continuous evaluation of existing processes and the identification of ways to improve upon it, resulting in a cycle of overall organizational improvement.
=== Knowledge management ===
Knowledge management is the definition of the knowledge that employees and systems use to perform their functions and maintaining it in a format that can be accessed by others. Duhon and the Gartner Group have defined it as "a discipline that promotes an integrated approach to identifying, capturing, evaluating, retrieving, and sharing all of an enterprise's information assets. These assets may include databases, documents, policies, procedures, and previously un-captured expertise and experience in individual workers."
Customer Service
Customer Service is a key component to an effective business business plan. Customer service in the 21st century is always evolving, and it is important to grow with your customer base. Not only does a social media presence matter, but also clear communication, clear expectation setting, speed, and accuracy. If the customer service provided by a business is not effective, it can be detrimental to the business success.
=== Total quality management ===
Total quality management (TQM) emerged in the early 1980s as organizations sought to improve the quality of their products and services. It was followed by the Six Sigma methodology in the mid-1980s, first introduced by Motorola. Six Sigma consists of statistical methods to improve business processes and thus reduce defects in outputs. The "lean approach" to quality management was introduced by the Toyota Motor Company in the 1990s and focused on customer needs and reducing of wastage.
Creating a Strong Brand Presence through Social Media
Creating a strong brand presence through social media is an important component to running a successful business. Companies can market, gain consumer insights, and advertise through social media. "According to a Salesforce survey, 85% of consumers conduct research before they make a purchase online, and among the most used channels for research are websites (74%) and social media (38%). Consequently, businesses need to have an effective online strategy to increase brand awareness and grow." (Paun, 2020)
Customers engage and interact through social media and businesses who are effectively part of social media drive more successful businesses. The most common social media sites that are used for business are Facebook, Instagram, and Twitter. Businesses with the strongest brand recognition and consumer engagement build social presences on all these platforms.
Resources:
Paun, Goran (2020). Building A Brand: Why A Strong Digital Presence Matters. Forbes. Sourced from
=== Information technology as an enabler for business process management ===
Advances in information technology over the years have changed business processes within and between business enterprises. In the 1960s, operating systems had limited functionality, and any workflow management systems that were in use were tailor-made for the specific organization. The 1970s and 1980s saw the development of data-driven approaches as data storage and retrieval technologies improved. Data modeling, rather than process modeling was the starting point for building an information system. Business processes had to adapt to information technology because process modeling was neglected. The shift towards process-oriented management occurred in the 1990s. Enterprise resource planning software with workflow management components such as SAP, Baan, PeopleSoft, Oracle and JD Edwards emerged, as did business process management systems (BPMS) later.
The world of e-business created a need to automate business processes across organizations, which in turn raised the need for standardized protocols and web services composition languages that can be understood across the industry. The Business Process Modeling Notation (BPMN) and Business Motivation Model (BMM) are widely used standards for business modeling. The Business Modeling and Integration Domain Task Force (BMI DTF) is a consortium of vendors and user companies that continues to work together to develop standards and specifications to promote collaboration and integration of people, systems, processes and information within and across enterprises.
The most recent trends in BPM are influenced by the emergence of cloud technology, the prevalence of social media and mobile technology, and the development of analytical techniques. Cloud-based technologies allow companies to purchase resources quickly and as required, independent of their location. Social media, websites and smart phones are the newest channels through which organizations reach and support their customers. The abundance of customer data collected through these channels as well as through call center interactions, emails, voice calls, and customer surveys has led to a huge growth in data analytics which in turn is utilized for performance management and improving the ways in which the company services its customers.
== Importance of the process chain ==
Business processes comprise a set of sequential sub-processes or tasks with alternative paths, depending on certain conditions as applicable, performed to achieve a given objective or produce given outputs. Each process has one or more needed inputs. The inputs and outputs may be received from, or sent to other business processes, other organizational units, or internal or external stakeholders.
Business processes are designed to be operated by one or more business functional units, and emphasize the importance of the "process chain" rather than the individual units.
In general, the various tasks of a business process can be performed in one of two ways:
manually
by means of business data processing systems such as ERP systems
Typically, some process tasks will be manual, while some will be computer-based, and these tasks may be sequenced in many ways. In other words, the data and information that are being handled through the process may pass through manual or computer tasks in any given order.
== Policies, processes and procedures ==
The above improvement areas are equally applicable to policies, processes, detailed procedures (sub-processes/tasks) and work instructions. There is a cascading effect of improvements made at a higher level on those made at a lower level.
For example, if a recommendation to replace a given policy with a better one is made with proper justification and accepted in principle by business process owners, then corresponding changes in the consequent processes and procedures will follow naturally in order to enable implementation of the policies.
== Reporting as an essential base for execution ==
Business processes must include up-to-date and accurate reports to ensure effective action. An example of this is the availability of purchase order status reports for supplier delivery follow-up as described in the section on effectiveness above. There are numerous examples of this in every possible business process.
Another example from production is the process of analyzing line rejections occurring on the shop floor. This process should include systematic periodical analysis of rejections by reason and present the results in a suitable information report that pinpoints the major reasons and trends in these reasons for management to take corrective actions to control rejections and keep them within acceptable limits. Such a process of analysis and summarisation of line rejection events is clearly superior to a process which merely inquires into each individual rejection as it occurs.
Business process owners and operatives should realise that process improvement often occurs with introduction of appropriate transaction, operational, highlight, exception or M.I.S. reports, provided these are consciously used for day-to-day or periodical decision-making. With this understanding would hopefully come the willingness to invest time and other resources in business process improvement by introduction of useful and relevant reporting systems.
== Supporting theories and concepts ==
=== Span of control ===
The span of control is the number of subordinates a supervisor manages within a structural organization. Introducing a business process concept has a considerable impact on the structural elements of the organization and, thus also on the span of control.
Large organizations that are not organized as markets need to be organized in smaller units, or departments – which can be defined according to different principles.
=== Information management concepts ===
Information management and the organization's infrastructure strategies related to it, are a theoretical cornerstone of the business process concept, requiring "a framework for measuring the level of IT support for business processes."
== See also ==
Business functions
Business method patent
Business process automation
Business Process Definition Metamodel
Business process mapping
Business process outsourcing
== References ==
== Further reading ==
Paul's Harmon (2007). Business Process Change: 2nd Ed, A Guide for Business Managers and BPM and Six Sigma Professionals. Morgan Kaufmann
E. Obeng and S. Crainer S (1993). Making Re-engineering Happen. Financial Times Prentice Hall
Howard Smith and Peter Fingar (2003). Business Process Management. The Third Wave, MK Press
Slack et al., edited by: David Barnes (2000) The Open University, Understanding Business: Processes
Malakooti, B. (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons.
== External links ==
Media related to Business process at Wikimedia Commons | Wikipedia/Business_function |
Business Process Model and Notation (BPMN) is a graphical representation for specifying business processes in a business process model.
Originally developed by the Business Process Management Initiative (BPMI), BPMN has been maintained by the Object Management Group (OMG) since the two organizations merged in 2005. Version 2.0 of BPMN was released in January 2011, at which point the name was amended to Business Process Model and Notation to reflect the introduction of execution semantics, which were introduced alongside the existing notational and diagramming elements. Though it is an OMG specification, BPMN is also ratified as ISO 19510. The latest version is BPMN 2.0.2, published in January 2014.
== Overview ==
Business Process Model and Notation (BPMN) is a standard for business process modeling that provides a graphical notation for specifying business processes in a Business Process Diagram (BPD), based on a flowcharting technique very similar to activity diagrams from Unified Modeling Language (UML). The objective of BPMN is to support business process management, for both technical users and business users, by providing a notation that is intuitive to business users, yet able to represent complex process semantics. The BPMN specification also provides a mapping between the graphics of the notation and the underlying constructs of execution languages, particularly Business Process Execution Language (BPEL).
BPMN has been designed to provide a standard notation readily understandable by all business stakeholders, typically including business analysts, technical developers and business managers. BPMN can therefore be used to support the generally desirable aim of all stakeholders on a project adopting a common language to describe processes, helping to avoid communication gaps that can arise between business process design and implementation.
BPMN is one of a number of business process modeling language standards used by modeling tools and processes. While the current variety of languages may suit different modeling environments, there are those who advocate for the development or emergence of a single, comprehensive standard, combining the strengths of different existing languages. It is suggested that in time, this could help to unify the expression of basic business process concepts (e.g., public and private processes, choreographies), as well as advanced process concepts (e.g., exception handling, transaction compensation).
Two new standards, using a similar approach to BPMN have been developed, addressing case management modeling (Case Management Model and Notation) and decision modeling (Decision Model and Notation).
== Topics ==
=== Scope ===
BPMN is constrained to support only the concepts of modeling applicable to business processes. Other types of modeling done by organizations for non-process purposes are out of scope for BPMN. Examples of modeling excluded from BPMN are:
Organizational structures
Functional breakdowns
Data models
In addition, while BPMN shows the flow of data (messages), and the association of data artifacts to activities, it is not a data flow diagram.
=== Elements ===
BPMN models are expressed by simple diagrams constructed from a limited set of graphical elements. For both business users and developers, they simplify understanding of business activities' flow and process.
BPMN's four basic element categories are:
Flow objects
Events, activities, gateways
Connecting objects
Sequence flow, message flow, association
Swim lanes
Pool, lane, Dark Pool
Artifacts
Data object, group, annotation
These four categories enable creation of simple business process diagrams (BPDs). BPDs also permit making new types of flow object or artifact, to make the diagram more understandable.
=== Flow objects and connecting objects ===
Flow objects are the main describing elements within BPMN, and consist of three core elements: events, activities, and gateways.
==== Event ====
An Event is represented with a circle and denotes something that happens (compared with an activity, which is something that is done). Icons within the circle denote the type of event (e.g., an envelope representing a message, or a clock representing time). Events are also classified as Catching (for example, if catching an incoming message starts a process) or Throwing (such as throwing a completion message when a process ends).
Start event
Acts as a process trigger; indicated by a single narrow border, and can only be Catch, so is shown with an open (outline) icon.
Intermediate event
Represents something that happens between the start and end events; is indicated by a double border, and can Throw or Catch (using solid or open icons as appropriate). For example, a task could flow to an event that throws a message across to another pool, where a subsequent event waits to catch the response before continuing.
End event
Represents the result of a process; indicated by a single thick or bold border, and can only Throw, so is shown with a solid icon.
==== Activity ====
An activity is represented with a rounded-corner rectangle and describes the kind of work which must be done. An activity is a generic term for work that a company performs. It can be atomic or compound.
Task
A task represents a single unit of work that is not or cannot be broken down to a further level of business process detail. It is referred to as an atomic activity. A task is the lowest level activity illustrated on a process diagram. A set of tasks may represent a high-level procedure.
Sub-process
Used to hide or reveal additional levels of business process detail. When collapsed, a sub-process is indicated by a plus sign against the bottom line of the rectangle; when expanded, the rounded rectangle expands to show all flow objects, connecting objects, and artifacts. A sub-process is referred to as a compound activity.
Has its own self-contained start and end events; sequence flows from the parent process must not cross the boundary.
Transaction
A form of sub-process in which all contained activities must be treated as a whole; i.e., they must all be completed to meet an objective, and if any one of them fails, they must all be compensated (undone). Transactions are differentiated from expanded sub-processes by being surrounded by a double border.
Call Activity
A point in the process where a global process or a global Task is reused. A call activity is differentiated from other activity types by a bolded border around the activity area.
==== Gateway ====
A gateway is represented with a diamond shape and determines forking and merging of paths, depending on the conditions expressed.
Exclusive
Used to create alternative flows in a process. Because only one of the paths can be taken, it is called exclusive.
Event Based
The condition determining the path of a process is based on an evaluated event.
Parallel
Used to create parallel paths without evaluating any conditions.
Inclusive
Used to create alternative flows where all paths are evaluated.
Exclusive Event Based
An event is being evaluated to determine which of mutually exclusive paths will be taken.
Complex
Used to model complex synchronization behavior.
Parallel Event Based
Two parallel processes are started based on an event, but there is no evaluation of the event.
==== Connections ====
Flow objects are connected to each other using Connecting objects, which are of three types: sequences, messages, and associations.
Sequence Flow
A Sequence Flow is represented with a solid line and arrowhead, and shows in which order the activities are performed. The sequence flow may also have a symbol at its start, a small diamond indicates one of a number of conditional flows from an activity, while a diagonal slash indicates the default flow from a decision or activity with conditional flows.
Message Flow
A Message Flow is represented with a dashed line, an open circle at the start, and an open arrowhead at the end. It tells us what messages flow across organizational boundaries (i.e., between pools). A message flow can never be used to connect activities or events within the same pool.
Association
An Association is represented with a dotted line. It is used to associate an Artifact or text to a Flow Object, and can indicate some directionality using an open arrowhead (toward the artifact to represent a result, from the artifact to represent an input, and both to indicate it is read and updated). No directionality is used when the Artifact or text is associated with a sequence or message flow (as that flow already shows the direction).
=== Pools, Lanes, and artifacts ===
Swim lanes are a visual mechanism of organising and categorising activities, based on cross functional flowcharting, and in BPMN consist of two types:
Pool
Represents major participants in a process, typically separating different organisations. A pool contains one or more lanes (like a real swimming pool). A pool can be open (i.e., showing internal detail) when it is depicted as a large rectangle showing one or more lanes, or collapsed (i.e., hiding internal detail) when it is depicted as an empty rectangle stretching the width or height of the diagram.
Lane
Used to organise and categorise activities within a pool according to function or role, and depicted as a rectangle stretching the width or height of the pool. A lane contains the flow objects, connecting objects and artifacts.
Artifacts allow developers to bring some more information into the model/diagram. In this way the model/diagram becomes more readable. There are three pre-defined Artifacts, and they are:
Data objects: Data objects show the reader which data is required or produced in an activity.
Group: A Group is represented with a rounded-corner rectangle and dashed lines. The group is used to group different activities but does not affect the flow in the diagram.
Annotation: An annotation is used to give the reader of the model/diagram an understandable impression.
=== Examples of business process diagrams ===
Click on small images for full-size version
=== BPMN 2.0.2 ===
The vision of BPMN 2.0.2 is to have one single specification for a new Business Process Model and Notation that defines the notation, metamodel and interchange format but with a modified name that still preserves the "BPMN" brand. The features include:
Formalizes the execution semantics for all BPMN elements.
Defines an extensibility mechanism for both Process model extensions and graphical extensions.
Refines Event composition and correlation.
Extends the definition of human interactions.
Defines a Choreography model.
The current version of the specification was released in January 2014.
== Comparison of BPMN versions ==
== Types of BPMN sub-model ==
Business process modeling is used to communicate a wide variety of information to a wide variety of audiences. BPMN is designed to cover this wide range of usage and allows modeling of end-to-end business processes to allow the viewer of the Diagram to be able to easily differentiate between sections of a BPMN Diagram. There are three basic types of sub-models within an end-to-end BPMN model: Private (internal) business processes, Abstract (public) processes, and Collaboration (global) processes:
Private (internal) business processes
Private business processes are those internal to a specific organization and are the type of processes that have been generally called workflow or BPM processes. If swim lanes are used then a private business process will be contained within a single Pool. The Sequence Flow of the Process is therefore contained within the Pool and cannot cross the boundaries of the Pool. Message Flow can cross the Pool boundary to show the interactions that exist between separate private business processes.
Abstract (public) processes
This represents the interactions between a private business process and another process or participant. Only those activities that communicate outside the private business process are included in the abstract process. All other “internal” activities of the private business process are not shown in the abstract process. Thus, the abstract process shows to the outside world the sequence of messages that are required to interact with that business process. Abstract processes are contained within a Pool and can be modeled separately or within a larger BPMN Diagram to show the Message Flow between the abstract process activities and other entities. If the abstract process is in the same Diagram as its corresponding private business process, then the activities that are common to both processes can be associated.
Collaboration (global) processes
A collaboration process depicts the interactions between two or more business entities. These interactions are defined as a sequence of activities that represent the message exchange patterns between the entities involved. Collaboration processes may be contained within a Pool and the different participant business interactions are shown as Lanes within the Pool. In this situation, each Lane would represent two participants and a direction of travel between them. They may also be shown as two or more Abstract Processes interacting through Message Flow (as described in the previous section). These processes can be modeled separately or within a larger BPMN Diagram to show the Associations between the collaboration process activities and other entities. If the collaboration process is in the same Diagram as one of its corresponding private business process, then the activities that are common to both processes can be associated.
Within and between these three BPMN sub-models, many types of Diagrams can be created. The following are the types of business processes that can be modeled with BPMN (those with asterisks may not map to an executable language):
High-level private process activities (not functional breakdown)*
Detailed private business process
As-is or old business process*
To-be or new business process
Detailed private business process with interactions to one or more external entities (or “Black Box” processes)
Two or more detailed private business processes interacting
Detailed private business process relationship to Abstract Process
Detailed private business process relationship to Collaboration Process
Two or more Abstract Processes*
Abstract Process relationship to Collaboration Process*
Collaboration Process only (e.g., ebXML BPSS or RosettaNet)*
Two or more detailed private business processes interacting through their Abstract Processes and/or a Collaboration Process
BPMN is designed to allow all the above types of Diagrams. However, it should be cautioned that if too many types of sub-models are combined, such as three or more private processes with message flow between each of them, then the Diagram may become difficult to understand. Thus, the OMG recommends that the modeler pick a focused purpose for the BPD, such as a private or collaboration process.
== Comparison with other process modeling notations ==
Event-driven process chains (EPC) and BPMN are two notations with similar expressivity when process modeling is concerned. A BPMN model can be transformed into an EPC model. Conversely, an EPC model can be transformed into a BPMN model with only a slight loss of information. A study showed that for the same process, the BPMN model may need around 40% fewer elements than the corresponding EPC model, but with a slightly larger set of symbols. The BPMN model would therefore be easier to read. The conversion between the two notations can be automated.
UML activity diagrams and BPMN are two notations that can be used to model the same processes: a subset of the activity diagram elements have a similar semantic than BPMN elements, despite the smaller and less expressive set of symbols. A study showed that both types of process models appear to have the same level of readability for inexperienced users, despite the higher formal constraints of an activity diagram.
== BPM Certifications ==
The Business Process Management (BPM) world acknowledges the critical importance of modeling standards for optimizing and standardizing business processes. The Business Process Model and Notation (BPMN) version 2 has brought significant improvements in event and subprocess modeling, significantly enriching the capabilities for documenting, analyzing, and optimizing business processes.
Elemate positions itself as a guide in exploring the various BPM certifications and dedicated training paths, thereby facilitating the mastery of BPMN and continuous improvement of processes within companies.
=== OMG OCEB certification ===
The Object Management Group (OMG), the international consortium behind the BPMN standard, offers the OCEB certification (OMG Certified Expert in BPM). This certification specifically targets business process modeling with particular emphasis on BPMN 2. The OCEB certification is structured into five levels: Fundamental, Business Intermediate (BUS INT), Technical Intermediate (TECH INT), Business Advanced (BUS ADV), and Technical Advanced (TECH ADV), thus providing a comprehensive pathway for BPM professionals.
=== Other BPM certifications ===
Beyond the OCEB, there are other recognized certifications in the BPM field:
CBPA (Certified Business Process Associate): Offered by the ABPMP (Association of Business Process Management Professionals), this certification is aimed at professionals starting in BPM.
CBPP (Certified Business Process Professional): Also awarded by the ABPMP, the CBPP certification targets experienced professionals, offering validation of their global expertise in BPM.
=== The interest of a BPMN certification ===
While BPMN 2 has established itself as an essential standard in business process modeling, a specific certification for BPMN could provide an additional guarantee regarding the quality and compliance of the models used. This becomes particularly relevant when companies employ external providers for the modeling of their business processes.
=== BPM certifying training with BPMN 2 ===
Although OMG does not offer a certification exclusively dedicated to BPMN 2, various organizations provide certifying training that encompasses this standard. These trainings cover not just BPMN but also the principles of management, automation, and digitization of business processes. They enable learners to master process mapping and modeling using BPMN 2, essential for optimizing business operations.
== See also ==
DRAKON
Business process management
Business process modeling
Comparison of Business Process Model and Notation modeling tools
CMMN (Case Management Model and Notation)
Process Driven Messaging Service
Function model
Functional software architecture
Workflow patterns
Service Component Architecture
XPDL
YAWL
== References ==
== Further reading ==
Grosskopf, Decker and Weske. (Feb 28, 2009). The Process: Business Process Modeling using BPMN. Meghan Kiffer Press. ISBN 978-0-929652-26-9. Archived from the original on April 30, 2019. Retrieved July 9, 2020.
Ryan K. L. Ko, Stephen S. G. Lee, Eng Wah Lee (2009) Business Process Management (BPM) Standards: A Survey. In: Business Process Management Journal, Emerald Group Publishing Limited. Volume 15 Issue 5. ISSN 1463-7154. PDF
Stephen A. White; Conrad Bock (2011). BPMN 2.0 Handbook Second Edition: Methods, Concepts, Case Studies and Standards in Business Process Management Notation. Future Strategies Inc. ISBN 978-0-9849764-0-9.
== External links ==
OMG BPMN Specification
BPMN Tool Matrix
BPMN Information Home Page OMG information page for BPMN. | Wikipedia/Business_Process_Model_and_Notation |
The input–process–output (IPO) model, or input-process-output pattern, is a widely used approach in systems analysis and software engineering for describing the structure of an information processing program or other process. Many introductory programming and systems analysis texts introduce this as the most basic structure for describing a process.
== Overview ==
A computer program is useful for another sort of process using the input-process-output model receives inputs from a user or other source, does some computations on the inputs, and returns the results of the computations. In essence the system separates itself from the environment, thus defining both inputs and outputs as one united mechanism.
The system would divide the work into three categories:
A requirement from the environment (input)
A computation based on the requirement (process)
A provision for the environment (output)
In other words, such inputs may be materials, human resources, money or information, transformed into outputs, such as consumables, services, new information or money.
As a consequence, an input-process-output system becomes very vulnerable to misinterpretation. This is because, theoretically, it contains all the data, in regards to the environment outside the system. Yet, in practice, the environment contains a significant variety of objects that a system is unable to comprehend, as it exists outside the system's control. As a result, it is very important to understand where the boundary lies between the system and the environment, which is beyond the system's understanding. Various analysts often set their own boundaries, favoring their point of view, thus creating much confusion.
== Systems at work ==
The views differ, in regards to systems thinking. One of such definitions would outline the Input-process-output system, as a structure, would be:
"Systems thinking is the art and science of making reliable inferences about behaviour by developing an increasingly deep understanding of the understanding of the underlying structure"
Alternatively, it was also suggested that systems are not 'holistic' in the sense of bonding with remote objects (for example: trying to connect a crab, ozone layer and capital life cycle together).
== Types of systems ==
There are five major categories that are the most cited in information systems literature:
=== Natural systems ===
A system which has not been created as a result of human interference. Examples of such would be the Solar System as well as the human body, evolving into its current form
=== Designed physical systems ===
A system which has been created as a result of human interference, and is physically identifiable. Examples of such would be various computing machines, created by human mind for some specific purpose.
=== Designed abstract systems ===
A system which has been created as a result of human interference, and is not physically identifiable. Examples of such would be mathematical and philosophical systems, which have been created by human minds, for some specific purpose.
There are also some social systems, which allow humans to collectively achieve a specific
=== Social systems ===
A system created by humans, and derived from intangible purposes. For example: a family, that is a hierarchy of human relationships, which in essence create the boundary between natural and human systems.
=== Human activity systems ===
An organisation with hierarchy, created by humans for a specific purpose. For example: a company, which organises humans together to collaborate and achieve a specific purpose. The result of this system is physically identifiable. There are, however, some significant links between with previous types. It is clear that the idea of human activity system (HAS), would consist of a variety of smaller social system, with its unique development and organisation. Moreover, arguably HASes can include designed systems - computers and machinery. Majority of previous systems would overlap.
== System characteristics ==
There are several key characteristics, when it comes to the fundamental behaviour of any system.
Systems can be classified as open or closed:'
Those that interact with their environment, in form of money, data, energy or exchange materials, are generally understood as open. Openness of the system can vary significantly. This is because, a system would be classified as open, if it receives even a single input from the environment, yet a system that merely interacts with the environment, would be classified as open as well. The more open the system is, the more complex it normally would be, due to lower predictability of its components.
Those that have no interactions with the environment at all are closed. In practice, however, a completely closed system is merely liveable, due to loss of practical usage of the output. As a result, most of the systems would be open or open to a certain extent.
Systems can be classified as deterministic or stochastic:
Well-defined and clearly structured system in terms of behavioural patterns becomes predictable, thus becoming deterministic. In other words, it would only use empirical data. For example: mathematics or physics are set around specific laws, which make the results of calculation predictable. Deterministic systems would have simplistic interactions between inner components.
More complex, and often more open systems, would have relatively lower extent of predictability, due to absence of clearly structured behavioural patterns. Analysing such system, is therefore much harder. Such systems would be stochastic, or probabilistic, this is because of the stochastic nature of human beings whilst performing various activities. Having said that, designed systems would still be considered as deterministic, due to a rigid structure of rules incorporated into the design.
Systems can be classified as static or dynamic
Most systems would be known as dynamic, because of the constant evolution in computing power, yet some systems could find it hard to balance between being created and ceasing to exist. An example of such could be a printed map, which is not evolving, in contrast to a dynamic map, provided from constantly updating developers.
Systems can be classified as self-regulating or non-self-regulating
The greater the extent of self-control of systems activity is, the greater is the liveability of the final system is. It is vital for any system to be able to control its activities in order to remain stable.
== Real life applications ==
=== Corporate business ===
A manufacturing processes that take raw materials as inputs, applies a manufacturing process, and produces manufactured goods as output. The usage of such systems could help to create stronger human organisations, in terms of company operations in each and every department of the firm, no matter the size, which . IPOs can also restructure existing static and non-self-regulating systems, which in real world would be used in form of outsourcing the product fulfilment, due to inefficiency of current fulfilment.
=== Programming ===
The majority of existing programs for coding, such as Java, Python, C++, would be based upon a deterministic IPO model, with clear inputs coming from the coder, converting into outputs, such as applications.
A batch transaction processing system, which accepts large volumes of homogeneous transactions, processes it (possibly updating a database), and produces output such as reports or computations.
An interactive computer program, which accepts simple requests from a user and responds to them after some processing and/or database accesses.
=== Scientific ===
A calculator, which uses inputs, provided by the operator, and processes them into outputs to be used by the operator.
A thermostat, which senses the temperature (input), decides on an action (heat on/off), and executes the action (output).
== See also ==
Read–eval–print loop
Extract, transform, load
CIPO-model
== References == | Wikipedia/IPO_Model |
Structured analysis and design technique (SADT) is a systems engineering and software engineering methodology for describing systems as a hierarchy of functions. SADT is a structured analysis modelling language, which uses two types of diagrams: activity models and data models. It was developed in the late 1960s by Douglas T. Ross, and was formalized and published as IDEF0 in 1981.
== Overview ==
Structured analysis and design technique (SADT) is a diagrammatic notation designed specifically to help people describe and understand systems. It offers building blocks to represent entities and activities, and a variety of arrows to relate boxes. These boxes and arrows have an associated informal semantics. SADT can be used as a functional analysis tool of a given process, using successive levels of details. The SADT method not only allows one to define user needs for IT developments, which is often used in the industrial Information Systems, but also to explain and present an activity's manufacturing processes and procedures.
== History ==
SADT was developed and field-tested during the period of 1969 to 1973 by Douglas T. Ross and SofTech, Inc. The methodology was used in the MIT Automatic Programming Tool (APT) project. It received extensive use starting in 1973 by the US Air Force Integrated Computer Aided Manufacturing program.
According to Levitt (2000) SADT is "part of a series of structured methods, that represent a collection of analysis, design, and programming techniques that were developed in response to the problems facing the software world from the 1960s to the 1980s. In this timeframe most commercial programming was done in COBOL and Fortran, then C and BASIC. There was little guidance on "good" design and programming techniques, and there were no standard techniques for documenting requirements and designs. Systems were getting larger and more complex, and the information system development became harder and harder to do so. As a way to help manage large and complex software.
SADT was among a series of similar structured methods, which had emerged since the 1960 such as:
Structured programming in circa 1967 with Edsger W. Dijkstra.
Structured design around 1975 with Larry Constantine and Ed Yourdon
Structured analysis in circa 1978 with Tom DeMarco, Yourdon, Gane & Sarson, McMenamin & Palmer.
Information technology engineering in circa 1990 with James Martin.
In 1981 the IDEF0 formalism was published, based on SADT.
== SADT topics ==
=== Top-down approach ===
The structured analysis and design technique uses a decomposition with the top-down approach. This decomposition is conducted only in the physical domain from an axiomatic design viewpoint.
=== Diagrams ===
SADT uses two types of diagrams: activity models and data models. It uses arrows to build these diagrams.
The SADT's representation is the following:
A main box where the name of the process or the action is specified
On the left-hand side of this box, incoming arrows: inputs of the action.
On the upper part, the incoming arrows: data necessary for the action.
On the bottom of the box, incoming arrows: means used for the action.
On the right-hand side of the box, outgoing arrows: outputs of the action.
The semantics of arrows for activities:
Inputs enter from the left and represent data or consumables that are needed by the activity.
Outputs exit to the right and represent data or products that are produced by the activity.
Controls enter from the top and represent commands or conditions which influence the execution of an activity but are not consumed.
Mechanisms identify the means, components or tools used to accomplish the activity. Represents allocation of activities.
The semantics of arrows for data:
Inputs are activities that produce the data.
Outputs consume the data.
Controls influence the internal state of the data.
=== Roles ===
According to Mylopoulos (2004) in the software development process multiple roles can or should be distinguished:
Author or developer of the SADT models
Commenters, who review the author's work
Readers or users of the SADT models
Experts, who can advise the authors
Technical committee or reviewers of the SADT models in detail
Project librarian, who govern the project documentation
Project manager, who governs the system analysis and design.
Monitor or chief analyst to assists SADT developers and users
Instructor to train SADT developers and users
== Usage ==
SADT is used as diagrammatic notation in conceptual design of software engineering and systems engineering to sketch applications, for more detailed structured analysis, for requirements definition, and structured design.
== See also ==
IDEF0
Jackson structured programming
Structure chart
Structured systems analysis and design method
Systems analysis
== References ==
== Further reading ==
William S. Davis (1992). Tools and Techniques for Structured Systems Analysis and Design. Addison-Wesley. ISBN 0-201-10274-9
Marca, D.A., and C.L. McGowan. (1988). SADT: structured analysis and design technique. McGraw-Hill Book Co., Inc.: New York, NY.
Jerry FitzGerald and Ardra F. FitzGerald (1987). Fundamentals of Systems Analysis: Using Structured Analysis and Design Techniques. Wiley. ISBN 0-471-88597-5
David A. Marca and Clement L. McGowan (1988). SADT: Structured Analysis and Design Technique. McGraw-Hill. ISBN 0-07-040235-3
D. Millington (1981). Systems Analysis and Design for Computer Applications. E. Horwood. ISBN 0-85312-249-0
Robertson & Robertson (1999). Mastering the Requirements Process. Addison Wesley.
James C. Wetherbe (1984). Systems Analysis and Design: Traditional, Structured, and Advanced Concepts and Techniques. West Pub. Co. ISBN 0-314-77858-6
== External links ==
The IDEF0 method
A course about SADT diagrams | Wikipedia/Structured_analysis_and_design_technique |
Structured analysis and design technique (SADT) is a systems engineering and software engineering methodology for describing systems as a hierarchy of functions. SADT is a structured analysis modelling language, which uses two types of diagrams: activity models and data models. It was developed in the late 1960s by Douglas T. Ross, and was formalized and published as IDEF0 in 1981.
== Overview ==
Structured analysis and design technique (SADT) is a diagrammatic notation designed specifically to help people describe and understand systems. It offers building blocks to represent entities and activities, and a variety of arrows to relate boxes. These boxes and arrows have an associated informal semantics. SADT can be used as a functional analysis tool of a given process, using successive levels of details. The SADT method not only allows one to define user needs for IT developments, which is often used in the industrial Information Systems, but also to explain and present an activity's manufacturing processes and procedures.
== History ==
SADT was developed and field-tested during the period of 1969 to 1973 by Douglas T. Ross and SofTech, Inc. The methodology was used in the MIT Automatic Programming Tool (APT) project. It received extensive use starting in 1973 by the US Air Force Integrated Computer Aided Manufacturing program.
According to Levitt (2000) SADT is "part of a series of structured methods, that represent a collection of analysis, design, and programming techniques that were developed in response to the problems facing the software world from the 1960s to the 1980s. In this timeframe most commercial programming was done in COBOL and Fortran, then C and BASIC. There was little guidance on "good" design and programming techniques, and there were no standard techniques for documenting requirements and designs. Systems were getting larger and more complex, and the information system development became harder and harder to do so. As a way to help manage large and complex software.
SADT was among a series of similar structured methods, which had emerged since the 1960 such as:
Structured programming in circa 1967 with Edsger W. Dijkstra.
Structured design around 1975 with Larry Constantine and Ed Yourdon
Structured analysis in circa 1978 with Tom DeMarco, Yourdon, Gane & Sarson, McMenamin & Palmer.
Information technology engineering in circa 1990 with James Martin.
In 1981 the IDEF0 formalism was published, based on SADT.
== SADT topics ==
=== Top-down approach ===
The structured analysis and design technique uses a decomposition with the top-down approach. This decomposition is conducted only in the physical domain from an axiomatic design viewpoint.
=== Diagrams ===
SADT uses two types of diagrams: activity models and data models. It uses arrows to build these diagrams.
The SADT's representation is the following:
A main box where the name of the process or the action is specified
On the left-hand side of this box, incoming arrows: inputs of the action.
On the upper part, the incoming arrows: data necessary for the action.
On the bottom of the box, incoming arrows: means used for the action.
On the right-hand side of the box, outgoing arrows: outputs of the action.
The semantics of arrows for activities:
Inputs enter from the left and represent data or consumables that are needed by the activity.
Outputs exit to the right and represent data or products that are produced by the activity.
Controls enter from the top and represent commands or conditions which influence the execution of an activity but are not consumed.
Mechanisms identify the means, components or tools used to accomplish the activity. Represents allocation of activities.
The semantics of arrows for data:
Inputs are activities that produce the data.
Outputs consume the data.
Controls influence the internal state of the data.
=== Roles ===
According to Mylopoulos (2004) in the software development process multiple roles can or should be distinguished:
Author or developer of the SADT models
Commenters, who review the author's work
Readers or users of the SADT models
Experts, who can advise the authors
Technical committee or reviewers of the SADT models in detail
Project librarian, who govern the project documentation
Project manager, who governs the system analysis and design.
Monitor or chief analyst to assists SADT developers and users
Instructor to train SADT developers and users
== Usage ==
SADT is used as diagrammatic notation in conceptual design of software engineering and systems engineering to sketch applications, for more detailed structured analysis, for requirements definition, and structured design.
== See also ==
IDEF0
Jackson structured programming
Structure chart
Structured systems analysis and design method
Systems analysis
== References ==
== Further reading ==
William S. Davis (1992). Tools and Techniques for Structured Systems Analysis and Design. Addison-Wesley. ISBN 0-201-10274-9
Marca, D.A., and C.L. McGowan. (1988). SADT: structured analysis and design technique. McGraw-Hill Book Co., Inc.: New York, NY.
Jerry FitzGerald and Ardra F. FitzGerald (1987). Fundamentals of Systems Analysis: Using Structured Analysis and Design Techniques. Wiley. ISBN 0-471-88597-5
David A. Marca and Clement L. McGowan (1988). SADT: Structured Analysis and Design Technique. McGraw-Hill. ISBN 0-07-040235-3
D. Millington (1981). Systems Analysis and Design for Computer Applications. E. Horwood. ISBN 0-85312-249-0
Robertson & Robertson (1999). Mastering the Requirements Process. Addison Wesley.
James C. Wetherbe (1984). Systems Analysis and Design: Traditional, Structured, and Advanced Concepts and Techniques. West Pub. Co. ISBN 0-314-77858-6
== External links ==
The IDEF0 method
A course about SADT diagrams | Wikipedia/Structured_Analysis_and_Design_Technique |
In software engineering, a software development process or software development life cycle (SDLC) is a process of planning and managing software development. It typically involves dividing software development work into smaller, parallel, or sequential steps or sub-processes to improve design and/or product management. The methodology may include the pre-definition of specific deliverables and artifacts that are created and completed by a project team to develop or maintain an application.
Most modern development processes can be vaguely described as agile. Other methodologies include waterfall, prototyping, iterative and incremental development, spiral development, rapid application development, and extreme programming.
A life-cycle "model" is sometimes considered a more general term for a category of methodologies and a software development "process" is a particular instance as adopted by a specific organization. For example, many specific software development processes fit the spiral life-cycle model. The field is often considered a subset of the systems development life cycle.
== History ==
The software development methodology framework did not emerge until the 1960s. According to Elliott (2004), the systems development life cycle can be considered to be the oldest formalized methodology framework for building information systems. The main idea of the software development life cycle has been "to pursue the development of information systems in a very deliberate, structured and methodical way, requiring each stage of the life cycle––from the inception of the idea to delivery of the final system––to be carried out rigidly and sequentially" within the context of the framework being applied. The main target of this methodology framework in the 1960s was "to develop large scale functional business systems in an age of large scale business conglomerates. Information systems activities revolved around heavy data processing and number crunching routines."
Requirements gathering and analysis:
The first phase of the custom software development process involves understanding the client's requirements and objectives. This stage typically involves engaging in thorough discussions and conducting interviews with stakeholders to identify the desired features, functionalities, and overall scope of the software. The development team works closely with the client to analyze existing systems and workflows, determine technical feasibility, and define project milestones.
Planning and design:
Once the requirements are understood, the custom software development team proceeds to create a comprehensive project plan. This plan outlines the development roadmap, including timelines, resource allocation, and deliverables. The software architecture and design are also established during this phase. User interface (UI) and user experience (UX) design elements are considered to ensure the software's usability, intuitiveness, and visual appeal.
Development:
With the planning and design in place, the development team begins the coding process. This phase involves writing, testing, and debugging the software code. Agile methodologies, such as scrum or kanban, are often employed to promote flexibility, collaboration, and iterative development. Regular communication between the development team and the client ensures transparency and enables quick feedback and adjustments.
Testing and quality assurance:
To ensure the software's reliability, performance, and security, rigorous testing and quality assurance (QA) processes are carried out. Different testing techniques, including unit testing, integration testing, system testing, and user acceptance testing, are employed to identify and rectify any issues or bugs. QA activities aim to validate the software against the predefined requirements, ensuring that it functions as intended.
Deployment and implementation:
Once the software passes the testing phase, it is ready for deployment and implementation. The development team assists the client in setting up the software environment, migrating data if necessary, and configuring the system. User training and documentation are also provided to ensure a smooth transition and enable users to maximize the software's potential.
Maintenance and support:
After the software is deployed, ongoing maintenance and support become crucial to address any issues, enhance performance, and incorporate future enhancements. Regular updates, bug fixes, and security patches are released to keep the software up-to-date and secure. This phase also involves providing technical support to end users and addressing their queries or concerns.
Methodologies, processes, and frameworks range from specific prescriptive steps that can be used directly by an organization in day-to-day work, to flexible frameworks that an organization uses to generate a custom set of steps tailored to the needs of a specific project or group. In some cases, a "sponsor" or "maintenance" organization distributes an official set of documents that describe the process. Specific examples include:
1970s
Structured programming since 1969
Cap Gemini SDM, originally from PANDATA, the first English translation was published in 1974. SDM stands for System Development Methodology
1980s
Structured systems analysis and design method (SSADM) from 1980 onwards
Information Requirement Analysis/Soft systems methodology
1990s
Object-oriented programming (OOP) developed in the early 1960s and became a dominant programming approach during the mid-1990s
Rapid application development (RAD), since 1991
Dynamic systems development method (DSDM), since 1994
Scrum, since 1995
Team software process, since 1998
Rational Unified Process (RUP), maintained by IBM since 1998
Extreme programming, since 1999
2000s
Agile Unified Process (AUP) maintained since 2005 by Scott Ambler
Disciplined agile delivery (DAD) Supersedes AUP
2010s
Scaled Agile Framework (SAFe)
Large-Scale Scrum (LeSS)
DevOps
Since DSDM in 1994, all of the methodologies on the above list except RUP have been agile methodologies - yet many organizations, especially governments, still use pre-agile processes (often waterfall or similar). Software process and software quality are closely interrelated; some unexpected facets and effects have been observed in practice.
Among these, another software development process has been established in open source. The adoption of these best practices known and established processes within the confines of a company is called inner source.
== Prototyping ==
Software prototyping is about creating prototypes, i.e. incomplete versions of the software program being developed.
The basic principles are:
Prototyping is not a standalone, complete development methodology, but rather an approach to try out particular features in the context of a full methodology (such as incremental, spiral, or rapid application development (RAD)).
Attempts to reduce inherent project risk by breaking a project into smaller segments and providing more ease of change during the development process.
The client is involved throughout the development process, which increases the likelihood of client acceptance of the final implementation.
While some prototypes are developed with the expectation that they will be discarded, it is possible in some cases to evolve from prototype to working system.
A basic understanding of the fundamental business problem is necessary to avoid solving the wrong problems, but this is true for all software methodologies.
== Methodologies ==
=== Agile development ===
"Agile software development" refers to a group of software development frameworks based on iterative development, where requirements and solutions evolve via collaboration between self-organizing cross-functional teams. The term was coined in the year 2001 when the Agile Manifesto was formulated.
Agile software development uses iterative development as a basis but advocates a lighter and more people-centric viewpoint than traditional approaches. Agile processes fundamentally incorporate iteration and the continuous feedback that it provides to successively refine and deliver a software system.
The Agile model also includes the following software development processes:
Dynamic systems development method (DSDM)
Kanban
Scrum
Lean software development
=== Continuous integration ===
Continuous integration is the practice of merging all developer working copies to a shared mainline several times a day.
Grady Booch first named and proposed CI in his 1991 method, although he did not advocate integrating several times a day. Extreme programming (XP) adopted the concept of CI and did advocate integrating more than once per day – perhaps as many as tens of times per day.
=== Incremental development ===
Various methods are acceptable for combining linear and iterative systems development methodologies, with the primary objective of each being to reduce inherent project risk by breaking a project into smaller segments and providing more ease-of-change during the development process.
There are three main variants of incremental development:
A series of mini-waterfalls are performed, where all phases of the waterfall are completed for a small part of a system, before proceeding to the next increment, or
Overall requirements are defined before proceeding to evolutionary, mini-waterfall development of individual increments of a system, or
The initial software concept, requirements analysis, and design of architecture and system core are defined via waterfall, followed by incremental implementation, which culminates in installing the final version, a working system.
=== Rapid application development ===
Rapid application development (RAD) is a software development methodology, which favors iterative development and the rapid construction of prototypes instead of large amounts of up-front planning. The "planning" of software developed using RAD is interleaved with writing the software itself. The lack of extensive pre-planning generally allows software to be written much faster and makes it easier to change requirements.
The rapid development process starts with the development of preliminary data models and business process models using structured techniques. In the next stage, requirements are verified using prototyping, eventually to refine the data and process models. These stages are repeated iteratively; further development results in "a combined business requirements and technical design statement to be used for constructing new systems".
The term was first used to describe a software development process introduced by James Martin in 1991. According to Whitten (2003), it is a merger of various structured techniques, especially data-driven information technology engineering, with prototyping techniques to accelerate software systems development.
The basic principles of rapid application development are:
Key objective is for fast development and delivery of a high-quality system at a relatively low investment cost.
Attempts to reduce inherent project risk by breaking a project into smaller segments and providing more ease of change during the development process.
Aims to produce high-quality systems quickly, primarily via iterative Prototyping (at any stage of development), active user involvement, and computerized development tools. These tools may include graphical user interface (GUI) builders, Computer Aided Software Engineering (CASE) tools, Database Management Systems (DBMS), fourth-generation programming languages, code generators, and object-oriented techniques.
Key emphasis is on fulfilling the business need, while technological or engineering excellence is of lesser importance.
Project control involves prioritizing development and defining delivery deadlines or “timeboxes”. If the project starts to slip, the emphasis is on reducing requirements to fit the timebox, not on increasing the deadline.
Generally includes joint application design (JAD), where users are intensely involved in system design, via consensus building in either structured workshops, or electronically facilitated interaction.
Active user involvement is imperative.
Iteratively produces production software, as opposed to a throwaway prototype.
Produces documentation necessary to facilitate future development and maintenance.
Standard systems analysis and design methods can be fitted into this framework.
=== Waterfall development ===
The waterfall model is a sequential development approach, in which development is seen as flowing steadily downwards (like a waterfall) through several phases, typically:
Requirements analysis resulting in a software requirements specification
Software design
Implementation
Testing
Integration, if there are multiple subsystems
Deployment (or Installation)
Maintenance
The first formal description of the method is often cited as an article published by Winston W. Royce in 1970, although Royce did not use the term "waterfall" in this article. Royce presented this model as an example of a flawed, non-working model.
The basic principles are:
The Project is divided into sequential phases, with some overlap and splashback acceptable between phases.
Emphasis is on planning, time schedules, target dates, budgets, and implementation of an entire system at one time.
Tight control is maintained over the life of the project via extensive written documentation, formal reviews, and approval/signoff by the user and information technology management occurring at the end of most phases before beginning the next phase. Written documentation is an explicit deliverable of each phase.
The waterfall model is a traditional engineering approach applied to software engineering. A strict waterfall approach discourages revisiting and revising any prior phase once it is complete. This "inflexibility" in a pure waterfall model has been a source of criticism by supporters of other more "flexible" models. It has been widely blamed for several large-scale government projects running over budget, over time and sometimes failing to deliver on requirements due to the big design up front approach. Except when contractually required, the waterfall model has been largely superseded by more flexible and versatile methodologies developed specifically for software development. See Criticism of waterfall model.
=== Spiral development ===
In 1988, Barry Boehm published a formal software system development "spiral model," which combines some key aspects of the waterfall model and rapid prototyping methodologies, in an effort to combine advantages of top-down and bottom-up concepts. It provided emphasis on a key area many felt had been neglected by other methodologies: deliberate iterative risk analysis, particularly suited to large-scale complex systems.
The basic principles are:
Focus is on risk assessment and on minimizing project risk by breaking a project into smaller segments and providing more ease-of-change during the development process, as well as providing the opportunity to evaluate risks and weigh consideration of project continuation throughout the life cycle.
"Each cycle involves a progression through the same sequence of steps, for each part of the product and for each of its levels of elaboration, from an overall concept-of-operation document down to the coding of each individual program."
Each trip around the spiral traverses four basic quadrants: (1) determine objectives, alternatives, and constraints of the iteration, and (2) evaluate alternatives; Identify and resolve risks; (3) develop and verify deliverables from the iteration; and (4) plan the next iteration.
Begin each cycle with an identification of stakeholders and their "win conditions", and end each cycle with review and commitment.
=== Shape Up ===
Shape Up is a software development approach introduced by Basecamp in 2018. It is a set of principles and techniques that Basecamp developed internally to overcome the problem of projects dragging on with no clear end. Its primary target audience is remote teams. Shape Up has no estimation and velocity tracking, backlogs, or sprints, unlike waterfall, agile, or scrum. Instead, those concepts are replaced with appetite, betting, and cycles. As of 2022, besides Basecamp, notable organizations that have adopted Shape Up include UserVoice and Block.
=== Advanced methodologies ===
Other high-level software project methodologies include:
Behavior-driven development and business process management.
Chaos model - The main rule always resolves the most important issue first.
Incremental funding methodology - an iterative approach
Lightweight methodology - a general term for methods that only have a few rules and practices
Structured systems analysis and design method - a specific version of waterfall
Slow programming, as part of the larger Slow Movement, emphasizes careful and gradual work without (or minimal) time pressures. Slow programming aims to avoid bugs and overly quick release schedules.
V-Model (software development) - an extension of the waterfall model
Unified Process (UP) is an iterative software development methodology framework, based on Unified Modeling Language (UML). UP organizes the development of software into four phases, each consisting of one or more executable iterations of the software at that stage of development: inception, elaboration, construction, and guidelines.
== Process meta-models ==
Some "process models" are abstract descriptions for evaluating, comparing, and improving the specific process adopted by an organization.
ISO/IEC 12207 is the international standard describing the method to select, implement, and monitor the life cycle for software.
The Capability Maturity Model Integration (CMMI) is one of the leading models and is based on best practices. Independent assessments grade organizations on how well they follow their defined processes, not on the quality of those processes or the software produced. CMMI has replaced CMM.
ISO 9000 describes standards for a formally organized process to manufacture a product and the methods of managing and monitoring progress. Although the standard was originally created for the manufacturing sector, ISO 9000 standards have been applied to software development as well. Like CMMI, certification with ISO 9000 does not guarantee the quality of the end result, only that formalized business processes have been followed.
ISO/IEC 15504 Information technology—Process assessment is also known as Software Process Improvement Capability Determination (SPICE), is a "framework for the assessment of software processes". This standard is aimed at setting out a clear model for process comparison. SPICE is used much like CMMI. It models processes to manage, control, guide, and monitor software development. This model is then used to measure what a development organization or project team actually does during software development. This information is analyzed to identify weaknesses and drive improvement. It also identifies strengths that can be continued or integrated into common practice for that organization or team.
ISO/IEC 24744 Software Engineering—Metamodel for Development Methodologies, is a power type-based metamodel for software development methodologies.
Soft systems methodology - a general method for improving management processes.
Method engineering - a general method for improving information system processes.
== See also ==
Systems development life cycle
Computer-aided software engineering (some of these tools support specific methodologies)
List of software development philosophies
Outline of software engineering
Software Project Management
Software development
Software development effort estimation
Software documentation
Software release life cycle
Top-down and bottom-up design#Computer science
== References ==
== External links ==
Selecting a development approach Archived January 2, 2019, at the Wayback Machine at cms.hhs.gov.
Gerhard Fischer, "The Software Technology of the 21st Century: From Software Reuse to Collaborative Software Design" Archived September 15, 2009, at the Wayback Machine, 2001 | Wikipedia/Software_engineering_methodology |
Business reference model (BRM) is a reference model, concentrating on the functional and organizational aspects of the core business of an enterprise, service organization or government agency.
In enterprise engineering a business reference model is part of an Enterprise Architecture Framework or Architecture Framework. An Enterprise Architecture Framework defines in a series of reference models, how to organize the structure and views associated with an Enterprise Architecture.
== Overview ==
A reference model in general is a model of something that embodies the basic goal or idea of something and can then be looked at as a reference for various purposes. A business reference model is a means to describe the business operations of an organization, independent of the organizational structure that perform them. Other types of business reference model can also depict the relationship between the business processes, business functions, and the business area’s business reference model. These reference model can be constructed in layers, and offer a foundation for the analysis of service components, technology, data, and performance.
The most familiar business reference model is the "Business Reference Model", one of five reference models of the Federal Enterprise Architecture of the US Federal Government. That model is a function-driven framework for describing the business operations of the Federal Government independent of the agencies that perform them. The Business Reference Model provides an organized, hierarchical construct for describing the day-to-day business operations of the Federal government. While many models exist for describing organizations - organizational charts, location maps, etc. - this model presents the business using a functionally driven approach.
== History ==
One of the first business reference models ever defined was the "IMPPACT Business Reference Model" around 1990, which was the result of a research project in the Computer Integrated Manufacturing (CIM) field of the ESPRIT1 programme. Gielingh et al. (1933) described:
The IMPPACT Business Reference Model is expressed in the generic language constructs provided by IDEF0... It describes the requirements for CIM seen from a business point of view. Views modelled are manufacturing activities, real and information flow objects resource objects (information and material processing components) and organisational aspects (departments and their relations to activities and resources). The complete manufacturing system (including the production system and its management) is modelled by the IMPPACT Business Reference Model. Management covers both the planning of the production and the planning and control of this production.
The term IMPPACT stood for Integrated Manufacturing of Products and Processes using Advanced Computer Technologies Furthermore, in its framework were incorporated CIMOSA as reference model, NIAM for information modelling, and the data modeling language EXPRESS for information structure implementation.
In the 1990s, business reference models were hardly an item. An exception was a 1991 book about IT management, which mentioned that the Kodak management had developed a business reference model 10 years earlier. A 1996 manual of the SAP R/3 enterprise resource planning software stipulated the existence on the business reference model of the R/3 System. However, in the 1990s there was a significant development of reference models in related fields, which, resulted in the developments of Integrated business planning, the Open System Environment Reference Model, the Workflow Reference Model, TOGAF and the Zachman Framework.
In the new millennium business reference models started emerging in several fields from network management systems, and E-business, to the US Federal government. The US Federal government published its "Business Reference Model", Version 1.0 in February 2002. Related developments in this decade were the development of the Treasury Enterprise Architecture Framework, and the OASIS SOA Reference Model.
== Specific models ==
The US Federal Government has defined a Federal Enterprise Architecture structures of the five FEA reference models:
Performance Reference Model (PRM)
Business Reference Model (BRM)
Service Component Reference Model (SRM)
Technical Reference Model (TRM)
Data Reference Model (DRM)
The Federal Government Business Reference Model (FA BRM) provides an organized, hierarchical construct for describing the day-to-day business operations of the Federal government. While many models exist for describing organizations - org charts, location maps, etc. - this model presents the business using a functionally driven approach. The Lines of Business and Sub-functions that comprise the BRM represent a departure from previous models of the Federal government that use antiquated, stovepiped, agency-oriented frameworks. The BRM is the first layer of the Federal Enterprise Architecture and it is the main viewpoint for the analysis of data, service components and technology.
== See also ==
Business model
Business process modeling
Enterprise Architecture framework
Enterprise modelling
Organizational architecture
Outline of consulting
View model
== References ==
== Further reading ==
Peter Fettke, Peter Loos (2006). Reference Modeling for Business Systems Analysis. Idea Group Inc (IGI). ISBN 1-59904-054-9 | Wikipedia/Business_reference_model |
Decomposition in computer science, also known as factoring, is breaking a complex problem or system into parts that are easier to conceive, understand, program, and maintain.
== Overview ==
Different types of decomposition are defined in computer sciences:
In structured programming, algorithmic decomposition breaks a process down into well-defined steps.
Structured analysis breaks down a software system from the system context level to system functions and data entities as described by Tom DeMarco.
Object-oriented decomposition breaks a large system down into progressively smaller classes or objects that are responsible for part of the problem domain.
According to Booch, algorithmic decomposition is a necessary part of object-oriented analysis and design, but object-oriented systems start with and emphasize decomposition into objects.
More generally, functional decomposition in computer science is a technique for mastering the complexity of the function of a model. A functional model of a system is thereby replaced by a series of functional models of subsystems.
== Decomposition topics ==
=== Decomposition paradigm ===
A decomposition paradigm in computer programming is a strategy for organizing a program as a number of parts, and usually implies a specific way to organize a program text. Typically the aim of using a decomposition paradigm is to optimize some metric related to program complexity, for example a program's modularity or its maintainability.
Most decomposition paradigms suggest breaking down a program into parts to minimize the static dependencies between those parts, and to maximize each part's cohesiveness. Popular decomposition paradigms include the procedural, modules, abstract data type, and object oriented paradigms.
Though the concept of decomposition paradigm is entirely distinct from that of model of computation, they are often confused. For example, the functional model of computation is often confused with procedural decomposition, and the actor model of computation is often confused with object oriented decomposition.
=== Decomposition diagram ===
A decomposition diagram shows a complex, process, organization, data subject area, or other type of object broken down into lower level, more detailed components. For example, decomposition diagrams may represent organizational structure or functional decomposition into processes. Decomposition diagrams provide a logical hierarchical decomposition of a system.
== See also ==
Code refactoring
Component-based software engineering
Dynamization
Duplicate code
Event partitioning
How to Solve It
Integrated Enterprise Modeling
Personal information management
Readability
Subroutine
== References ==
== External links ==
Object Oriented Analysis and Design
On the Criteria To Be Used in Decomposing Systems into Modules | Wikipedia/Decomposition_(computer_science) |
Dynamic enterprise modeling (DEM) is an enterprise modeling approach developed by the Baan company, and used for the Baan enterprise resource planning system which aims "to align and implement it in the organizational architecture of the end-using company".
According to Koning (2008), Baan introduced dynamic enterprise modelling in 1996 as a "means for implementing the Baan ERP product. The modelling focused on a Petri net–based technique for business process modelling to which the Baan application units were to be linked. DEM also contains a supply-chain diagram tool for the logistic network of the company and of an enterprise function modelling diagram".
== Overview ==
To align a specific company with dynamic enterprise modeling, the organizational structure is blueprinted top-down from high-level business processes to low-level processes. This blueprint is used as a roadmap of the organization, that is compatible with the structural roadmap of the software package. Having both roadmaps, the software package and the organizational structure are alienable. The blueprint of an organizational structure in dynamic enterprise modeling is called a reference model. A reference model is the total view of visions, functions, and organizational structures and processes, which together can be defined as a representative way of doing business in a certain organizational typology.
The DEM reference model consists of a set of underlying models that depict the organizational architecture in a top-down direction. The underlying models are:
Enterprise structure diagrams: The company site structure is visualized with the dispersed geographic locations, the headquarters, manufacturing plants, warehouses, and supplier and customer locations. Physical as well as logical multi-site organizations for internal logistic or financial flow optimization can be diagrammed.
Business control model : The business control model represents the primary processes of the organization and their control, grouped in business functions. The DEM reference model exists of one main Business Control Model, resulting in several other Business Control Models per function area of the organization.
Business function model : The business function model is a function model that focuses on the targets of the several functions within the company.
Business process model : The business process model focuses on the execution of the functions and processes that originate from the business control model, and the business function model. Processes flows are depicted and processes are detailed out.
Business organization model : The business organization model focuses less on the processes and more on the organizational aspects such as roles and responsibilities.
Together these models are capable of depicting the total organizational structure and aspects that are necessary during the implementation of the dynamic enterprise modeling. The models can have differentiations, which are based on the typology of the organization (i.e.: engineer-to-order organizations require different model structures than assemble-to-order organizations. To elaborate on the way that the reference model is used to implement software and to keep track of the scope of implementation methods, the business control model and the business process model will be explained in detail.
== Dynamic enterprise modeling topics ==
=== Business control model ===
The business control model exists of the business functions of the organization and their internal and external links. Basic features in the model are:
Request-feedback-loop: A link from, to, or between business functions is called a request-feedback-loop, which consists of 4 states that complete the process and information flows between both business functions. The states are labeled: requested, committed, completed, and accepted.
Workflow case. A workflow case is the description of the execution and the target of the process that occurs between two business functions. The most important critical factors of the workflow case are quantity, quality, and time. The 4 states of Request-feedback-loop the together represent the workflow case.
Triggers: Business functions are aggregates of business processes and focus mainly on the triggers (control) between processes, thus not on the information flows.
Business functions : In an optimal situation for the modeling process, a company has only one business function. Business functions are however subdivided when:
The nature and characteristics of workflow cases fluctuate
The frequency in underlying processes fluctuate
Detail-level fluctuates
More than 1 type of request triggers a function
Next to interaction between two business functions, interaction can also exist between objects that are not in the scope of the reference model. These objects can be external business functions and agents.
External business function : this is a group of processes that are part of the organization (meaning that the organization can control the functions), but that is outside of the scope of the reference model.
Agents on the other hand are entities similar to business functions with the exception that they are external of the business (i.e.: customers and suppliers).
Processes within or between business functions are executed by triggers, which can be event-driven or time-driven.
Exceptions in a system are handled, according to the set handling level in the business process configuration, when the success path of the model is not met in practice.
Subroutines of processes can be modeled in the Business Control Model to take care of possible exceptions that can occur during the execution of a process (i.e.: delay handling in the delivery of goods).
In addition to business functions that consist of the main processes of the organization, management functions exist.
Management business functions: These are functions that manage the business process itself, and that thus, support the execution and triggering of the main business functions.
Having this reference, the main processes of the organization can be captured in the Business Control Model. The main functions of the organization are grouped in the business functions, which consist of the processes that are part of the specific business function. Interactions between the business functions are then depicted using the request-feedback loops.
=== Constructing the business control model ===
A business control model is constructed according to a set path.
First, the scope of the business is defined. The scope includes scoping what to model and includes the definition of the agents and external business functions that relate to the business.
Next, the scope is depicted to a model of the black box with al the agents and external business functions surrounding the black box.
The next step is to define the process and information flows (request-feedback flows) between the agents and external business functions to and from the black box of the business control model. Defining the request-feedback flows enables the modeler to define what processes are inside the black box.
After creating the main business functions within the business control model, the several business functions are detailed out.
In case of a production business it is vital to define the customer order decoupling point, referring to the split in the physical process where processes are based on the customer order instead of forecasts.
Service based businesses on the other hand do not have a physical goods flow and thus do not require a physical process model. It is however imaginable that the same type of process flow can be utilized to construct a business control model for a service based business, as a service can be interpreted as a product as well. In this way, a business control model can be constructed similarly for a service based business as for a physical goods production business, having intangible goods instead of tangible.
Next to the low-level physical production process, the high-level business functions need to be defined as well. In most cases the higher level business functions relate to planning functions and other tactical and strategical business functions, followed by functions as sales and purchase.
After high-level detail definitions, the business functions are decomposed to lower-level detail definitions to make the business control model alienable to the lower models within the reference model, for this practice, mainly the Business Process Model. In the Business Process Model the processes are elaborated until the lowest level of detail. Given this level of detail, the Baan software functionality is then projected on the processes, depicted in the Business Process Model.
=== Business process model ===
The modeling of processes in DEM, modeling the business process model is done using Petri net building blocks. DEM uses 4 construction elements:
State : A state element represents the state of a job token and is followed by the activity that executes the job token of the state.
Processing activity : A processing activity is the activity that processes the job token of a state, transforming the state of the job token to another state.
Control activity: A control activity navigates the process activity but does not execute it.
Sub-process : A sub-process is a collection of different other processes, aggregated in a single element by means of complexity management.
These 4 construction elements enables the modeling of DEM models. The modeling is due to a set collection of modeling constraints, guiding the modeling process in order to have similarly created models by different modelers. Control activities exist in different structures in order to set different possible routes for process flows. The used structures for control activities are:
OR-split / XOR-split : This structure creates 2 new states out of 1 state, signaling the creation of 2 job tokens out of 1 job token. If the new state can be both of the output tokens, the split is OR, if not, the split is an exclusive OR split (XOR).
AND-join construction : 2 job tokens are both needed to enable the control activity, creating 1 new job token (thus 1 new state).
OR-join / XOR-join : 2 job tokens are needed to enable the control activity, creating 1 new job token.
OR means one of the two starting job tokens can be used or both, XOR means only one of the tokens can be used to create the output job token.
=== An example ===
The example below demonstrates the modeling of the concept of marriage and divorce using Petri net building blocks.
The Petri net built model expresses the transformation from a single man and woman to a married couple through marriage and back to single individuals through divorce.
The model starts with the two states called man and woman.
Through an AND-join construction (both man and woman are needed in order to form a couple) the two states are joined within the control activity called coupling to the new state called couple.
The couple state then is transformed through the processing activity called marriage, resulting in the transformed state of married couple.
The state married couple is then transformed to the state divorced couple using the process activity called divorce, resulting in the state called divorced couple.
The control activity called decoupling finally splits the divorced couple state into the states of man and woman.
=== Assessments ===
Using an embedded method, brings the power that the method is designed to implement the software product that the method comes with. This suggests a less complicated usage of the method and more support possibilities.
The negative aspect of an embedded method obviously is that it can only be used for specific product software. Engineers and consultants, operating with several software products, could have more use of a general method, to have just one way of working.
== See also ==
Dynamic enterprise
Dynamic enterprise architecture (DYA)
Enterprise resource planning
SAP R/3
== References ==
== Further reading ==
Fred Driese and Martin Hromek (1999). "Some aspects of strategic tactical and operational usage of dynamic enterprise modeling".
Van Es, R.M., Post, H.A. eds. (1996). Dynamic Enterprise Modelling : A Paradigm Shift in Software Implementation. Kluwer.
== External links ==
Baan Dynamic Enterprise Management Archived 2011-07-10 at the Wayback Machine short intro
DynamicEnterprise Modeling presentation 1999. | Wikipedia/Dynamic_Enterprise_Modeling |
Axiomatic design is a systems design methodology using matrix methods to systematically analyze the transformation of customer needs into functional requirements, design parameters, and process variables. Specifically, a set of functional requirements(FRs) are related to a set of design parameters (DPs) by a Design Matrix A:
[
F
R
1
F
R
2
]
=
[
A
11
A
12
A
21
A
22
]
[
D
P
1
D
P
2
]
{\displaystyle {\begin{bmatrix}FR_{1}\\FR_{2}\end{bmatrix}}={\begin{bmatrix}A_{11}&A_{12}\\A_{21}&A_{22}\end{bmatrix}}{\begin{bmatrix}DP_{1}\\DP_{2}\end{bmatrix}}}
The method gets its name from its use of design principles or design Axioms (i.e., given without proof) governing the analysis and decision making process in developing high quality product or system designs. The two axioms used in Axiomatic Design (AD) are:
Axiom 1: The Independence Axiom. Maintain the independence of the functional requirements (FRs).
Axiom 2: The Information Axiom. Minimize the information content of the design.
Axiomatic design is considered to be a design method that addresses fundamental issues in Taguchi methods.
Coupling is the term Axiomatic Design uses to describe a lack of independence between the FRs of the system as determined by the DPs. I.e., if varying one DP has a resulting significant impact on two separate FRs, it is said the FRs are coupled. Axiomatic Design introduces matrix analysis of the Design Matrix to both assess and mitigate the effects of coupling.
Axiom 2, the Information Axiom, provides a metric of the probability that a specific DP will deliver the functional performance required to satisfy the FR. The metric is normalized to be summed up for the entire system being modeled. Systems with less functional performance risk (minimal information content) are preferred over alternative systems with higher information content.
The methodology was developed by Dr. Suh Nam Pyo at MIT, Department of Mechanical Engineering since the 1990s. A series of academic conferences have been held to present current developments of the methodology.
== See also ==
Design structure matrix (DSM)
New product development (NPD)
Design for Six Sigma
Six Sigma
Taguchi methods
Axiomatic product development lifecycle (APDL)
C-K theory
== References ==
== External links ==
A discussion of the methodology is given here:
Axiomatic Design for Complex Systems is a professional short course offered at MIT
Axiomatic Design Technology described by Axiomatic Design Solutions, Inc.
Axiomatic Design Conferences:
"2021 International Conference on Axiomatic Design (ICAD 2021)". NOVA School of Science and Technology. NOVA University of Lisbon, Portugal. Retrieved 21 January 2021.
"2019 International Conference on Axiomatic Design (ICAD)". School of Mechanical and Manufacturing Engineering. University of New South Wales, Kensington, Australia. Retrieved 16 December 2018.
Past proceedings of International Conferences on Axiomatic Design can be downloaded here:
ICAD2016
ICAD2015
ICAD2014
ICAD2013
ICAD2011
ICAD2009
ICAD2006
ICAD2004
ICAD2002
ICAD2000 | Wikipedia/Axiomatic_design |
The function block diagram (FBD) is a graphical language for programmable logic controller design, that can describe the function between input variables and output variables. A function is described as a set of elementary blocks. Input and output variables are connected to blocks by connection lines.
== Design ==
Inputs and outputs of the blocks are wired together with connection lines or links. Single lines may be used to connect two logical points of the diagram:
An input variable and an input of a block
An output of a block and an input of another block
An output of a block and an output variable
The connection is oriented, meaning that the line carries associated data from the left end to the right end. The left and right ends of the connection line must be of the same type.
Multiple right connection, also called divergence, can be used to broadcast information from its left end to each of its right ends. All ends of the connection must be of the same type.
== Language ==
Function Block Diagram is one of five languages for logic or control configuration supported by standard IEC 61131-3 for a control system such as a programmable logic controller (PLC) or a Distributed Control System (DCS). The other supported languages are ladder logic, sequential function chart, structured text, and instruction list.
== References ==
== External links ==
Runpower PLC | Wikipedia/Function_Block_Diagram |
Multilevel Flow Modeling (MFM) is a framework for modeling industrial processes.
MFM is a kind of functional modeling employing the concepts of abstraction, decomposition, and functional representation. The approach regards the purpose, rather than the physical behavior of a system as its defining element. MFM hierarchically decomposes the function of a system along the means-end and whole-part dimensions in relation to intended actions. Functions are syntactically modeled by the relations of fundamental concepts contributing as part of a subsystem. Each subsystem is considered in the context of the overall system in terms of the purpose (end) of its function (means) in the system. Using only a few fundamental concepts as building blocks allows qualitative reasoning about action success or failure. MFM defines a graphical modeling language for representing the encompassed knowledge.
== History ==
MFM originated as a modeling language for capturing how human operators identify and handle unknown operation situations in order to improve the design of human-machine interfaces.
== Syntax ==
MFM describes the function of a system as a means for a specific end in terms of mass and energy flow. The flow is the defining element for the underlying function concepts. The concepts of transport and barrier play the most important role, as they connect pairs of the other function types, reflecting the physical flows in the system. Sink and source functions mark the boundary of the considered system and the end or beginning of a flow. Storage and balance concepts can both be collection or splitting points for multiple flow paths.
Accordingly, valid MFM syntax requires a transport or a barrier linking two functions of the remaining four types. In addition to the flow within one perspective (mass or energy) MFM connects the influence between mass and energy by the means-end relations (mediate and producer-product) as well as the causal links introduced by the way the system is controlled by using separate control flow structures.
Diagnostic information about the causality between abnormal states through the system is inferred from the physical effect between the functions. Petersen distinguishes direct and indirect influence between functions:
Direct influence is the effect of a transport taking in mass or energy from the upstream function and passing it on to the downstream function.
Indirect influence, on the other hand, is derived from different physical implementations and represented by influence or participate relation of another function toward the transport. The state of transport can be affected e.g. by an abnormal state of influencing downstream storage, while the state would not be affected by a participating one.
According to the underlying physical interpretation inference rules for all possible patterns of flow functions have been established. Zhang compiled these patterns and the implied causality.
== Example ==
The MFM diagram of a heat pump reflects the overarching objective (cob2) of maintaining the energy level on the warm side constant. The energy flow structure efs2 shows the system function from the most prevalent (energetic) perspective which is further decomposed in the mass flow of coolant (mfs1) as the means for the desired energy transport. Further hierarchical analysis produces efs1 that represents the energy needed for the pump as a means to produce a part of the mass flow. The operational constraints introduced by control systems such as a water flow controller are modeled by cfs1 and a temperature controller cfs2.
== Application ==
MFM based solutions for many aspects of industrial automation have been proposed. Research directions include:
Plant wide diagnosis
Alarm Management
Risk Assessment
Automatic procedure generation
== References == | Wikipedia/Multilevel_Flow_Modeling |
A functional block diagram, in systems engineering and software engineering, is a block diagram that describes the functions and interrelationships of a system.
The functional block diagram can picture:
functions of a system pictured by blocks
input and output elements of a block pictured with lines
the relationships between the functions, and
the functional sequences and paths for matter and or signals
The block diagram can use additional schematic symbols to show particular properties.
Since the late 1950s, functional block diagrams have been used in a wide range applications, from systems engineering to software engineering. They became a necessity in complex systems design to "understand thoroughly from exterior design the operation of the present system and the relationship of each of the parts to the whole."
Many specific types of functional block diagrams have emerged. For example, the functional flow block diagram is a combination of the functional block diagram and the flowchart. Many software development methodologies are built with specific functional block diagram techniques. An example from the field of industrial computing is the Function Block Diagram (FBD), a graphical language for the development of software applications for programmable logic controllers.
== See also ==
Function model
Functional flow block diagram
== References == | Wikipedia/Functional_block_diagram |
Building information modeling (BIM) is an approach involving the generation and management of digital representations of the physical and functional characteristics of buildings or other physical assets and facilities. BIM is supported by various tools, processes, technologies and contracts. Building information models (BIMs) are computer files (often but not always in proprietary formats and containing proprietary data) which can be extracted, exchanged or networked to support decision-making regarding a built asset. BIM software is used by individuals, businesses and government agencies who plan, design, construct, operate and maintain buildings and diverse physical infrastructures, such as water, refuse, electricity, gas, communication utilities, roads, railways, bridges, ports and tunnels.
The concept of BIM has been in development since the 1970s, but it only became an agreed term in the early 2000s. The development of standards and the adoption of BIM has progressed at different speeds in different countries. Developed by buildingSMART, Industry Foundation Classes (IFCs) – data structures for representing information – became an international standard, ISO 16739, in 2013, and BIM process standards developed in the United Kingdom from 2007 onwards formed the basis of an international standard, ISO 19650, launched in January 2019.
== History ==
The concept of BIM has existed since the 1970s. The first software tools developed for modeling buildings emerged in the late 1970s and early 1980s, and included workstation products such as Chuck Eastman's Building Description System and GLIDE, RUCAPS, Sonata, Reflex and Gable 4D Series. The early applications, and the hardware needed to run them, were expensive, which limited widespread adoption.
The pioneering role of applications such as RUCAPS, Sonata and Reflex has been recognized by Laiserin as well as the UK's Royal Academy of Engineering; former GMW employee Jonathan Ingram worked on all three products. What became known as BIM products differed from architectural drafting tools such as AutoCAD by allowing the addition of further information (time, cost, manufacturers' details, sustainability, and maintenance information, etc.) to the building model.
As Graphisoft had been developing such solutions for longer than its competitors, Laiserin regarded its ArchiCAD application as then "one of the most mature BIM solutions on the market." Following its launch in 1987, ArchiCAD became regarded by some as the first implementation of BIM, as it was the first CAD product on a personal computer able to create both 2D and 3D geometry, as well as the first commercial BIM product for personal computers. However, Graphisoft founder Gábor Bojár has acknowledged to Jonathan Ingram in an open letter, that Sonata "was more advanced in 1986 than ArchiCAD at that time", adding that it "surpassed already the matured definition of 'BIM' specified only about one and a half decade later".
The term 'building model' (in the sense of BIM as used today) was first used in papers in the mid-1980s: in a 1985 paper by Simon Ruffle eventually published in 1986, and later in a 1986 paper by Robert Aish – then at GMW Computers Ltd, developer of RUCAPS software – referring to the software's use at London's Heathrow Airport. The term 'Building Information Model' first appeared in a 1992 paper by G.A. van Nederveen and F. P. Tolman.
However, the terms 'Building Information Model' and 'Building Information Modeling' (including the acronym "BIM") did not become popularly used until some 10 years later. Facilitating exchange and interoperability of information in digital format was variously with differing terminology: by Graphisoft as "Virtual Building" or "Single Building Model", Bentley Systems as "Integrated Project Models", and by Autodesk or Vectorworks as "Building Information Modeling". In 2002, Autodesk released a white paper entitled "Building Information Modeling," and other software vendors also started to assert their involvement in the field. By hosting contributions from Autodesk, Bentley Systems and Graphisoft, plus other industry observers, in 2003, Jerry Laiserin helped popularize and standardize the term as a common name for the digital representation of the building process.
=== Interoperability and BIM standards ===
As some BIM software developers have created proprietary data structures in their software, data and files created by one vendor's applications may not work in other vendor solutions. To achieve interoperability between applications, neutral, non-proprietary or open standards for sharing BIM data among different software applications have been developed.
Poor software interoperability has long been regarded as an obstacle to industry efficiency in general and to BIM adoption in particular. In August 2004 a US National Institute of Standards and Technology (NIST) report conservatively estimated that $15.8 billion was lost annually by the U.S. capital facilities industry due to inadequate interoperability arising from "the highly fragmented nature of the industry, the industry’s continued paper-based business practices, a lack of standardization, and inconsistent technology adoption among stakeholders".
An early BIM standard was the CIMSteel Integration Standard, CIS/2, a product model and data exchange file format for structural steel project information (CIMsteel: Computer Integrated Manufacturing of Constructional Steelwork). CIS/2 enables seamless and integrated information exchange during the design and construction of steel framed structures. It was developed by the University of Leeds and the UK's Steel Construction Institute in the late 1990s, with inputs from Georgia Tech, and was approved by the American Institute of Steel Construction as its data exchange format for structural steel in 2000.
BIM is often associated with Industry Foundation Classes (IFCs) and aecXML – data structures for representing information – developed by buildingSMART. IFC is recognised by the ISO and has been an international standard, ISO 16739, since 2013. OpenBIM is an initiative by buildingSMART that promotes open standards and interoperability. Based on the IFC standard, it allows vendor-neutral BIM data exchange. OpenBIM standards also include BIM Collaboration Format (BCF) for issue tracking and Information Delivery Specification (IDS) for defining model requirements.
Construction Operations Building information exchange (COBie) is also associated with BIM. COBie was devised by Bill East of the United States Army Corps of Engineers in 2007, and helps capture and record equipment lists, product data sheets, warranties, spare parts lists, and preventive maintenance schedules. This information is used to support operations, maintenance and asset management once a built asset is in service. In December 2011, it was approved by the US-based National Institute of Building Sciences as part of its National Building Information Model (NBIMS-US) standard. COBie has been incorporated into software, and may take several forms including spreadsheet, IFC, and ifcXML. In early 2013 BuildingSMART was working on a lightweight XML format, COBieLite, which became available for review in April 2013. In September 2014, a code of practice regarding COBie was issued as a British Standard: BS 1192-4.
In January 2019, ISO published the first two parts of ISO 19650, providing a framework for building information modelling, based on process standards developed in the United Kingdom. UK BS and PAS 1192 specifications form the basis of further parts of the ISO 19650 series, with parts on asset management (Part 3) and security management (Part 5) published in 2020.
The IEC/ISO 81346 series for reference designation has published 81346-12:2018, also known as RDS-CW (Reference Designation System for Construction Works). The use of RDS-CW offers the prospect of integrating BIM with complementary international standards based classification systems being developed for the Power Plant sector.
== Definition ==
ISO 19650-1:2018 defines BIM as:
Use of a shared digital representation of a built asset to facilitate design, construction and operation processes to form a reliable basis for decisions.
The US National Building Information Model Standard Project Committee has the following definition:
Building Information Modeling (BIM) is a digital representation of physical and functional characteristics of a facility. A BIM is a shared knowledge resource for information about a facility forming a reliable basis for decisions during its life-cycle; defined as existing from earliest conception to demolition.
Traditional building design was largely reliant upon two-dimensional technical drawings (plans, elevations, sections, etc.). Building information modeling extends the three primary spatial dimensions (width, height and depth), incorporating information about time (so-called 4D BIM), cost (5D BIM), asset management, sustainability, etc. BIM therefore covers more than just geometry. It also covers spatial relationships, geospatial information, quantities and properties of building components (for example, manufacturers' details), and enables a wide range of collaborative processes relating to the built asset from initial planning through to construction and then throughout its operational life.
BIM authoring tools present a design as combinations of "objects" – vague and undefined, generic or product-specific, solid shapes or void-space oriented (like the shape of a room), that carry their geometry, relations, and attributes. BIM applications allow extraction of different views from a building model for drawing production and other uses. These different views are automatically consistent, being based on a single definition of each object instance. BIM software also defines objects parametrically; that is, the objects are defined as parameters and relations to other objects so that if a related object is amended, dependent ones will automatically also change. Each model element can carry attributes for selecting and ordering them automatically, providing cost estimates as well as material tracking and ordering.
For the professionals involved in a project, BIM enables a virtual information model to be shared by the design team (architects, landscape architects, surveyors, civil, structural and building services engineers, etc.), the main contractor and subcontractors, and the owner/operator. Each professional adds discipline-specific data to the shared model – commonly, a 'federated' model which combines several different disciplines' models into one. Combining models enables visualisation of all models in a single environment, better coordination and development of designs, enhanced clash avoidance and detection, and improved time and cost decision-making.
=== BIM wash ===
"BIM wash" or "BIM washing" is a term sometimes used to describe inflated, and/or deceptive, claims of using or delivering BIM services or products.
== Usage throughout the asset life cycle ==
Use of BIM goes beyond the planning and design phase of a project, extending throughout the life cycle of the asset. The supporting processes of building lifecycle management include cost management, construction management, project management, facility operation and application in green building.
=== Common Data Environment ===
A 'Common Data Environment' (CDE) is defined in ISO 19650 as an:
Agreed source of information for any given project or asset, for collecting, managing and disseminating each information container through a managed process.
A CDE workflow describes the processes to be used while a CDE solution can provide the underlying technologies. A CDE is used to share data across a project or asset lifecycle, supporting collaboration across a whole project team. The concept of a CDE overlaps with enterprise content management, ECM, but with a greater focus on BIM issues.
=== Management of building information models ===
Building information models span the whole concept-to-occupation time-span. To ensure efficient management of information processes throughout this span, a BIM manager might be appointed. The BIM manager is retained by a design build team on the client's behalf from the pre-design phase onwards to develop and to track the object-oriented BIM against predicted and measured performance objectives, supporting multi-disciplinary building information models that drive analysis, schedules, take-off and logistics. Companies are also now considering developing BIMs in various levels of detail, since depending on the application of BIM, more or less detail is needed, and there is varying modeling effort associated with generating building information models at different levels of detail.
=== BIM in construction management ===
Participants in the building process are constantly challenged to deliver successful projects despite tight budgets, limited staffing, accelerated schedules, and limited or conflicting information. The significant disciplines such as architectural, structural and MEP designs should be well-coordinated, as two things can't take place at the same place and time. BIM additionally is able to aid in collision detection, identifying the exact location of discrepancies.
The BIM concept envisages virtual construction of a facility prior to its actual physical construction, in order to reduce uncertainty, improve safety, work out problems, and simulate and analyze potential impacts. Sub-contractors from every trade can input critical information into the model before beginning construction, with opportunities to pre-fabricate or pre-assemble some systems off-site. Waste can be minimised on-site and products delivered on a just-in-time basis rather than being stock-piled on-site.
Quantities and shared properties of materials can be extracted easily. Scopes of work can be isolated and defined. Systems, assemblies and sequences can be shown in a relative scale with the entire facility or group of facilities. BIM also prevents errors by enabling conflict or 'clash detection' whereby the computer model visually highlights to the team where parts of the building (e.g.:structural frame and building services pipes or ducts) may wrongly intersect.
=== BIM in facility operation and asset management ===
BIM can bridge the information loss associated with handing a project from design team, to construction team and to building owner/operator, by allowing each group to add to and reference back to all information they acquire during their period of contribution to the BIM model. Enabling an effective handover of information from design and construction (including via IFC or COBie) can thus yield benefits to the facility owner or operator. BIM-related processes relating to longer-term asset management are also covered in ISO-19650 Part 3.
For example, a building owner may find evidence of a water leak in a building. Rather than exploring the physical building, the owner may turn to the model and see that a water valve is located in the suspect location. The owner could also have in the model the specific valve size, manufacturer, part number, and any other information ever researched in the past, pending adequate computing power. Such problems were initially addressed by Leite and Akinci when developing a vulnerability representation of facility contents and threats for supporting the identification of vulnerabilities in building emergencies.
Dynamic information about the building, such as sensor measurements and control signals from the building systems, can also be incorporated within software to support analysis of building operation and maintenance. As such, BIM in facility operation can be related to internet of things approaches; rapid access to data may also be aided by use of mobile devices (smartphones, tablets) and machine-readable RFID tags or barcodes; while integration and interoperability with other business systems - CAFM, ERP, BMS, IWMS, etc - can aid operational reuse of data.
There have been attempts at creating information models for older, pre-existing facilities. Approaches include referencing key metrics such as the Facility Condition Index (FCI), or using 3D laser-scanning surveys and photogrammetry techniques (separately or in combination) or digitizing traditional building surveying methodologies by using mobile technology to capture accurate measurements and operation-related information about the asset that can be used as the basis for a model. Trying to retrospectively model a building constructed in, say 1927, requires numerous assumptions about design standards, building codes, construction methods, materials, etc, and is, therefore, more complex than building a model during design.
One of the challenges to the proper maintenance and management of existing facilities is understanding how BIM can be utilized to support a holistic understanding and implementation of building management practices and "cost of ownership" principles that support the full product lifecycle of a building. An American National Standard entitled APPA 1000 – Total Cost of Ownership for Facilities Asset Management incorporates BIM to factor in a variety of critical requirements and costs over the life-cycle of the building, including but not limited to: replacement of energy, utility, and safety systems; continual maintenance of the building exterior and interior and replacement of materials; updates to design and functionality; and recapitalization costs.
=== BIM in green building ===
BIM in green building, or "green BIM", is a process that can help architecture, engineering and construction firms to improve sustainability in the built environment. It can allow architects and engineers to integrate and analyze environmental issues in their design over the life cycle of the asset.
In the ERANet projects EPC4SES and FinSESCo projects worked on the digital representation of the energy demand of the building. The nucleus is the XML from issuing Energy Performance Certificates, amended by roof data to be able to retrieve the position and size of PV or PV/T.
== International developments ==
=== Asia ===
==== China ====
China began its exploration on informatisation in 2001. The Ministry of Construction announced BIM was as the key application technology of informatisation in "Ten new technologies of construction industry" (by 2010). The Ministry of Science and Technology (MOST) clearly announced BIM technology as a national key research and application project in "12th Five-Year" Science and Technology Development Planning. Therefore, the year 2011 was described as "The First Year of China's BIM".
==== Hong Kong ====
In 2006 the Hong Kong Housing Authority introduced BIM, and then set a target of full BIM implementation in 2014/2015. BuildingSmart Hong Kong was inaugurated in Hong Kong SAR in late April 2012. The Government of Hong Kong mandates the use of BIM for all government projects over HK$30M since 1 January 2018.
==== India ====
India Building Information Modelling Association (IBIMA) is a national-level society that represents the entire Indian BIM community. In India BIM is also known as VDC: Virtual Design and Construction. Due to its population and economic growth, India has an expanding construction market. In spite of this, BIM usage was reported by only 22% of respondents in a 2014 survey. In 2019, government officials said BIM could help save up to 20% by shortening construction time, and urged wider adoption by infrastructure ministries.
==== Iran ====
The Iran Building Information Modeling Association (IBIMA) was founded in 2012 by professional engineers from five universities in Iran, including the Civil and Environmental Engineering Department at Amirkabir University of Technology. While it is not currently active, IBIMA aims to share knowledge resources to support construction engineering management decision-making.
==== Malaysia ====
BIM implementation is targeted towards BIM Stage 2 by the year 2020 led by the Construction Industry Development Board (CIDB Malaysia). Under the Construction Industry Transformation Plan (CITP 2016–2020), it is hoped more emphasis on technology adoption across the project life-cycle will induce higher productivity.
==== Singapore ====
The Building and Construction Authority (BCA) has announced that BIM would be introduced for architectural submission (by 2013), structural and M&E submissions (by 2014) and eventually for plan submissions of all projects with gross floor area of more than 5,000 square meters by 2015. The BCA Academy is training students in BIM.
==== Japan ====
The Ministry of Land, Infrastructure and Transport (MLIT) has announced "Start of BIM pilot project in government building and repairs" (by 2010). Japan Institute of Architects (JIA) released the BIM guidelines (by 2012), which showed the agenda and expected effect of BIM to architects. MLIT announced " BIM will be mandated for all of its public works from the fiscal year of 2023, except those having particular reasons". The works subject to WTO Government Procurement Agreement shall comply with the published ISO standards related to BIM such as ISO19650 series as determined by the Article 10 (Technical Specification) of the Agreement.
==== South Korea ====
Small BIM-related seminars and independent BIM effort existed in South Korea even in the 1990s. However, it was not until the late 2000s that the Korean industry paid attention to BIM. The first industry-level BIM conference was held in April 2008, after which, BIM has been spread very rapidly. Since 2010, the Korean government has been gradually increasing the scope of BIM-mandated projects. McGraw Hill published a detailed report in 2012 on the status of BIM adoption and implementation in South Korea.
==== United Arab Emirates ====
Dubai Municipality issued a circular (196) in 2014 mandating BIM use for buildings of a certain size, height or type. The one page circular initiated strong interest in BIM and the market responded in preparation for more guidelines and direction. In 2015 the Municipality issued another circular (207) titled 'Regarding the expansion of applying the (BIM) on buildings and facilities in the emirate of Dubai' which made BIM mandatory on more projects by reducing the minimum size and height requirement for projects requiring BIM. This second circular drove BIM adoption further with several projects and organizations adopting UK BIM standards as best practice. In 2016, the UAE's Quality and Conformity Commission set up a BIM steering group to investigate statewide adoption of BIM.
=== Europe ===
==== Austria ====
Austrian standards for digital modeling are summarized in the ÖNORM A 6241, published on 15 March 2015. The ÖNORM A 6241-1 (BIM Level 2), which replaced the ÖNORM A 6240-4, has been extended in the detailed and executive design stages, and corrected in the lack of definitions. The ÖNORM A 6241-2 (BIM Level 3) includes all the requirements for the BIM Level 3 (iBIM).
==== Czech Republic ====
The Czech BIM Council, established in May 2011, aims to implement BIM methodologies into the Czech building and designing processes, education, standards and legislation.
==== Estonia ====
In Estonia digital construction cluster (Digitaalehituse Klaster) was formed in 2015 to develop BIM solutions for the whole life-cycle of construction. The strategic objective of the cluster is to develop an innovative digital construction environment as well as VDC new product development, Grid and e-construction portal to increase the international competitiveness and sales of Estonian businesses in the construction field. The cluster is equally co-funded by European Structural and Investment Funds through Enterprise Estonia and by the members of the cluster with a total budget of 600 000 euros for the period 2016–2018.
==== France ====
The French arm of buildingSMART, called Mediaconstruct (existing since 1989), is supporting digital transformation in France. A building transition digital plan – French acronym PTNB – was created in 2013 (mandated since 2015 to 2017 and under several ministries). A 2013 survey of European BIM practice showed France in last place, but, with government support, in 2017 it had risen to third place with more than 30% of real estate projects carried out using BIM. PTNB was superseded in 2018 by Plan BIM 2022, administered by an industry body, the Association for the Development of Digital in Construction (AND Construction), founded in 2017, and supported by a digital platform, KROQI, developed and launched in 2017 by CSTB (France's Scientific and Technical Centre for Building).
==== Germany ====
In December 2015, the German minister for transport Alexander Dobrindt announced a timetable for the introduction of mandatory BIM for German road and rail projects from the end of 2020. Speaking in April 2016, he said digital design and construction must become standard for construction projects in Germany, with Germany two to three years behind The Netherlands and the UK in aspects of implementing BIM. BIM was piloted in many areas of German infrastructure delivery and in July 2022 Volker Wissing, Federal Minister for Digital and Transport, announced that, from 2025, BIM will be used as standard in the construction of federal trunk roads in addition to the rail sector.
==== Ireland ====
In November 2017, Ireland's Department for Public Expenditure and Reform launched a strategy to increase use of digital technology in delivery of key public works projects, requiring the use of BIM to be phased in over the next four years.
==== Italy ====
Through the new D.l. 50, in April 2016 Italy has included into its own legislation several European directives including 2014/24/EU on Public Procurement. The decree states among the main goals of public procurement the "rationalization of designing activities and of all connected verification processes, through the progressive adoption of digital methods and electronic instruments such as Building and Infrastructure Information Modelling". A norm in 8 parts is also being written to support the transition: UNI 11337-1, UNI 11337-4 and UNI 11337-5 were published in January 2017, with five further chapters to follow within a year.
In early 2018 the Italian Ministry of Infrastructure and Transport issued a decree (DM 01/12/17) creating a governmental BIM Mandate compelling public client organisations to adopt a digital approach by 2025, with an incremental obligation which will start on 1 January 2019.
==== Lithuania ====
Lithuania is moving towards adoption of BIM infrastructure by founding a public body "Skaitmeninė statyba" (Digital Construction), which is managed by 13 associations. Also, there is a BIM work group established by Lietuvos Architektų Sąjunga (a Lithuanian architects body). The initiative intends Lithuania to adopt BIM, Industry Foundation Classes (IFC) and National Construction Classification as standard. An international conference "Skaitmeninė statyba Lietuvoje" (Digital Construction in Lithuania) has been held annually since 2012.
==== The Netherlands ====
On 1 November 2011, the Rijksgebouwendienst, the agency within the Dutch Ministry of Housing, Spatial Planning and the Environment that manages government buildings, introduced the Rgd BIM Standard, which it updated on 1 July 2012.
==== Norway ====
In Norway BIM has been used increasingly since 2008. Several large public clients require use of BIM in open formats (IFC) in most or all of their projects. The Government Building Authority bases its processes on BIM in open formats to increase process speed and quality, and all large and several small and medium-sized contractors use BIM. National BIM development is centred around the local organisation, buildingSMART Norway which represents 25% of the Norwegian construction industry.
==== Poland ====
BIMKlaster (BIM Cluster) is a non-governmental, non-profit organisation established in 2012 with the aim of promoting BIM development in Poland. In September 2016, the Ministry of Infrastructure and Construction began a series of expert meetings concerning the application of BIM methodologies in the construction industry.
==== Portugal ====
Created in 2015 to promote the adoption of BIM in Portugal and its normalisation, the Technical Committee for BIM Standardisation, CT197-BIM, has created the first strategic document for construction 4.0 in Portugal, aiming to align the country's industry around a common vision, integrated and more ambitious than a simple technology change.
==== Russia ====
The Russian government has approved a list of the regulations that provide the creation of a legal framework for the use of information modeling of buildings in construction and encourages the use of BIM in government projects.
==== Slovakia ====
The BIM Association of Slovakia, "BIMaS", was established in January 2013 as the first Slovak professional organisation focused on BIM. Although there are neither standards nor legislative requirements to deliver projects in BIM, many architects, structural engineers and contractors, plus a few investors are already applying BIM. A Slovak implementation strategy created by BIMaS and supported by the Chamber of Civil Engineers and Chamber of Architects has yet to be approved by Slovak authorities due to their low interest in such innovation.
==== Spain ====
A July 2015 meeting at Spain's Ministry of Infrastructure [Ministerio de Fomento] launched the country's national BIM strategy, making BIM a mandatory requirement on public sector projects with a possible starting date of 2018. Following a February 2015 BIM summit in Barcelona, professionals in Spain established a BIM commission (ITeC) to drive the adoption of BIM in Catalonia.
==== Switzerland ====
Since 2009 through the initiative of buildingSmart Switzerland, then 2013, BIM awareness among a broader community of engineers and architects was raised due to the open competition for Basel's Felix Platter Hospital where a BIM coordinator was sought. BIM has also been a subject of events by the Swiss Society for Engineers and Architects, SIA.
==== United Kingdom ====
In May 2011 UK Government Chief Construction Adviser Paul Morrell called for BIM adoption on UK government construction projects. Morrell also told construction professionals to adopt BIM or be "Betamaxed out". In June 2011 the UK government published its BIM strategy, announcing its intention to require collaborative 3D BIM (with all project and asset information, documentation and data being electronic) on its projects by 2016. Initially, compliance would require building data to be delivered in a vendor-neutral 'COBie' format, thus overcoming the limited interoperability of BIM software suites available on the market. The UK Government BIM Task Group led the government's BIM programme and requirements, including a free-to-use set of UK standards and tools that defined 'level 2 BIM'. In April 2016, the UK Government published a new central web portal as a point of reference for the industry for 'level 2 BIM'. The work of the BIM Task Group then continued under the stewardship of the Cambridge-based Centre for Digital Built Britain (CDBB), announced in December 2017 and formally launched in early 2018.
Outside of government, industry adoption of BIM since 2016 has been led by the UK BIM Alliance, an independent, not-for-profit, collaboratively-based organisation formed to champion and enable the implementation of BIM, and to connect and represent organisations, groups and individuals working towards digital transformation of the UK's built environment industry. In November 2017, the UK BIM Alliance merged with the UK and Ireland chapter of BuildingSMART. In October 2019, CDBB, the UK BIM Alliance and the BSI Group launched the UK BIM Framework. Superseding the BIM levels approach, the framework describes an overarching approach to implementing BIM in the UK, giving free guidance on integrating the international ISO 19650 series of standards into UK processes and practice.
National Building Specification (NBS) has published research into BIM adoption in the UK since 2011, and in 2020 published its 10th annual BIM report. In 2011, 43% of respondents had not heard of BIM; in 2020 73% said they were using BIM.
=== North America ===
==== Canada ====
BIM is not mandatory in Canada. Several organizations support BIM adoption and implementation in Canada: the Canada BIM Council (CANBIM, founded in 2008), the Institute for BIM in Canada, and buildingSMART Canada (the Canadian chapter of buildingSMART International). Public Services and Procurement Canada (formerly Public Works and Government Services Canada) is committed to using non-proprietary or "OpenBIM" BIM standards and avoids specifying any specific proprietary BIM format. Designers are required to use the international standards of interoperability for BIM (IFC).
==== United States ====
The Associated General Contractors of America and US contracting firms have developed various working definitions of BIM that describe it generally as:
an object-oriented building development tool that utilizes 5-D modeling concepts, information technology and software interoperability to design, construct and operate a building project, as well as communicate its details.
Although the concept of BIM and relevant processes are being explored by contractors, architects and developers alike, the term itself has been questioned and debated with alternatives including Virtual Building Environment (VBE) also considered. Unlike some countries such as the UK, the US has not adopted a set of national BIM guidelines, allowing different systems to remain in competition. In 2021, the National Institute of Building Sciences (NIBS) looked at applying UK BIM experiences to developing shared US BIM standards and processes. The US National BIM Standard had largely been developed through volunteer efforts; NIBS aimed to create a national BIM programme to drive effective adoption at a national scale.
BIM is seen to be closely related to Integrated Project Delivery (IPD) where the primary motive is to bring the teams together early on in the project. A full implementation of BIM also requires the project teams to collaborate from the inception stage and formulate model sharing and ownership contract documents.
The American Institute of Architects has defined BIM as "a model-based technology linked with a database of project information",[3] and this reflects the general reliance on database technology as the foundation. In the future, structured text documents such as specifications may be able to be searched and linked to regional, national, and international standards.
=== Africa ===
==== Nigeria ====
BIM has the potential to play a vital role in the Nigerian AEC sector. In addition to its potential clarity and transparency, it may help promote standardization across the industry. For instance, Utiome suggests that, in conceptualizing a BIM-based knowledge transfer framework from industrialized economies to urban construction projects in developing nations, generic BIM objects can benefit from rich building information within specification parameters in product libraries, and used for efficient, streamlined design and construction. Similarly, an assessment of the current 'state of the art' by Kori found that medium and large firms were leading the adoption of BIM in the industry. Smaller firms were less advanced with respect to process and policy adherence. There has been little adoption of BIM in the built environment due to construction industry resistance to changes or new ways of doing things. The industry is still working with conventional 2D CAD systems in services and structural designs, although production could be in 3D systems. There is virtually no utilisation of 4D and 5D systems.
BIM Africa Initiative, primarily based in Nigeria, is a non-profit institute advocating the adoption of BIM across Africa. Since 2018, it has been engaging with professionals and the government towards the digital transformation of the built industry. Produced annually by its research and development committee, the African BIM Report gives an overview of BIM adoption across the African continent.
==== South Africa ====
The South African BIM Institute, established in May 2015, aims to enable technical experts to discuss digital construction solutions that can be adopted by professionals working within the construction sector. Its initial task was to promote the SA BIM Protocol.
There are no mandated or national best practice BIM standards or protocols in South Africa. Organisations implement company-specific BIM standards and protocols at best (there are isolated examples of cross-industry alliances).
=== Oceania ===
==== Australia ====
In February 2016, Infrastructure Australia recommended: "Governments should make the use of Building Information Modelling (BIM) mandatory for the design of large-scale complex infrastructure projects. In support of a mandatory rollout, the Australian Government should commission the Australasian Procurement and Construction Council, working with industry, to develop appropriate guidance around the adoption and use of BIM; and common standards and protocols to be applied when using BIM".
==== New Zealand ====
In 2015, many projects in the rebuilding of Christchurch were being assembled in detail on a computer using BIM well before workers set foot on the site. The New Zealand government started a BIM acceleration committee, as part of a productivity partnership with the goal of 20 per cent more efficiency in the construction industry by 2020. Today, BIM use is still not mandated in the country while several challenges have been identified for its implementation in the country. However, members of the AEC industry and academia have developed a national BIM handbook providing definitions, case studies and templates.
== Purposes or dimensionality ==
Some purposes or uses of BIM may be described as 'dimensions'. However, there is little consensus on definitions beyond 5D. Some organisations dismiss the term; for example, the UK Institution of Structural Engineers does not recommend using nD modelling terms beyond 4D, adding "cost (5D) is not really a 'dimension'."
=== 3D ===
3D BIM, an acronym for three-dimensional building information modeling, refers to the graphical representation of an asset's geometric design, augmented by information describing attributes of individual components. 3D BIM work may be undertaken by professional disciplines such as architectural, structural, and MEP, and the use of 3D models enhances coordination and collaboration between disciplines. A 3D virtual model can also be created by creating a point cloud of the building or facility using laser scanning technology.
=== 4D ===
4D BIM, an acronym for 4-dimensional building information modeling, refers to the intelligent linking of individual 3D CAD components or assemblies with time- or scheduling-related information. The term 4D refers to the fourth dimension: time, i.e. 3D plus time.
4D modelling enables project participants (architects, designers, contractors, clients) to plan, sequence the physical activities, visualise the critical path of a series of events, mitigate the risks, report and monitor progress of activities through the lifetime of the project. 4D BIM enables a sequence of events to be depicted visually on a time line that has been populated by a 3D model, augmenting traditional Gantt charts and critical path (CPM) schedules often used in project management. Construction sequences can be reviewed as a series of problems using 4D BIM, enabling users to explore options, manage solutions and optimize results.
As an advanced construction management technique, it has been used by project delivery teams working on larger projects. 4D BIM has traditionally been used for higher end projects due to the associated costs, but technologies are now emerging that allow the process to be used by laymen or to drive processes such as manufacture.
=== 5D ===
5D BIM, an acronym for 5-dimensional building information modeling refers to the intelligent linking of individual 3D components or assemblies with time schedule (4D BIM) constraints and then with cost-related information. 5D models enable participants to visualise construction progress and related costs over time. This BIM-centric project management technique has potential to improve management and delivery of projects of any size or complexity.
In June 2016, McKinsey & Company identified 5D BIM technology as one of five big ideas poised to disrupt construction. It defined 5D BIM as "a five-dimensional representation of the physical and functional characteristics of any project. It considers a project’s time schedule and cost in addition to the standard spatial design parameters in 3-D."
=== 6D ===
6D BIM, an acronym for 6-dimensional building information modeling, is sometimes used to refer to the intelligent linking of individual 3D components or assemblies with all aspects of project life-cycle management information. However, there is less consensus about the definition of 6D BIM; it is also sometimes used to cover use of BIM for sustainability purposes.
In the project life cycle context, a 6D model is usually delivered to the owner when a construction project is finished. The "As-Built" BIM model is populated with relevant building component information such as product data and details, maintenance/operation manuals, cut sheet specifications, photos, warranty data, web links to product online sources, manufacturer information and contacts, etc. This database is made accessible to the users/owners through a customized proprietary web-based environment. This is intended to aid facilities managers in the operation and maintenance of the facility.
The term is less commonly used in the UK and has been replaced with reference to the Asset Information Requirements (AIR) and an Asset Information Model (AIM) as specified in BS EN ISO 19650-3:2020.
== See also ==
Data model
Design computing
Digital twin (the physical manifestation instrumented and connected to the model)
BCF
GIS
Digital Building Logbook
Landscape design software
Lean construction
List of BIM software
Macro BIM
Open-source 3D file formats
OpenStreetMap
Pre-fire planning
System information modelling
Whole Building Design Guide
Facility management (or Building management)
Building automation (and Building management systems)
== Notes ==
== References ==
== Further reading ==
Kensek, Karen (2014). Building Information Modeling, Routledge. ISBN 978-0-415-71774-8
Kensek, Karen and Noble, Douglas (2014). Building Information Modeling: BIM in Current and Future Practice, Wiley. ISBN 978-1-118-76630-9
Eastman, Chuck; Teicholz, Paul; Sacks, Rafael; Liston, Kathleen (2011). 'BIM Handbook: A Guide to Building Information Modeling for Owners, Managers, Designers, Engineers, and Contractors (2 ed.). John Wiley. ISBN 978-0-470-54137-1.
Lévy, François (2011). BIM in Small-Scale Sustainable Design, Wiley. ISBN 978-0470590898
Weygant, Robert S. (2011) BIM Content Development: Standards, Strategies, and Best Practices, Wiley. ISBN 978-0-470-58357-9
Hardin, Brad (2009). Martin Viveros (ed.). BIM and Construction Management: Proven Tools, Methods and Workflows. Sybex. ISBN 978-0-470-40235-1.
Smith, Dana K. and Tardif, Michael (2009). Building Information Modeling: A Strategic Implementation Guide for Architects, Engineers, Constructors, and Real Estate Asset Managers, Wiley. ISBN 978-0-470-25003-7
Underwood, Jason, and Isikdag, Umit (2009). Handbook of Research on Building Information Modeling and Construction Informatics: Concepts and Technologies, Information Science Publishing. ISBN 978-1-60566-928-1
Krygiel, Eddy and Nies, Brad (2008). Green BIM: Successful Sustainable Design with Building Information Modeling, Sybex. ISBN 978-0-470-23960-5
Kymmell, Willem (2008). Building Information Modeling: Planning and Managing Construction Projects with 4D CAD and Simulations, McGraw-Hill Professional. ISBN 978-0-07-149453-3
Jernigan, Finith (2007). BIG BIM little bim. 4Site Press. ISBN 978-0-9795699-0-6. | Wikipedia/Informative_modelling |
Analogical modeling (AM) is a formal theory of exemplar based analogical reasoning, proposed by Royal Skousen, professor of Linguistics and English language at Brigham Young University in Provo, Utah. It is applicable to language modeling and other categorization tasks. Analogical modeling is related to connectionism and nearest neighbor approaches, in that it is data-based rather than abstraction-based; but it is distinguished by its ability to cope with imperfect datasets (such as caused by simulated short term memory limits) and to base predictions on all relevant segments of the dataset, whether near or far. In language modeling, AM has successfully predicted empirically valid forms for which no theoretical explanation was known (see the discussion of Finnish morphology in Skousen et al. 2002).
== Implementation ==
=== Overview ===
An exemplar-based model consists of a general-purpose modeling engine and a problem-specific dataset. Within the dataset, each exemplar (a case to be reasoned from, or an informative past experience) appears as a feature vector: a row of values for the set of parameters that define the problem. For example, in a spelling-to-sound task, the feature vector might consist of the letters of a word. Each exemplar in the dataset is stored with an outcome, such as a phoneme or phone to be generated. When the model is presented with a novel situation (in the form of an outcome-less feature vector), the engine algorithmically sorts the dataset to find exemplars that helpfully resemble it, and selects one, whose outcome is the model's prediction. The particulars of the algorithm distinguish one exemplar-based modeling system from another.
In AM, we think of the feature values as characterizing a context, and the outcome as a behavior that occurs within that context. Accordingly, the novel situation is known as the given context. Given the known features of the context, the AM engine systematically generates all contexts that include it (all of its supracontexts), and extracts from the dataset the exemplars that belong to each. The engine then discards those supracontexts whose outcomes are inconsistent (this measure of consistency will be discussed further below), leaving an analogical set of supracontexts, and probabilistically selects an exemplar from the analogical set with a bias toward those in large supracontexts. This multilevel search exponentially magnifies the likelihood of a behavior's being predicted as it occurs reliably in settings that specifically resemble the given context.
=== Analogical modeling in detail ===
AM performs the same process for each case it is asked to evaluate. The given context, consisting of n variables, is used as a template to generate
2
n
{\displaystyle 2^{n}}
supracontexts. Each supracontext is a set of exemplars in which one or more variables have the same values that they do in the given context, and the other variables are ignored. In effect, each is a view of the data, created by filtering for some criteria of similarity to the given context, and the total set of supracontexts exhausts all such views. Alternatively, each supracontext is a theory of the task or a proposed rule whose predictive power needs to be evaluated.
It is important to note that the supracontexts are not equal peers one with another; they are arranged by their distance from the given context, forming a hierarchy. If a supracontext specifies all of the variables that another one does and more, it is a subcontext of that other one, and it lies closer to the given context. (The hierarchy is not strictly branching; each supracontext can itself be a subcontext of several others, and can have several subcontexts.) This hierarchy becomes significant in the next step of the algorithm.
The engine now chooses the analogical set from among the supracontexts. A supracontext may contain exemplars that only exhibit one behavior; it is deterministically homogeneous and is included. It is a view of the data that displays regularity, or a relevant theory that has never yet been disproven. A supracontext may exhibit several behaviors, but contain no exemplars that occur in any more specific supracontext (that is, in any of its subcontexts); in this case it is non-deterministically homogeneous and is included. Here there is no great evidence that a systematic behavior occurs, but also no counterargument. Finally, a supracontext may be heterogeneous, meaning that it exhibits behaviors that are found in a subcontext (closer to the given context), and also behaviors that are not. Where the ambiguous behavior of the nondeterministically homogeneous supracontext was accepted, this is rejected because the intervening subcontext demonstrates that there is a better theory to be found. The heterogeneous supracontext is therefore excluded. This guarantees that we see an increase in meaningfully consistent behavior in the analogical set as we approach the given context.
With the analogical set chosen, each appearance of an exemplar (for a given exemplar may appear in several of the analogical supracontexts) is given a pointer to every other appearance of an exemplar within its supracontexts. One of these pointers is then selected at random and followed, and the exemplar to which it points provides the outcome. This gives each supracontext an importance proportional to the square of its size, and makes each exemplar likely to be selected in direct proportion to the sum of the sizes of all analogically consistent supracontexts in which it appears. Then, of course, the probability of predicting a particular outcome is proportional to the summed probabilities of all the exemplars that support it.
(Skousen 2002, in Skousen et al. 2002, pp. 11–25, and Skousen 2003, both passim)
=== Formulas ===
Given a context with
n
{\displaystyle n}
elements:
total number of pairings:
n
2
{\displaystyle n^{2}}
number of agreements for outcome i:
n
i
2
{\displaystyle n_{i}^{2}}
number of disagreements for outcome i:
n
i
(
n
−
n
i
)
{\displaystyle n_{i}(n-n_{i})}
total number of agreements:
∑
n
i
2
{\displaystyle \sum {n_{i}^{2}}}
total number of disagreements:
∑
n
i
(
n
−
n
i
)
=
n
2
−
∑
n
i
2
{\displaystyle \sum {n_{i}(n-n_{i})}=n^{2}-\sum {n_{i}^{2}}}
=== Example ===
This terminology is best understood through an example. In the example used in the second chapter of Skousen (1989), each context consists of three variables with potential values 0-3
Variable 1: 0,1,2,3
Variable 2: 0,1,2,3
Variable 3: 0,1,2,3
The two outcomes for the dataset are e and r, and the exemplars are:
3 1 0 e
0 3 2 r
2 1 0 r
2 1 2 r
3 1 1 r
We define a network of pointers like so:
The solid lines represent pointers between exemplars with matching outcomes; the dotted lines represent pointers between exemplars with non-matching outcomes.
The statistics for this example are as follows:
n
=
5
{\displaystyle n=5}
n
r
=
4
{\displaystyle n_{r}=4}
n
e
=
1
{\displaystyle n_{e}=1}
total number of pairings:
n
2
=
25
{\displaystyle n^{2}=25}
number of agreements for outcome r:
n
r
2
=
16
{\displaystyle n_{r}^{2}=16}
number of agreements for outcome e:
n
e
2
=
1
{\displaystyle n_{e}^{2}=1}
number of disagreements for outcome r:
n
r
(
n
−
n
r
)
=
4
{\displaystyle n_{r}(n-n_{r})=4}
number of disagreements for outcome e:
n
e
(
n
−
n
e
)
=
4
{\displaystyle n_{e}(n-n_{e})=4}
total number of agreements:
n
r
2
+
n
e
2
=
17
{\displaystyle n_{r}^{2}+n_{e}^{2}=17}
total number of disagreements:
n
r
(
n
−
n
r
)
+
n
e
(
n
−
n
e
)
=
n
2
−
(
n
r
2
+
n
e
2
)
=
8
{\displaystyle n_{r}(n-n_{r})+n_{e}(n-n_{e})=n^{2}-(n_{r}^{2}+n_{e}^{2})=8}
uncertainty or fraction of disagreement:
8
/
25
=
.32
{\displaystyle 8/25=.32}
Behavior can only be predicted for a given context; in this example, let us predict the outcome for the context "3 1 2". To do this, we first find all of the contexts containing the given context; these contexts are called supracontexts. We find the supracontexts by systematically eliminating the variables in the given context; with m variables, there will generally be
2
m
{\displaystyle 2^{m}}
supracontexts. The following table lists each of the sub- and supracontexts; x means "not x", and - means "anything".
These contexts are shown in the venn diagram below:
The next step is to determine which exemplars belong to which contexts in order to determine which of the contexts are homogeneous. The table below shows each of the subcontexts, their behavior in terms of the given exemplars, and the number of disagreements within the behavior:
Analyzing the subcontexts in the table above, we see that there is only 1 subcontext with any disagreements: "3 1 2", which in the dataset consists of "3 1 0 e" and "3 1 1 r". There are 2 disagreements in this subcontext; 1 pointing from each of the exemplars to the other (see the pointer network pictured above). Therefore, only supracontexts containing this subcontext will contain any disagreements. We use a simple rule to identify the homogeneous supracontexts:
If the number if disagreements in the supracontext is greater than the number of disagreements in the contained subcontext, we say that it is heterogeneous; otherwise, it is homogeneous.
There are 3 situations that produce a homogeneous supracontext:
The supracontext is empty. This is the case for "3 - 2", which contains no data points. There can be no increase in the number of disagreements, and the supracontext is trivially homogeneous.
The supracontext is deterministic, meaning that only one type of outcome occurs in it. This is the case for "- 1 2" and "- - 2", which contain only data with the r outcome.
Only one subcontext contains any data. The subcontext does not have to be deterministic for the supracontext to be homogeneous. For example, while the supracontexts "3 1 -" and "- 1 2" are deterministic and only contain one non-empty subcontext, "3 - -" contains only the subcontext "3 1 2". This subcontext contains "3 1 0 e" and "3 1 1 r", making it non-deterministic. We say that this type of supracontext is unobstructed and non-deterministic.
The only two heterogeneous supracontexts are "- 1 -" and "- - -". In both of them, it is the combination of the non-deterministic "3 1 2" with other subcontexts containing the r outcome which causes the heterogeneity.
There is actually a 4th type of homogeneous supracontext: it contains more than one non-empty subcontext and it is non-deterministic, but the frequency of outcomes in each sub-context is exactly the same. Analogical modeling does not consider this situation, however, for 2 reasons:
Determining whether this 4 situation has occurred requires a
χ
2
{\displaystyle \chi ^{2}}
test. This is the only test of homogeneity that requires arithmetic, and ignoring it allows our tests of homogeneity to become statistically free, which makes AM better for modeling human reasoning.
It is an extremely rare situation, and thus ignoring it will can be expected not to have a large effect on the predicted outcome.
Next we construct the analogical set, which consists of all of the pointers and outcomes from the homogeneous supracontexts.
The figure below shows the pointer network with the homogeneous contexts highlighted.
The pointers are summarized in the following table:
4 of the pointers in the analogical set are associated with the outcome e, and the other 9 are associated with r. In AM, a pointer is randomly selected and the outcome it points to is predicted. With a total of 13 pointers, the probability of the outcome e being predicted is 4/13 or 30.8%, and for outcome r it is 9/13 or 69.2%. We can create a more detailed account by listing the pointers for each of the occurrences in the homogeneous supracontexts:
We can then see the analogical effect of each of the instances in the data set.
== Historical context ==
Analogy has been considered useful in describing language at least since the time of Saussure. Noam Chomsky and others have more recently criticized analogy as too vague to really be useful (Bańko 1991), an appeal to a deus ex machina. Skousen's proposal appears to address that criticism by proposing an explicit mechanism for analogy, which can be tested for psychological validity.
== Applications ==
Analogical modeling has been employed in experiments ranging from phonology and morphology (linguistics) to orthography and syntax.
== Problems ==
Though analogical modeling aims to create a model free from rules seen as contrived by linguists, in its current form it still requires researchers to select which variables to take into consideration. This is necessary because of the so-called "exponential explosion" of processing power requirements of the computer software used to implement analogical modeling. Recent research suggests that quantum computing could provide the solution to such performance bottlenecks (Skousen et al. 2002, see pp 45–47).
== See also ==
Computational Linguistics
Connectionism
Instance-based learning
k-nearest neighbor algorithm
== References ==
Royal Skousen (1989). Analogical Modeling of Language (hardcover). Dordrecht: Kluwer Academic Publishers. xii+212pp. ISBN 0-7923-0517-5.
Miroslaw Bańko (June 1991). "Review: Analogical Modeling of Language" (PDF). Computational Linguistics. 17 (2): 246–248. Archived from the original (PDF) on 2003-08-02.
Royal Skousen (1992). Analogy and Structure. Dordrect: Kluwer Academic Publishers. ISBN 0-7923-1935-4.
Royal Skousen; Deryle Lonsdale; Dilworth B. Parkinson, eds. (2002). Analogical Modeling: An exemplar-based approach to language (Human Cognitive Processing vol. 10). Amsterdam/Philadelphia: John Benjamins Publishing Company. p. x+417pp. ISBN 1-58811-302-7.
Skousen, Royal. (2003). Analogical Modeling: Exemplars, Rules, and Quantum Computing. Presented at the Berkeley Linguistics Society conference.
== External links ==
Analogical Modeling Research Group Homepage
LINGUIST List Announcement of Analogical Modeling, Skousen et al. (2002) | Wikipedia/Analogical_modeling |
A goal model is an element of requirements engineering that may also be used more widely in business analysis. Related elements include stakeholder analysis, context analysis, and scenarios, among other business and technical areas.
== Principles ==
Goals are objectives which a system should achieve through cooperation of actors in the intended software and in the environment. Goal modeling is especially useful in the early phases of a project. Projects may consider how the intended system meets organizational goals (see also ), why the system is needed and how the stakeholders’ interests may be addressed.
A goal model:
Expresses the relationships between a system and its environment (i.e. not only on what the system is supposed to do, but why). The understanding this gives, of the reasons why a system is needed, in its context, is useful because "systems are increasingly used to fundamentally change business processes rather than to automate long-established practices".
Clarifies requirements : Specifying goals leads to asking "why", "how" and "how else". Stakeholders' requirements are often revealed in this process, with less risk of either missing requirements, or of over-specifying (asking for things that are not needed).
Allows large goals to be analyzed into small, realizable goals:
Deals with conflicts : goal modeling can identify and help to resolve tradeoffs between cost, performance, flexibility, security and other goals. It can reveal divergent interests between stakeholders. It can identify conflicts because meeting one goal can interfere with meeting other goals.
Enables requirement completeness to be measured: requirements can be considered complete if they fulfil all the goals in the goal model.
Connects requirements to design: for example, the i* "Non-Functional Requirements (NFR) framework" uses goals to guide the design process.
== Notations ==
There are several notations in use for goal models in software development, including:
i* (pronounced "eye-star") and a variant, GRL
KAOS
UML Use Case diagram
Other notations have been proposed by researchers, while the Goal Structuring Notation (GSN) and GRL are sometimes used to make safety cases to satisfy the regulator in safety-related industries.
=== Goal modeling in i* ===
The i* goal modeling notation provides two kinds of diagram:
"Strategic Dependency" (SD), defining relationships between roles in terms of specific goals that one role depends on the other role to provide.
"Strategic Rationale" (SR), analyzing the goals identified on the SD model into subsidiary goals and tasks.
i* shows each role (an actor, agent or position) as a large circle containing the goals, tasks, and resources which that role owns. Ownership in i* means that the role desires the satisfaction of its goals, either for its own benefit or for the benefit of some other role. Goals may be accompanied by "obstacles" (negative goals) to be surmounted. Non-functional goals can be modeled as "soft goals" in i*: they are diagrammed as clouds or indented ovals.
=== Goal modeling in KAOS ===
The KAOS goal modeling notation provides a way of defining goals and obstacles, underpinned by a formal (mathematical) method of analysis.
=== Goal modeling in UML ===
UML's use case diagram provides a simple goal modeling notation. The bubbles name functional goals, so a Use case diagram forms a simple functions-only goal model: as Cockburn writes, use cases cover only the behavioral requirements. Roles are shown as actors (stickmen on the diagram), linked to the use cases in which they take part. The use cases are drawn as elliptical bubbles, representing desired behavioral goals.
With the addition of misuse cases, the notation can model both desired goals and active threats. The misuse case notation shows negative (possibly hostile) stakeholders as the primary actors for the misuse cases; these may be grouped on the right-hand side of the diagram. The notation may assist in discovering suitable mitigating or preventative goals, shown as subsidiary use cases. These often have the aim of improving security, safety, or reliability, which are non-functional goals. Non-functional requirements can to some extent be described in use case style using misuse cases to define negative goals; but the (positive) goals thus discovered are often functional. For example, if theft is a threat to security, then fitting locks is a mitigation; but that a door can be locked is a functional requirement.
The counterpoint is that Use Cases are not from Cognitive Science roots, whereas i* and KAOS are. Indeed, the literature behind Use Cases does not include discussion Goal Intention, Goal Refinement, Ends-Means, does not call out Rasmussen et cetera. There may be a predilection to relate Use Cases to Goals because of the visual metaphor of Goals rather than the semantics of Goal Refinement per Cognitive Science.
== Bibliography ==
Alexander, Ian and Beus-Dukic, Ljerka. Discovering Requirements: How to Specify Products and Services. Wiley, 2009.
Alexander, Ian F. and Maiden, Neil. Scenarios, Stories, Use Cases. Wiley, 2004.
Cockburn, Alistair. Writing Effective Use Cases. Addison-Wesley, 2001.
Fowler, Martin. UML Distilled. 3rd Edition. Addison-Wesley, 2004.
van Lamsweerde, Axel. Requirements Engineering: from system goals to UML models to software specifications. Wiley, 2009.
Yu, Eric, Paolo Giorgini, Neil Maiden and John Mylopoulos. (editors) Social Modeling for Requirements Engineering. MIT Press, 2011.
== See also ==
Benefit dependency network
== References ==
== External links ==
i* Official Website, with tutorial and bibliography - "an agent- and goal-oriented modelling framework"
i* wiki with guidelines and examples
KAOS tutorial
Using EEML for Combined Goal and Process Oriented Modeling: A Case Study - John Krogstie | Wikipedia/Goal_modeling |
Modeling and simulation (M&S) is the use of models (e.g., physical, mathematical, behavioral, or logical representation of a system, entity, phenomenon, or process) as a basis for simulations to develop data utilized for managerial or technical decision making.
In the computer application of modeling and simulation a computer is used to build a mathematical model which contains key parameters of the physical model. The mathematical model represents the physical model in virtual form, and conditions are applied that set up the experiment of interest. The simulation starts – i.e., the computer calculates the results of those conditions on the mathematical model – and outputs results in a format that is either machine- or human-readable, depending upon the implementation.
The use of M&S within engineering is well recognized. Simulation technology belongs to the tool set of engineers of all application domains and has been included in the body of knowledge of engineering management. M&S helps to reduce costs, increase the quality of products and systems, and document and archive lessons learned. Because the results of a simulation are only as good as the underlying model(s), engineers, operators, and analysts must pay particular attention to its construction. To ensure that the results of the simulation are applicable to the real world, the user must understand the assumptions, conceptualizations, and constraints of its implementation. Additionally, models may be updated and improved using results of actual experiments. M&S is a discipline on its own. Its many application domains often lead to the assumption that M&S is a pure application. This is not the case and needs to be recognized by engineering management in the application of M&S.
The use of such mathematical models and simulations avoids actual experimentation, which can be costly and time-consuming. Instead, mathematical knowledge and computational power is used to solve real-world problems cheaply and in a time efficient manner. As such, M&S can facilitate understanding a system's behavior without actually testing the system in the real world. For example, to determine which type of spoiler would improve traction the most while designing a race car, a computer simulation of the car could be used to estimate the effect of different spoiler shapes on the coefficient of friction in a turn. Useful insights about different decisions in the design could be gleaned without actually building the car. In addition, simulation can support experimentation that occurs totally in software, or in human-in-the-loop environments where simulation represents systems or generates data needed to meet experiment objectives. Furthermore, simulation can be used to train persons using a virtual environment that would otherwise be difficult or expensive to produce.
== Interest in simulations ==
Technically, simulation is well accepted. The 2006 National Science Foundation (NSF) Report on "Simulation-based Engineering Science" showed the potential of using simulation technology and methods to revolutionize the engineering science. Among the reasons for the steadily increasing interest in simulation applications are the following:
Using simulations is generally cheaper, safer and sometimes more ethical than conducting real-world experiments. For example, supercomputers are sometimes used to simulate the detonation of nuclear devices and their effects in order to support better preparedness in the event of a nuclear explosion. Similar efforts are conducted to simulate hurricanes and other natural catastrophes.
Simulations can often be even more realistic than traditional experiments, as they allow the free configuration of the realistic range of environment parameters found in the operational application field of the final product. Examples are supporting deep water operation of the US Navy or the simulating the surface of neighbored planets in preparation of NASA missions.
Simulations can often be conducted faster than real time. This allows using them for efficient if-then-else analyses of different alternatives, in particular when the necessary data to initialize the simulation can easily be obtained from operational data. This use of simulation adds decision support simulation systems to the tool box of traditional decision support systems.
Simulations allow setting up a coherent synthetic environment that allows for integration of simulated systems in the early analysis phase via mixed virtual systems with first prototypical components to a virtual test environment for the final system. If managed correctly, the environment can be migrated from the development and test domain to the training and education domain in follow-on life cycle phases for the systems (including the option to train and optimize a virtual twin of the real system under realistic constraints even before first components are being built).
The military and defense domain, in particular within the United States, has been the main M&S champion, in form of funding as well as application of M&S. E.g., M&S in modern military organizations is part of the acquisition/procurement strategy. Specifically, M&S is used to conduct Events and Experiments that influence requirements and training for military systems. As such, M&S is considered an integral part of systems engineering of military systems. Other application domains, however, are currently catching up. M&S in the fields of medicine, transportation, and other industries is poised to rapidly outstrip DoD's use of M&S in the years ahead, if it hasn't already happened.
== Simulation in science ==
Modeling and simulation are important in research. Representing the real systems either via physical reproductions at smaller scale, or via mathematical models that allow representing the dynamics of the system via simulation, allows exploring system behavior in an articulated way which is often either not possible, or too risky in the real world.
== As an emerging discipline ==
"The emerging discipline of M&S is based on developments in diverse computer science areas as well as influenced by developments in Systems Theory, Systems Engineering, Software Engineering, Artificial Intelligence, and more. This foundation is as diverse as that of engineering management and brings elements of art, engineering, and science together in a complex and unique way that requires domain experts to enable appropriate decisions when it comes to application or development of M&S technology in the context of this paper. The diversity and application-oriented nature of this new discipline sometimes result in the challenge, that the supported application domains themselves already have vocabularies in place that are not necessarily aligned between disjunctive domains. A comprehensive and concise representation of concepts, terms, and activities is needed that make up a professional Body of Knowledge for the M&S discipline. Due to the broad variety of contributors, this process is still ongoing."
Padilla et al. recommend in "Do we Need M&S Science" to distinguish between M&S Science, Engineering, and Applications.
M&S Science contributes to the Theory of M&S, defining the academic foundations of the discipline.
M&S Engineering is rooted in Theory but looks for applicable solution patterns. The focus is general methods that can be applied in various problem domains.
M&S Applications solve real world problems by focusing on solutions using M&S. Often, the solution results from applying a method, but many solutions are very problem domain specific and are derived from problem domain expertise and not from any general M&S theory or method.
Models can be composed of different units (models at finer granularity) linked to achieving a specific goal; for this reason they can be also called modeling solutions.
More generally, modeling and simulation is a key enabler for systems engineering activities as the system representation in a computer readable (and possibly executable) model enables engineers to reproduce the system (or Systems of System) behavior. A collection of applicative modeling and simulation method to support systems engineering activities in provided in.
== Application domains ==
There are many categorizations possible, but the following taxonomy has been very successfully used in the defense domain, and is currently applied to medical simulation and transportation simulation as well.
Analyses Support is conducted in support of planning and experimentation. Very often, the search for an optimal solution that shall be implemented is driving these efforts. What-if analyses of alternatives fall into this category as well. This style of work is often accomplished by simulysts - those having skills in both simulation and as analysts. This blending of simulation and analyst is well noted in Kleijnen.
Systems Engineering Support is applied for the procurement, development, and testing of systems. This support can start in early phases and include topics like executable system architectures, and it can support testing by providing a virtual environment in which tests are conducted. This style of work is often accomplished by engineers and architects.
Training and Education Support provides simulators, virtual training environments, and serious games to train and educate people. This style of work is often accomplished by trainers working in concert with computer scientists.
A special use of Analyses Support is applied to ongoing business operations. Traditionally, decision support systems provide this functionality. Simulation systems improve their functionality by adding the dynamic element and allow to compute estimates and predictions, including optimization and what-if analyses.
== Individual concepts ==
Although the terms "modeling" and "simulation" are often used as synonyms within disciplines applying M&S exclusively as a tool, within the discipline of M&S both are treated as individual and equally important concepts. Modeling is understood as the purposeful abstraction of reality, resulting in the formal specification of a conceptualization and underlying assumptions and constraints. M&S is in particular interested in models that are used to support the implementation of an executable version on a computer. The execution of a model over time is understood as the simulation. While modeling targets the conceptualization, simulation challenges mainly focus on implementation, in other words, modeling resides on the abstraction level, whereas simulation resides on the implementation level.
Conceptualization and implementation – modeling and simulation – are two activities that are mutually dependent, but can nonetheless be conducted by separate individuals. Management and engineering knowledge and guidelines are needed to ensure that they are well connected. Like an engineering management professional in systems engineering needs to make sure that the systems design captured in a systems architecture is aligned with the systems development, this task needs to be conducted with the same level of professionalism for the model that has to be implemented as well. As the role of big data and analytics continues to grow, the role of combined simulation of analysis is the realm of yet another professional called a simplest – in order to blend algorithmic and analytic techniques through visualizations available directly to decision makers. A study designed for the Bureau of Labor and Statistics by Lee et al. provides an interesting look at how bootstrap techniques (statistical analysis) were used with simulation to generate population data where there existed none.
== Academic programs ==
Modeling and Simulation has only recently become an academic discipline of its own. Formerly, those working in the field usually had a background in engineering.
The following institutions offer degrees in Modeling and Simulation:
Ph D. Programs
University of Pennsylvania (Philadelphia, PA)
Old Dominion University (Norfolk, VA)
University of Alabama in Huntsville (Huntsville, AL)
University of Central Florida (Orlando, FL)
Naval Postgraduate School (Monterey, CA)
University of Genoa (Genoa, Italy)
Masters Programs
National University of Science and Technology, Pakistan (Islamabad, Pakistan)
Arizona State University (Tempe, AZ)
Old Dominion University (Norfolk, VA)
University of Central Florida (Orlando, FL)
the University of Alabama in Huntsville (Huntsville, AL)
Middle East Technical University (Ankara, Turkey)
University of New South Wales (Australia)
Naval Postgraduate School (Monterey, CA)
Department of Scientific Computing, Modeling and Simulation (M.Tech (Modelling & Simulation)) (Savitribai Phule Pune University, India)
Columbus State University (Columbus, GA)
Purdue University Calumet (Hammond, IN)
Delft University of Technology (Delft, The Netherlands)
University of Genoa (Genoa, Italy)
Hamburg University of Applied Sciences (Hamburg, Germany)
Professional Science Masters Programs
University of Central Florida (Orlando, FL)
Graduate Certificate Programs
Portland State University Systems Science
Columbus State University (Columbus, GA)
the University of Alabama in Huntsville (Huntsville, AL)
Undergraduate Programs
Old Dominion University (Norfolk, VA)
Ghulam Ishaq Khan Institute of Engineering Sciences and Technology (Swabi, Pakistan)
== Modeling and Simulation Body of Knowledge ==
The Modeling and Simulation Body of Knowledge (M&S BoK) is the domain of knowledge (information) and capability (competency) that identifies the modeling and simulation community of practice and the M&S profession, industry, and market.
The M&S BoK Index is a set of pointers providing handles so that subject information content can be denoted, identified, accessed, and manipulated.
== Summary ==
Three activities have to be conducted and orchestrated to ensure success:
a model must be produced that captures formally the conceptualization,
a simulation must implement this model, and
management must ensure that model and simulation are interconnected and on the current state (which means that normally the model needs to be updated in case the simulation is changed as well).
== See also ==
== References ==
Master of Science, Purdue University Calumet. "Modeling, Simulation and Visualization". Archived from the original on 2014-10-08. Retrieved 2014-10-08.
== Further reading ==
The Springer Publishing House publishes the Simulation Foundations, Methods, and Applications Series [1].
Recently, Wiley started their own Series on Modeling and Simulation.
== External links ==
US Department of Defense (DoD) Modeling and Simulation Coordination Office (M&SCO)
MODSIM World Conference
Society for Modeling and Simulation
Association for Computing Machinery (ACM) Special Interest Group (SIG) on SImulation and Modeling (SIM)
US Congressional Modeling and Simulation Caucus
Example of an M&S BoK Index developed by Tuncer Ören
SimSummit collaborative environment supporting an M&S BoK | Wikipedia/Modelling_and_simulation |
Modelling biological systems is a significant task of systems biology and mathematical biology. Computational systems biology aims to develop and use efficient algorithms, data structures, visualization and communication tools with the goal of computer modelling of biological systems. It involves the use of computer simulations of biological systems, including cellular subsystems (such as the networks of metabolites and enzymes which comprise metabolism, signal transduction pathways and gene regulatory networks), to both analyze and visualize the complex connections of these cellular processes.
An unexpected emergent property of a complex system may be a result of the interplay of the cause-and-effect among simpler, integrated parts (see biological organisation). Biological systems manifest many important examples of emergent properties in the complex interplay of components. Traditional study of biological systems requires reductive methods in which quantities of data are gathered by category, such as concentration over time in response to a certain stimulus. Computers are critical to analysis and modelling of these data. The goal is to create accurate real-time models of a system's response to environmental and internal stimuli, such as a model of a cancer cell in order to find weaknesses in its signalling pathways, or modelling of ion channel mutations to see effects on cardiomyocytes and in turn, the function of a beating heart.
== Standards ==
By far the most widely accepted standard format for storing and exchanging models in the field is the Systems Biology Markup Language (SBML). The SBML.org website includes a guide to many important software packages used in computational systems biology. A large number of models encoded in SBML can be retrieved from BioModels. Other markup languages with different emphases include BioPAX, CellML and MorpheusML.
== Particular tasks ==
=== Cellular model ===
Creating a cellular model has been a particularly challenging task of systems biology and mathematical biology. It involves the use of computer simulations of the many cellular subsystems such as the networks of metabolites, enzymes which comprise metabolism and transcription, translation, regulation and induction of gene regulatory networks.
The complex network of biochemical reaction/transport processes and their spatial organization make the development of a predictive model of a living cell a grand challenge for the 21st century, listed as such by the National Science Foundation (NSF) in 2006.
A whole cell computational model for the bacterium Mycoplasma genitalium, including all its 525 genes, gene products, and their interactions, was built by scientists from Stanford University and the J. Craig Venter Institute and published on 20 July 2012 in Cell.
A dynamic computer model of intracellular signaling was the basis for Merrimack Pharmaceuticals to discover the target for their cancer medicine MM-111.
Membrane computing is the task of modelling specifically a cell membrane.
=== Multi-cellular organism simulation ===
An open source simulation of C. elegans at the cellular level is being pursued by the OpenWorm community. So far the physics engine Gepetto has been built and models of the neural connectome and a muscle cell have been created in the NeuroML format.
=== Protein folding ===
Protein structure prediction is the prediction of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of a protein's tertiary structure from its primary structure. It is one of the most important goals pursued by bioinformatics and theoretical chemistry. Protein structure prediction is of high importance in medicine (for example, in drug design) and biotechnology (for example, in the design of novel enzymes). Every two years, the performance of current methods is assessed in the CASP experiment.
=== Human biological systems ===
==== Brain model ====
The Blue Brain Project is an attempt to create a synthetic brain by reverse-engineering the mammalian brain down to the molecular level. The aim of this project, founded in May 2005 by the Brain and Mind Institute of the École Polytechnique in Lausanne, Switzerland, is to study the brain's architectural and functional principles. The project is headed by the Institute's director, Henry Markram. Using a Blue Gene supercomputer running Michael Hines's NEURON software, the simulation does not consist simply of an artificial neural network, but involves a partially biologically realistic model of neurons. It is hoped by its proponents that it will eventually shed light on the nature of consciousness.
There are a number of sub-projects, including the Cajal Blue Brain, coordinated by the Supercomputing and Visualization Center of Madrid (CeSViMa), and others run by universities and independent laboratories in the UK, U.S., and Israel. The Human Brain Project builds on the work of the Blue Brain Project. It is one of six pilot projects in the Future Emerging Technologies Research Program of the European Commission, competing for a billion euro funding.
==== Model of the immune system ====
The last decade has seen the emergence of a growing number of simulations of the immune system.
==== Virtual liver ====
The Virtual Liver project is a 43 million euro research program funded by the German Government, made up of seventy research group distributed across Germany. The goal is to produce a virtual liver, a dynamic mathematical model that represents human liver physiology, morphology and function.
=== Tree model ===
Electronic trees (e-trees) usually use L-systems to simulate growth. L-systems are very important in the field of complexity science and A-life.
A universally accepted system for describing changes in plant morphology at the cellular or modular level has yet to be devised.
The most widely implemented tree generating algorithms are described in the papers "Creation and Rendering of Realistic Trees" and Real-Time Tree Rendering.
=== Ecological models ===
Ecosystem models are mathematical representations of ecosystems. Typically they simplify complex foodwebs down to their major components or trophic levels, and quantify these as either numbers of organisms, biomass or the inventory/concentration of some pertinent chemical element (for instance, carbon or a nutrient species such as nitrogen or phosphorus).
=== Models in ecotoxicology ===
The purpose of models in ecotoxicology is the understanding, simulation and prediction of effects caused by toxicants in the environment. Most current models describe effects on one of many different levels of biological organization (e.g. organisms or populations). A challenge is the development of models that predict effects across biological scales. Ecotoxicology and models discusses some types of ecotoxicological models and provides links to many others.
=== Modelling of infectious disease ===
It is possible to model the progress of most infectious diseases mathematically to discover the likely outcome of an epidemic or to help manage them by vaccination. This field tries to find parameters for various infectious diseases and to use those parameters to make useful calculations about the effects of a mass vaccination programme.
== See also ==
Biological data visualization
Biosimulation
Gillespie algorithm
Molecular modelling software
Stochastic simulation
== Notes ==
== References ==
== Sources ==
Antmann, S. S.; Marsden, J. E.; Sirovich, L., eds. (2009). Mathematical Physiology (2nd ed.). New York, New York: Springer. ISBN 978-0-387-75846-6.
Barnes, D.J.; Chu, D. (2010), Introduction to Modelling for Biosciences, Springer Verlag
An Introduction to Infectious Disease Modelling by Emilia Vynnycky and Richard G White. An introductory book on infectious disease modelling and its applications.
== Further reading ==
== External links ==
The Center for Modeling Immunity to Enteric Pathogens (MIEP) | Wikipedia/Modeling_biological_systems |
Empirical modelling refers to any kind of (computer) modelling based on empirical observations rather than on mathematically describable relationships of the system modelled.
== Empirical Modelling ==
=== Empirical Modelling as a variety of empirical modelling ===
Empirical modelling is a generic term for activities that create models by observation and experiment. Empirical Modelling (with the initial letters capitalised, and often abbreviated to EM) refers to a specific variety of empirical modelling in which models are constructed following particular principles. Though the extent to which these principles can be applied to model-building without computers is an interesting issue (to be revisited below), there are at least two good reasons to consider Empirical Modelling in the first instance as computer-based. Without doubt, computer technologies have had a transformative impact where the full exploitation of Empirical Modelling principles is concerned. What is more, the conception of Empirical Modelling has been closely associated with thinking about the role of the computer in model-building.
An empirical model operates on a simple semantic principle: the maker observes a close correspondence between the behaviour of the model and that of its referent. The crafting of this correspondence can be 'empirical' in a wide variety of senses: it may entail a trial-and-error process, may be based on computational approximation to analytic formulae, it may be derived as a black-box relation that affords no insight into 'why it works'.
Empirical Modelling is rooted on the key principle of William James's radical empiricism, which postulates that all knowing is rooted in connections that are given-in-experience. Empirical Modelling aspires to craft the correspondence between the model and its referent in such a way that its derivation can be traced to connections given-in-experience. Making connections in experience is an essentially individual human activity that requires skill and is highly context-dependent. Examples of such connections include: identifying familiar objects in the stream of thought, associating natural languages words with objects to which they refer, and subliminally interpreting the rows and columns of a spreadsheet as exam results of particular students in particular subjects.
=== Principles ===
In Empirical Modelling, the process of construction is an incremental one in which the intermediate products are artefacts that evoke aspects of the intended (and sometimes emerging) referent through live interaction and observation. The connections evoked in this way have distinctive qualities: they are of their essence personal and experiential in character and are provisional in so far as they may be undermined, refined and reinforced as the model builder's experience and understanding of the referent develops. Following a precedent established by David Gooding in his account of the role that artefacts played in Michael Faraday's experimental investigation of electromagnetism, the intermediate products of the Empirical Modelling process are described as 'construals'. Gooding's account is a powerful illustration of how making construals can support the sense-making activities that lead to conceptual insights (cf. the contribution that Faraday's work made to electromagnetic theory) and to practical products (cf. Faraday's invention of the electric motor).
The activities associated with making a construal in the Empirical Modelling framework are depicted in Figure 1.
The eye icon at the centre the figure represents the maker's observation of the current state of development of the construal and its referent. The two arrows emanating from the eye represent the connection given-in-experience between the construal and its referent that is established in the mind of the maker. This connection is crafted through experimental interaction with the construal under construction and its emerging referent. As in genuine experiment, the scope of the interactions that can be entertained by the maker is inconceivably broad. At the maker's discretion, the interactions that characterise the construal are those that respect the connection given in the maker's experience. As the Empirical Modelling process unfolds, the construal, the referent, the maker's understanding and the context for the maker's engagement co-evolve in such a way that:
the interactive experience that the construal affords is enhanced;
the interactive experience that characterises the referent is refined;
the repertoire of characteristic interactions with the construal and its referent is enlarged;
the contextual constraints on characteristic interactions with the construal and its referent are identified.
=== Empirical Modelling concepts ===
In Empirical Modelling. making and maintaining the connection given-in-experience between the construal and referent is based on three primary concepts: observables, dependencies and agency. Within both the construal and its referent, the maker identifies observables as entities that can take on a range of different values, and whose current values determine its current state. All state-changing interactions with the construal and referent are conceived as changes to the values of observables. A change to the value of one observable may be directly attributable to a change in the value of another observable, in which case these values are linked by a dependency. Changes to observable values are attributed to agents, amongst which the most important is the maker of the construal. When changes to observable values are observed to occur simultaneously, this can be construed as concurrent action on the part of different agents, or as concomitant changes to observables derived from a single agent action via dependencies. To craft the connection given-in-experience between the construal and referent, the maker constructs the construal in such a way that its observables, dependencies and agency correspond closely to those that are observed in the referent. To this end, the maker must conceive appropriate ways in which observables and agent actions in the referent can be given suitable experiential counterparts in the construal.
The semantic framework shown in Figure 1 resembles that adopted in working with spreadsheets, where the state that is currently displayed in the grid is meaningful only when experienced in conjunction with an external referent. In this setting, the cells serve as observables, their definitions specify the dependencies, and agency is enacted by changing the values or the definitions of cells. In making a construal, the maker explores the roles of each relevant agent by projecting agency upon it as if it were a human agent and identifying observables and dependencies from that perspective. By automating agency, construals can then be used to specify behaviours in much the same way that behaviours can be expressed using macros in conjunction with spreadsheets. In this way, animated construals can emulate program-like behaviours in which the intermediate states are meaningful and live to auditing by the maker.
=== Environments to support Empirical Modelling ===
The development of computer environments for making construals has been an ongoing subject of research over the last thirty years. The many variants of such environments that have been implemented are based on common principles. The network of dependencies that currently connect observables is recorded as a family of definitions. Semantically such definitions resemble the definitions of spreadsheet cells, whereby changes to the values of observables on the right hand side propagate so as to change the value of the observable on the LHS in a conceptually indivisible manner. The dependencies in these networks are acyclic but are also reconfigurable: redefining an observable may introduce a new definition that alters the dependency structure. Observables built into the environment include scalars, geometric and screen display elements: these can be elaborated using multi-level list structures. A dependency is typically represented by a definition which uses a relatively simple functional expression to relate the value of an observable to the values of other observables. Such functions have typically been expressed in fragments of simple procedural code, but the most recent variants of environments of making construals also enable dependency relations to be expressed by suitably contextualised families of definitions. The maker can interact with a construal through redefining existing observables or introducing new observables in an open-ended unconstrained manner. Such interaction has a crucial role in the experimental activity that informs the incremental development of the construal. Triggered actions can be introduced to automate state-change: these perform redefinitions in response to specified changes in the values of observables.
=== Empirical Modelling as a broader view of computing ===
In Figure 1, identifying 'the computer' as the medium in which the construal is created is potentially misleading. The term COMPUTER is not merely a reference to a powerful computational device. In making construals, the primary emphasis is on the rich potential scope for interaction and perceptualisation that the computer enables when used in conjunction with other technologies and devices. The primary motivation for developing Empirical Modelling is to give a satisfactory account of computing that integrates these two complementary roles of the computer. The principles by which James and Dewey sought to reconcile perspectives on agency informed by logic and experience play a crucial role in achieving this integration.
The dual role for the computer implicit in Figure 1 is widely relevant to contemporary computing applications. On this basis, Empirical Modelling can be viewed as providing a foundation for a broader view of computing. This perspective is reflected in numerous Empirical Modelling publications on topics such as educational technology, computer-aided design and software development. Making construals has also been proposed as a suitable technique to support constructionism, as conceived by Seymour Papert, and to meet the guarantees for 'construction' as identified by Bruno Latour.
=== Empirical Modelling as generic sense-making? ===
The Turing machine provides the theoretical foundation for the role of the computer as a computational device: it can be regarded as modelling 'a mind following rules'. The practical applications of Empirical Modelling to date suggest that making construals is well-suited to supporting the supplementary role the computer can play in orchestrating rich experience. In particular, in keeping with the pragmatic philosophical stance of James and Dewey, making construals can fulfill an explanatory role by offering contingent explanations for human experience in contexts where computational rules cannot be invoked. In this respect, making construals may be regarded as modelling 'a mind making sense of a situation'.
In the same way that the Turing machine is a conceptual tool for understanding the nature of algorithms whose value is independent of the existence of the computer, Empirical Modelling principles and concepts may have generic relevance as a framework for thinking about sense-making without specific reference to the use of a computer. The contribution that William James's analysis of human experience makes to the concept of Empirical Modelling may be seen as evidence for this. By this token, Empirical Modelling principles may be an appropriate way to analyse varieties of empirical modelling that are not computer-based. For instance, it is plausible that the analysis in terms of observables, dependencies and agency that applies to interaction with electronic spreadsheets would also be appropriate for the manual spreadsheets that predated them.
=== Background ===
Empirical Modelling has been pioneered since the early 1980s by Meurig Beynon and the Empirical Modelling Research Group in Computer Science at the University of Warwick.
The term 'Empirical Modelling' (EM) has been adopted for this work since about 1995 to reflect the experiential basis of the modelling process in observation and experiment. Special purpose software supporting the central concepts of observable, dependency and agency has been under continuous development (mainly led by research students) since the late 1980s.
The principles and tools of EM have been used and developed by many hundreds of students within coursework, project work, and research theses. The undergraduate and MSc module 'Introduction to Empirical Modelling' was taught for many years up to 2013-14 until the retirement of Meurig Beynon and Steve Russ (authors of this article). There is a large website [1] containing research and teaching material with an extensive collection of refereed publications and conference proceedings.
The term 'construal' has been used since the early 2000s for the artefacts, or models, made with EM tools. The term has been adapted from its use by David Gooding in the book 'Experiment and the Making of Meaning' (1990) to describe the emerging, provisional ideas that formed in Faraday's mind, and were recorded in his notebooks, as he investigated electromagnetism, and made the first electric motors, in the 1800s.
The main practical activity associated with EM - that of 'making construals' - was the subject of an Erasmus+ Project CONSTRUIT! (2014-2017)[2].
== See also ==
Multi-agent system
== External links ==
http://www.dcs.warwick.ac.uk/modelling/ Empirical Modelling Research Group
https://warwick.ac.uk/fac/sci/dcs/research/em/welcome/ CONSTRUIT! Project web pages
== Notes, References == | Wikipedia/Empirical_modelling |
Predictive intake modelling uses mathematical modelling strategies to estimate intake of food, personal care products, and their formulations.
== Definition ==
Predictive intake modelling seeks to estimate intake of products and/or their constituents which may enter the body through various routes such as ingestion, inhalation and absorption.
Predictive intake modelling can be applied to determine trends in food consumption and product use for the purpose of extrapolation.
== Applications ==
A predictive intake modelling approach is used to estimate voluntary food intake (VFI) by animals where their eating habits cannot be exactly measured. For humans, predictive intake modelling is used to make estimations of intake from foods, pesticides, cosmetics and inhalants as well as substances that can be contained in these like nutrients, functional ingredients, chemicals and contaminants.
Predictive intake modelling has applications in public health, risk assessment and exposure assessment, where estimating intake or exposure to different substances can influence the decision making process.
== Predictive intake modelling strategies ==
=== Regression approach ===
The regression analysis approach is based on estimations through extrapolation or interpolation where there is a cause-and-effect relationship found by data fitting. These trends tend to be phenomenological.
=== Mechanistic modelling approach ===
A mechanistic modelling approach is one where a model is derived from basic theory. Examples of these include compartmental models which can be used to describe the circulation and concentration of airborne particles in a room or household for estimating intake of inhalants.
=== Population-based approach ===
A population-based approach tracks consumer intake from individual members of a sample population over time. Mathematical models are used to combine these habits and practices databases with separate databases on product or food formulation to estimate intake or exposure for the sample population. Moreover, survey weights may be applied to each subject in the study based on their age, demographic and location allowing the sample of subjects to correctly represent an entire population, and thus estimate intake for that population.
=== Probabilistic modelling approach ===
Probabilistic models are based on the Monte Carlo method where distributions of data from various sources are randomly sampled from to calculate percentile statistics. Such probabilistic techniques typically utilise product or consumption survey data from a sample population combined with distributions of substances that may be found within those foods or products. For example, The Food and Drug Administration (FDA) suggest that the estimation of intake of substances in food can be probabilistically conducted through food consumption surveys (NHANES/CSFII) from sample populations combined with distributions of substance concentration data to calculate the Estimated Daily Intake. The European Food Safety Authority (EFSA) funded the Monte Carlo Risk Assessment (MCRA) tool to estimate usual intake exposure distributions based on statistical models which utilise the EFSA Comprehensive Database, which contains detailed food consumption survey data. EFSA also funded Creme Global to develop a model and databases of European food consumption on which statistical models can be run to assess intake and exposure on a pan-European basis.
== See also ==
Predictive modelling
Exposure science
Exposure Assessment
== References == | Wikipedia/Predictive_intake_modelling |
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential equations and are converse to discrete modelling.
Modelling is generally broken down into several steps:
Making assumptions about the data: The modeller decides what is influencing the data and what can be safely ignored.
Making equations to fit the assumptions.
Solving the equations.
Verifying the results: Various statistical tests are applied to the data and the model and compared.
If the model passes the verification progress, putting it into practice.
If the model fails the verification progress, altering it and subjecting it again to verification; if it persists in fitting the data more poorly than a competing model, it is abandoned.
== References ==
== External links ==
Definition by the UK National Physical Laboratory | Wikipedia/Continuous_modelling |
Econometric models are statistical models used in econometrics. An econometric model specifies the statistical relationship that is believed to hold between the various economic quantities pertaining to a particular economic phenomenon. An econometric model can be derived from a deterministic economic model by allowing for uncertainty, or from an economic model which itself is stochastic. However, it is also possible to use econometric models that are not tied to any specific economic theory.
A simple example of an econometric model is one that assumes that monthly spending by consumers is linearly dependent on consumers' income in the previous month. Then the model will consist of the equation
C
t
=
a
+
b
Y
t
−
1
+
e
t
,
{\displaystyle C_{t}=a+bY_{t-1}+e_{t},}
where Ct is consumer spending in month t, Yt-1 is income during the previous month, and et is an error term measuring the extent to which the model cannot fully explain consumption. Then one objective of the econometrician is to obtain estimates of the parameters a and b; these estimated parameter values, when used in the model's equation, enable predictions for future values of consumption to be made contingent on the prior month's income.
== Formal definition ==
In econometrics, as in statistics in general, it is presupposed that the quantities being analyzed can be treated as random variables. An econometric model then is a set of joint probability distributions to which the true joint probability distribution of the variables under study is supposed to belong. In the case in which the elements of this set can be indexed by a finite number of real-valued parameters, the model is called a parametric model; otherwise it is a nonparametric or semiparametric model. A large part of econometrics is the study of methods for selecting models, estimating them, and carrying out inference on them.
The most common econometric models are structural, in that they convey causal and counterfactual information, and are used for policy evaluation. For example, an equation modeling consumption spending based on income could be used to see what consumption would be contingent on any of various hypothetical levels of income, only one of which (depending on the choice of a fiscal policy) will end up actually occurring.
== Basic models ==
Some of the common econometric models are:
Linear regression
Generalized linear models
Probit
Logit
Tobit
ARIMA
Vector Autoregression
Cointegration
Hazard
== Use in policy-making ==
Comprehensive models of macroeconomic relationships are used by central banks and governments to evaluate and guide economic policy. One famous econometric model of this nature is the Federal Reserve Bank econometric model.
== See also ==
Benefit financing model
== References ==
== Further reading ==
Asteriou, Dimitros; Hall, Stephen G. (2011). "The Classical Linear Regression Model". Applied Econometrics (Second ed.). Palgrave MacMillan. pp. 29–91. ISBN 978-0-230-27182-1.
Davidson, Russell; James G. MacKinnon (1993). Estimation and Inference in Econometrics. Oxford University Press. ISBN 0-19-506011-3.
Granger, Clive (1991). Modelling Economic Series: Readings in Econometric Methodology. Oxford University Press. ISBN 0-19-828736-4.
Pagan, Adrian; Aman Ullah (1999). Nonparametric Econometrics. Cambridge University Press. ISBN 0-521-58611-9.
Pedace, Roberto (2013). "Building the Classical Linear Regression Model". Econometrics for Dummies. Hoboken, NJ: Wiley. pp. 59–134. ISBN 978-1-118-53384-0.
== External links ==
Manuscript of Bruce Hansen's book on Econometrics
Econometrics lecture (introduction to regression models) on YouTube by Mark Thoma | Wikipedia/Econometric_model |
Models of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at genuine knowledge. The philosopher Wesley C. Salmon described scientific inquiry:
The search for scientific knowledge ends far back into antiquity. At some point in the past, at least by the time of Aristotle, philosophers recognized that a fundamental distinction should be drawn between two kinds of scientific knowledge—roughly, knowledge that and knowledge why. It is one thing to know that each planet periodically reverses the direction of its motion with respect to the background of fixed stars; it is quite a different matter to know why. Knowledge of the former type is descriptive; knowledge of the latter type is explanatory. It is explanatory knowledge that provides scientific understanding of the world. (Salmon, 2006, pg. 3)
According to the National Research Council (United States): "Scientific inquiry refers to the diverse ways in which scientists study the natural world and propose explanations based on the evidence derived from their work."
== Accounts of scientific inquiry ==
=== Classical model ===
The classical model of scientific inquiry derives from Aristotle, who distinguished the forms of approximate and exact reasoning, set out the threefold scheme of abductive, deductive, and inductive inference, and also treated the compound forms such as reasoning by analogy.
=== Pragmatic model ===
=== Logical empiricism ===
Wesley Salmon (1989) began his historical survey of scientific explanation with what he called the received view, as it was received from Hempel and Oppenheim in the years beginning with their Studies in the Logic of Explanation (1948) and culminating in Hempel's Aspects of Scientific Explanation (1965). Salmon summed up his analysis of these developments by means of the following Table.
In this classification, a deductive-nomological (D-N) explanation of an occurrence is a valid deduction whose conclusion states that the outcome to be explained did in fact occur. The deductive argument is called an explanation, its premisses are called the explanans (L: explaining) and the conclusion is called the explanandum (L: to be explained). Depending on a number of additional qualifications, an explanation may be ranked on a scale from potential to true.
Not all explanations in science are of the D-N type, however. An inductive-statistical (I-S) explanation accounts for an occurrence by subsuming it under statistical laws, rather than categorical or universal laws, and the mode of subsumption is itself inductive instead of deductive. The D-N type can be seen as a limiting case of the more general I-S type, the measure of certainty involved being complete, or probability 1, in the former case, whereas it is less than complete, probability < 1, in the latter case.
In this view, the D-N mode of reasoning, in addition to being used to explain particular occurrences, can also be used to explain general regularities, simply by deducing them from still more general laws.
Finally, the deductive-statistical (D-S) type of explanation, properly regarded as a subclass of the D-N type, explains statistical regularities by deduction from more comprehensive statistical laws. (Salmon 1989, pp. 8–9).
Such was the received view of scientific explanation from the point of view of logical empiricism, that Salmon says "held sway" during the third quarter of the last century (Salmon, p. 10).
== Choice of a theory ==
During the course of history, one theory has succeeded another, and some have suggested further work while others have seemed content just to explain the phenomena. The reasons why one theory has replaced another are not always obvious or simple. The philosophy of science includes the question: What criteria are satisfied by a 'good' theory. This question has a long history, and many scientists, as well as philosophers, have considered it. The objective is to be able to choose one theory as preferable to another without introducing cognitive bias. Several often proposed criteria were summarized by Colyvan. A good theory:
contains few arbitrary elements (simplicity/parsimony);
agrees with and explains all existing observations (unificatory/explanatory power) and makes detailed predictions about future observations that can disprove or falsify the theory if they are not borne out;
is fruitful, where the emphasis by Colyvan is not only upon prediction and falsification, but also upon a theory's seminality in suggesting future work;
is elegant (formal elegance; no ad hoc modifications).
Stephen Hawking supported items 1, 2 and 4, but did not mention fruitfulness. On the other hand, Kuhn emphasizes the importance of seminality.
The goal here is to make the choice between theories less arbitrary. Nonetheless, these criteria contain subjective elements, and are heuristics rather than part of scientific method. Also, criteria such as these do not necessarily decide between alternative theories. Quoting Bird:
"They [such criteria] cannot determine scientific choice. First, which features of a theory satisfy these criteria may be disputable (e.g. does simplicity concern the ontological commitments of a theory or its mathematical form?). Secondly, these criteria are imprecise, and so there is room for disagreement about the degree to which they hold. Thirdly, there can be disagreement about how they are to be weighted relative to one another, especially when they conflict."
It also is debatable whether existing scientific theories satisfy all these criteria, which may represent goals not yet achieved. For example, explanatory power over all existing observations (criterion 3) is satisfied by no one theory at the moment.
Whatever might be the ultimate goals of some scientists, science, as it is currently practiced, depends on multiple overlapping descriptions of the world, each of which has a domain of applicability. In some cases this domain is very large, but in others quite small.
The desiderata of a "good" theory have been debated for centuries, going back perhaps even earlier than Occam's razor, which often is taken as an attribute of a good theory. Occam's razor might fall under the heading of "elegance", the first item on the list, but too zealous an application was cautioned by Albert Einstein: "Everything should be made as simple as possible, but no simpler." It is arguable that parsimony and elegance "typically pull in different directions". The falsifiability item on the list is related to the criterion proposed by Popper as demarcating a scientific theory from a theory like astrology: both "explain" observations, but the scientific theory takes the risk of making predictions that decide whether it is right or wrong:
"It must be possible for an empirical scientific system to be refuted by experience."
"Those among us who are unwilling to expose their ideas to the hazard of refutation do not take part in the game of science."
Thomas Kuhn argued that changes in scientists' views of reality not only contain subjective elements, but result from group dynamics, "revolutions" in scientific practice which result in paradigm shifts. As an example, Kuhn suggested that the heliocentric "Copernican Revolution" replaced the geocentric views of Ptolemy not because of empirical failures, but because of a new "paradigm" that exerted control over what scientists felt to be the more fruitful way to pursue their goals.
== Aspects of scientific inquiry ==
=== Deduction and induction ===
Deductive reasoning and inductive reasoning are quite different in their approaches.
==== Deduction ====
Deductive reasoning is the reasoning of proof, or logical implication. It is the logic used in mathematics and other axiomatic systems such as formal logic. In a deductive system, there will be axioms (postulates) which are not proven. Indeed, they cannot be proven without circularity. There will also be primitive terms which are not defined, as they cannot be defined without circularity. For example, one can define a line as a set of points, but to then define a point as the intersection of two lines would be circular. Because of these interesting characteristics of formal systems, Bertrand Russell humorously referred to mathematics as "the field where we don't know what we are talking about, nor whether or not what we say is true". All theorems and corollaries are proven by exploring the implications of the axiomata and other theorems that have previously been developed. New terms are defined using the primitive terms and other derived definitions based on those primitive terms.
In a deductive system, one can correctly use the term "proof", as applying to a theorem. To say that a theorem is proven means that it is impossible for the axioms to be true and the theorem to be false. For example, we could do a simple syllogism such as the following:
Arches National Park lies within the state of Utah.
I am standing in Arches National Park.
Therefore, I am standing in the state of Utah.
Notice that it is not possible (assuming all of the trivial qualifying criteria are supplied) to be in Arches and not be in Utah. However, one can be in Utah while not in Arches National Park. The implication only works in one direction. Statements (1) and (2) taken together imply statement (3). Statement (3) does not imply anything about statements (1) or (2). Notice that we have not proven statement (3), but we have shown that statements (1) and (2) together imply statement (3). In mathematics, what is proven is not the truth of a particular theorem, but that the axioms of the system imply the theorem. In other words, it is impossible for the axioms to be true and the theorem to be false. The strength of deductive systems is that they are sure of their results. The weakness is that they are abstract constructs which are, unfortunately, one step removed from the physical world. They are very useful, however, as mathematics has provided great insights into natural science by providing useful models of natural phenomena. One result is the development of products and processes that benefit mankind.
==== Induction ====
===== Inductive generalization =====
Learning about the physical world often involves the use of inductive reasoning. It is useful in enterprises as science and crime scene detective work. One makes a set of specific observations, and seeks to make a general principle based on those observations, which will point to certain other observations that would naturally result from either a repeat of the experiment or making more observations from a slightly different set of circumstances. If the predicted observations hold true, one may be on the right track. However, the general principle has not been proven. The principle implies that certain observations should follow, but positive observations do not imply the principle. It is quite possible that some other principle could also account for the known observations, and may do better with future experiments. The implication flows in only one direction, as in the syllogism used in the discussion on deduction. Therefore, it is never correct to say that a scientific principle or hypothesis/theory has been "proven" in the rigorous sense of proof used in deductive systems.
A classic example of this is the study of gravitation. Newton formed a law for gravitation stating that the force of gravitation is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. For over 170 years, all observations seemed to validate his equation. However, telescopes eventually became powerful enough to see a slight discrepancy in the orbit of Mercury. Scientists tried everything imaginable to explain the discrepancy, but they could not do so using the objects that would bear on the orbit of Mercury. Eventually, Einstein developed his theory of general relativity and it explained the orbit of Mercury and all other known observations dealing with gravitation. During the long period of time when scientists were making observations that seemed to validate Newton's theory, they did not, in fact, prove his theory to be true. However, it must have seemed at the time that they did. It only took one counterexample (Mercury's orbit) to prove that there was something wrong with his theory.
This is typical of inductive reasoning. All of the observations that seem to validate the theory, do not prove its truth. But one counter-example can prove it false. That means that deductive logic is used in the evaluation of a theory. In other words, if A implies B, then not B implies not A. Einstein's theory of General Relativity has been supported by many observations using the best scientific instruments and experiments. However, his theory now has the same status as Newton's theory of gravitation prior to seeing the problems in the orbit of Mercury. It is highly credible and validated with all we know, but it is not proven. It is only the best we have at this point in time.
Another example of correct scientific reasoning is shown in the current search for the Higgs boson. Scientists on the Compact Muon Solenoid experiment at the Large Hadron Collider have conducted experiments yielding data suggesting the existence of the Higgs boson. However, realizing that the results could possibly be explained as a background fluctuation and not the Higgs boson, they are cautious and waiting for further data from future experiments. Said Guido Tonelli:
"We cannot exclude the presence of the Standard Model Higgs between 115 and 127 GeV because of a modest excess of events in this mass region that appears, quite consistently, in five independent channels [...] As of today what we see is consistent either with a background fluctuation or with the presence of the boson."
One way of describing scientific method would then contain these steps as a minimum:
Make a set of observations regarding the phenomenon being studied.
Form a hypothesis that might explain the observations. (This may involve inductive and/or abductive reasoning.)
Identify the implications and outcomes that must follow, if the hypothesis is to be true.
Perform other experiments or observations to see if any of the predicted outcomes fail.
If any predicted outcomes fail, the hypothesis is proven false since if A implies B, then not B implies not A (by deduction). It is then necessary to change the hypothesis and go back to step 3. If the predicted outcomes are confirmed, the hypothesis is not proved, but rather can be said to be consistent with known data.
When a hypothesis has survived a sufficient number of tests, it may be promoted to a scientific theory. A theory is a hypothesis that has survived many tests and seems to be consistent with other established scientific theories. Since a theory is a promoted hypothesis, it is of the same 'logical' species and shares the same logical limitations. Just as a hypothesis cannot be proven but can be disproved, that same is true for a theory. It is a difference of degree, not kind.
===== Argument from analogy =====
Arguments from analogy are another type of inductive reasoning. In arguing from analogy, one infers that since two things are alike in several respects, they are likely to be alike in another respect. This is, of course, an assumption. It is natural to attempt to find similarities between two phenomena and wonder what one can learn from those similarities. However, to notice that two things share attributes in several respects does not imply any similarities in other respects. It is possible that the observer has already noticed all of the attributes that are shared and any other attributes will be distinct. Argument from analogy is an unreliable method of reasoning that can lead to erroneous conclusions, and thus cannot be used to establish scientific facts.
== See also ==
Deductive-nomological
Explanandum and explanans
Hypothetico-deductive method
Inquiry
== References ==
== Further reading ==
An Introduction to Logic and Scientific Method (1934) by Ernest Nagel and Morris Raphael Cohen
Dictionary of Philosophy (1942) by Dagobert D. Runes
Understanding Scientific Progress: Aim-Oriented Empiricism, 2017, Paragon House, St. Paul by Nicholas Maxwell
== External links ==
Precession of the perihelion of Mercury | Wikipedia/Models_of_scientific_inquiry |
Water quality modeling involves water quality based data using mathematical simulation techniques. Water quality modeling helps people understand the eminence of water quality issues and models provide evidence for policy makers to make decisions in order to properly mitigate water. Water quality modeling also helps determine correlations to constituent sources and water quality along with identifying information gaps. Due to the increase in freshwater usage among people, water quality modeling is especially relevant both in a local level and global level. In order to understand and predict the changes over time in water scarcity, climate change, and the economic factor of water resources, water quality models would need sufficient data by including water bodies from both local and global levels.
A typical water quality model consists of a collection of formulations representing physical mechanisms that determine position and momentum of pollutants in a water body. Models are available for individual components of the hydrological system such as surface runoff; there also exist basin wide models addressing hydrologic transport and for ocean and estuarine applications. Often finite difference methods are used to analyze these phenomena, and, almost always, large complex computer models are required.
== Building A Model ==
Water quality models have different information, but generally have the same purpose, which is to provide evidentiary support of water issues. Models can be either deterministic or statistical depending on the scale with the base model, which is dependent on if the area is on a local, regional, or a global scale. Another aspect to consider for a model is what needs to be understood or predicted about that research area along with setting up any parameters to define the research. Another aspect of building a water quality model is knowing the audience and the exact purpose for presenting data like to enhance water quality management for water quality law makers for the best possible outcomes.
== Formulations and associated Constants ==
=== Water quality is modeled by one or more of the following formulations ===
Advective Transport formulation
Dispersive Transport formulation
Surface Heat Budget formulation
Dissolved Oxygen Saturation formulation
Reaeration formulation
Carbonaceous Deoxygenation formulation
Nitrogenous Biochemical Oxygen Demand formulation
Sediment oxygen demand formulation (SOD)
Photosynthesis and Respiration formulation
pH and Alkalinity formulation
Nutrients formulation (fertilizers)
Algae formulation
Zooplankton formulation
Coliform bacteria formulation (e.g. Escherichia coli )
=== SPARROW Models ===
A SPARROW model is a SPAtially-Referenced Regression on Watershed attributes, which helps integrate water quality data with landscape information. More specifically the USGS used this model to display long-term changes within watersheds to further explain in-stream water measurement in relation to upstream sources, water quality, and watershed properties. These models predict data for various spatial scales and integrate streamflow data with water quality at numerous locations across the US. A SPARROW model used by the USGS focused on the nutrients in the Nation's major rivers and estuaries; this model helped create a better understanding of where nutrients come from, where they are transported to while in the water bodies, and where they end up (reservoirs, other estuaries, etc.).
== See also ==
Hydrological transport models
Stochastic Empirical Loading and Dilution Model
Storm Water Management Model
Volumes of water on earth
Water resources
Water quality
Wastewater quality indicators
Streeter-Phelps equation
PCLake
== References ==
== External links ==
SPARROW Water-Quality Modeling - US Geological Survey- US Geological Survey
BASINS - EPA environmental analysis system integrating GIS, national watershed data, environmental assessment and modeling tools
Water Quality Models and Tools - EPA
Models for Total Maximum Daily Load Studies - Washington State Department of Ecology
Catchment Modelling Toolkit - eWater Cooperative Research Centre, Australia
Water Evaluation And Planning (WEAP), an integrated water resources planning model, including water quality - Stockholm Environmental Institute (US)
Stochastic Empirical Loading and Dilution Model (SELDM) - US Geological Survey stormwater quality model
U.S. Army Corps of Engineers Water Quality - New water quality modeling software developed by the U.S. Army Corps of Engineers | Wikipedia/Water_quality_modelling |
A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, engineering, chemistry and biology to economics, psychology, cognitive science and computer science.
The system under study is often a complex nonlinear system for which simple, intuitive analytical solutions are not readily available. Rather than deriving a mathematical analytical solution to the problem, experimentation with the model is done by adjusting the parameters of the system in the computer, and studying the differences in the outcome of the experiments. Operation theories of the model can be derived/deduced from these computational experiments.
Examples of common computational models are weather forecasting models, earth simulator models, flight simulator models, molecular protein folding models, Computational Engineering Models (CEM), and neural network models.
== See also ==
Computational engineering
Computational cognition
Reversible computing
Agent-based model
Artificial neural network
Computational linguistics
Data-driven model
Decision field theory
Dynamical systems model of cognition
Membrane computing
Ontology (information science)
Programming language theory
Microscale and macroscale models
== References == | Wikipedia/Computational_models |
The Joint Program in Design (also called the Graduate Design Program or simply the Design Program) was a graduate program jointly offered by the Department of Mechanical Engineering and the Department of Art & Art History at Stanford University. It was discontinued with the last cohort of students graduating in Spring 2017 and is succeeded by the Stanford Design Impact Engineering Master's Degree. The program offered degrees in Mechanical Engineering and in Fine Arts/Design and was closely connected with the Stanford d.school (The d.school is not one of the seven schools at Stanford and does not grant degrees).
The program was founded in 1958, and had three full-time faculty. It maintained close links with the design and technology firms of nearby Silicon Valley.
== History ==
Stanford's Design program dates from 1958 when Professor John E. Arnold, formerly of the Massachusetts Institute of Technology, first proposed the idea that design engineering should be human-centered. This was a radical concept in the era of Sputnik and the early Cold War. Building on Arnold's work, Bob McKim (Emeritus, Engineering) along with Matt Kahn (Art), created the Product Design major and the graduate-level Joint Program in Design. This curriculum was formalized in the mid-1960s, making the Joint Program in Design (JPD) one of the first inter-departmental programs at Stanford or other nationally prominent Universities. The key texts in those days were McKim's recently published Experiences in Visual Thinking, and Jim Adams', Conceptual Blockbusting, a Guide to Better Ideas. The "loft" was a bootleg attic space in Building 500 that the University didn't know about (and the faculty pretended didn't exist). ME101: Visual Thinking was the introductory class for all product design students and the class included four "voyages" in the Imaginarium, a 16-foot geodesic dome that presented state-of-the art multimedia shows designed to stimulate creativity.
The Loft moved to its current location behind the Old Firehouse. Bob McKim went Emeritus; Matt Kahn, Rolf Faste and David Kelley continued instruction in the tradition of merging art, science and needfinding though the 1980s and 1990s. Today ME101 is still taught, although the Mechanical Engineering Department and the Department of Art no longer continue their historic collaboration with faculty drawn from both schools in its instruction.
== See also ==
Stanford Hasso Plattner Institute of Design ("the d.school")
Silicon Valley
Leadership
Entrepreneurship
Globalization
Social responsibility
== References == | Wikipedia/Stanford_Joint_Program_in_Design |
Agile modeling (AM) is a methodology for modeling and documenting software systems based on best practices. It is a collection of values and principles that can be applied on an (agile) software development project. This methodology is more flexible than traditional modeling methods, making it a better fit in a fast-changing environment. It is part of the agile software development tool kit.
Agile modeling is a supplement to other agile development methodologies such as Scrum, extreme programming (XP), and Rational Unified Process (RUP). It is explicitly included as part of the disciplined agile delivery (DAD) framework. As per 2011 stats, agile modeling accounted for 1% of all agile software development.
Agile modeling is one form of Agile model-driven engineering (Agile MDE), which has been adopted in several application areas such as web application development, finance, and automotive systems
== Core practices ==
There are several core practices:
=== Documentation ===
Document continuously. Documentation is made throughout the life-cycle, in parallel to the creation of the rest of the solution.
Document late. Documentation is made as late as possible, avoiding speculative ideas that are likely to change in favor of stable information.
Executable specifications. Requirements are specified in the form of executable "customer tests", instead of non-executable "static" documentation.
Single-source information. Information (models, documentation, software), is stored in one place and one place only, to prevent questions about what the "correct" version / information is.
=== Modeling ===
Active stakeholder participation. Stakeholders of the solution/software being modeled should be actively involved with doing so. This is an extension of the on-site customer practice from Extreme Programming.
Architecture envisioning. The team performs light-weight, high-level modeling that is just barely good enough (JBGE) at the beginning of a software project so as to explore the architecture strategy that the team believes will work.
Inclusive tools. Prefer modelling tools, such as whiteboards and paper, that are easy to work with (they're inclusive).
Iteration modeling. When a requirement/work item has not been sufficiently explored in detail via look-ahead modeling the team may choose to do that exploration during their iteration/sprint planning session. The need to do this is generally seen as a symptom that the team is not doing sufficient look-ahead modeling.
Just barely good enough (JBGE). All artifacts, including models and documents, should be just sufficient for the task at hand. JBGE is contextual in nature, in the case of the model it is determined by a combination of the complexity of whatever the model describes and the skills of the audience for that model.
Look-ahead modeling. An agile team will look down their backlog one or more iterations/sprints ahead to ensure that a requirement/work item is ready to be worked on. Also called "backlog grooming" or "backlog refinement" in Scrum.
Model storming. A short, often impromptu, agile modeling session. Model storming sessions are held to explore the details of a requirement or aspect of your design.
Multiple models. Agile modelers should know how to create a range of model types (such as user stories, story maps, data models, Unified Modeling Language (UML) diagrams, and more) so as to apply the best model for the situation at hand.
Prioritized requirements. Requirements should be worked on in priority order.
Requirements envisioning. The team performs light-weight, high-level modeling that is JBGE at the beginning of a software project to explore the stakeholder requirements.
== Limitations ==
There is significant dependence on personal communication and customer collaboration. Agile modeling disciplines can be difficult to apply :
On large teams (say 30 or more) without adequate tooling support
Where team members are unable to share and collaborate on models (which would make agile software development in general difficult)
When modeling skills are weak or lacking.
== See also ==
Story-driven modelling
Agile software development
Robustness diagram
== References ==
== External links ==
The Agile Modeling Home Page
Agile Model Driven Development (AMDD) | Wikipedia/Agile_modeling |
The following tables provide a comparison of computer algebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language. A CAS may include a user interface and graphics capability; and to be effective may require a large library of algorithms, efficient data structures and a fast kernel.
== General ==
These computer algebra systems are sometimes combined with "front end" programs that provide a better user interface, such as the general-purpose GNU TeXmacs.
=== Functionality ===
Below is a summary of significantly developed symbolic functionality in each of the systems.
^ via SymPy
^ via qepcad optional package
Those which do not "edit equations" may have a GUI, plotting, ASCII graphic formulae and math font printing. The ability to generate plaintext files is also a sought-after feature because it allows a work to be understood by people who do not have a computer algebra system installed.
=== Operating system support ===
The software can run under their respective operating systems natively without emulation. Some systems must be compiled first using an appropriate compiler for the source language and target platform. For some platforms, only older releases of the software may be available.
== Graphing calculators ==
Some graphing calculators have CAS features.
== See also ==
Category:Computer algebra systems
Comparison of numerical-analysis software
Comparison of statistical packages
List of information graphics software
List of numerical-analysis software
List of numerical libraries
List of statistical software
Mathematical software
Web-based simulation
== References ==
== External links == | Wikipedia/Comparison_of_computer_algebra_systems |
Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio of a business, project, or any other investment.
Typically, then, financial modeling is understood to mean an exercise in either asset pricing or corporate finance, of a quantitative nature. It is about translating a set of hypotheses about the behavior of markets or agents into numerical predictions. At the same time, "financial modeling" is a general term that means different things to different users; the reference usually relates either to accounting and corporate finance applications or to quantitative finance applications.
== Accounting ==
In corporate finance and the accounting profession, financial modeling typically entails financial statement forecasting; usually the preparation of detailed company-specific models used for decision making purposes, valuation and financial analysis.
Applications include:
Business valuation, stock valuation, and project valuation - especially via discounted cash flow, but including other valuation approaches
Scenario planning, FP&A and management decision making ("what is"; "what if"; "what has to be done")
Budgeting: revenue forecasting and analytics; production budgeting; operations budgeting
Capital budgeting, including cost of capital (i.e. WACC) calculations
Cash flow forecasting; working capital- and treasury management; asset and liability management
Financial statement analysis / ratio analysis (including of operating- and finance leases, and R&D)
Transaction analytics: M&A, PE, VC, LBO, IPO, Project finance, P3
Credit decisioning: Credit analysis, Consumer credit risk; impairment- and provision-modeling
Management accounting: Activity-based costing, Profitability analysis, Cost analysis, Whole-life cost, Managerial risk accounting
Public sector procurement
To generalize as to the nature of these models:
firstly, as they are built around financial statements, calculations and outputs are monthly, quarterly or annual;
secondly, the inputs take the form of "assumptions", where the analyst specifies the values that will apply in each period for external / global variables (exchange rates, tax percentage, etc....; may be thought of as the model parameters), and for internal / company specific variables (wages, unit costs, etc....). Correspondingly, both characteristics are reflected (at least implicitly) in the mathematical form of these models:
firstly, the models are in discrete time;
secondly, they are deterministic.
For discussion of the issues that may arise, see below; for discussion as to more sophisticated approaches sometimes employed, see Corporate finance § Quantifying uncertainty and Financial economics § Corporate finance theory.
Modelers are often designated "financial analyst" (and are sometimes referred to, tongue in cheek, as "number crunchers"). Typically, the modeler will have completed an MBA or MSF with (optional) coursework in "financial modeling". Accounting qualifications and finance certifications such as the CIIA and CFA generally do not provide direct or explicit training in modeling. At the same time, numerous commercial training courses are offered, both through universities and privately.
For the components and steps of business modeling here, see Outline of finance § Financial modeling; see also Valuation using discounted cash flows § Determine cash flow for each forecast period for further discussion and considerations.
Although purpose-built business software does exist, the vast proportion of the market is spreadsheet-based; this is largely since the models are almost always company-specific. Also, analysts will each have their own criteria and methods for financial modeling. Microsoft Excel now has by far the dominant position, having overtaken Lotus 1-2-3 in the 1990s. Spreadsheet-based modelling can have its own problems, and several standardizations and "best practices" have been proposed. "Spreadsheet risk" is increasingly studied and managed; see model audit.
One critique here, is that model outputs, i.e. line items, often inhere "unrealistic implicit assumptions" and "internal inconsistencies". (For example, a forecast for growth in revenue but without corresponding increases in working capital, fixed assets and the associated financing, may imbed unrealistic assumptions about asset turnover, debt level and/or equity financing. See Sustainable growth rate § From a financial perspective.) What is required, but often lacking, is that all key elements are explicitly and consistently forecasted.
Related to this, is that modellers often additionally "fail to identify crucial assumptions" relating to inputs, "and to explore what can go wrong". Here, in general, modellers "use point values and simple arithmetic instead of probability distributions and statistical measures"
— i.e., as mentioned, the problems are treated as deterministic in nature — and thus calculate a single value for the asset or project, but without providing information on the range, variance and sensitivity of outcomes;
see Valuation using discounted cash flows § Determine equity value.
A further, more general critique relates to the lack of basic computer programming concepts amongst modelers,
with the result that their models are often poorly structured, and difficult to maintain. Serious criticism is also directed at the nature of budgeting, and its impact on the organization.
== Quantitative finance ==
In quantitative finance, financial modeling entails the development of a sophisticated mathematical model. Models here deal with asset prices, market movements, portfolio returns and the like.
Relatedly, applications include:
Option pricing and calculation of their "Greeks" ( accommodating volatility surfaces - via local / stochastic volatility models - and multi-curves)
Other derivatives, especially interest rate derivatives, credit derivatives and exotic derivatives
Credit valuation adjustment, CVA, as well as the various XVA
Modeling the term structure of interest rates (bootstrapping / multi-curves, short-rate models, HJM framework) and any related credit spread
Credit risk, counterparty credit risk, and regulatory capital: EAD, PD, LGD, PFE, EE; Jarrow–Turnbull model, Merton model, KMV model
Portfolio optimization and Quantitative investing more generally; see further re optimization methods employed.
Credit scoring and provisioning; Credit scorecards and IFRS 9 § Impairment
Structured product design and manufacture
Financial risk modeling: value at risk (parametric- and / or historical, CVaR, EVT), stress testing, "sensitivities" analysis (Greeks, duration, convexity, DV01, KRD, CS01, JTD)
Corporate finance applications: cash flow analytics, corporate financing activity prediction problems, and risk analysis in capital investment
Real options
Actuarial applications: Dynamic financial analysis (DFA), UIBFM, investment modeling
These problems are generally stochastic and continuous in nature, and models here thus require complex algorithms, entailing computer simulation, advanced numerical methods (such as numerical differential equations, numerical linear algebra, dynamic programming) and/or the development of optimization models. The general nature of these problems is discussed under Mathematical finance § History: Q versus P, while specific techniques are listed under Outline of finance § Mathematical tools.
For further discussion here see also: Brownian model of financial markets; Martingale pricing; Financial models with long-tailed distributions and volatility clustering; Extreme value theory; Historical simulation (finance).
Modellers are generally referred to as "quants", i.e. quantitative analysts (or "rocket scientists") and typically have advanced (Ph.D. level) backgrounds in quantitative disciplines such as statistics, physics, engineering, computer science, mathematics or operations research.
Alternatively, or in addition to their quantitative background, they complete a finance masters with a quantitative orientation, such as the Master of Quantitative Finance, or the more specialized Master of Computational Finance or Master of Financial Engineering; the CQF certificate is increasingly common.
Although spreadsheets are widely used here also (almost always requiring extensive VBA);
custom C++, Fortran or Python, or numerical-analysis software such as MATLAB, are often preferred, particularly where stability or speed is a concern.
MATLAB is often used at the research or prototyping stage because of its intuitive programming, graphical and debugging tools, but C++/Fortran are preferred for conceptually simple but high computational-cost applications where MATLAB is too slow;
Python is increasingly used due to its simplicity, and large standard library / available applications, including QuantLib.
Additionally, for many (of the standard) derivative and portfolio applications, commercial software is available, and the choice as to whether the model is to be developed in-house, or whether existing products are to be deployed, will depend on the problem in question.
See Quantitative analysis (finance) § Library quantitative analysis.
The complexity of these models may result in incorrect pricing or hedging or both. This Model risk is the subject of ongoing research by finance academics, and is a topic of great, and growing, interest in the risk management arena.
Criticism of the discipline (often preceding the 2008 financial crisis by several years) emphasizes the differences between finance and the mathematical / physical sciences, and stresses the resultant caution to be applied by modelers, and by traders and risk managers using their models. Notable here are Emanuel Derman and Paul Wilmott, authors of the Financial Modelers' Manifesto. Some go further and question whether the mathematical- and statistical modeling techniques usually applied to finance are at all appropriate (see the assumptions made for options and for portfolios).
In fact, these may go so far as to question the "empirical and scientific validity... of modern financial theory".
Notable here are Nassim Taleb and Benoit Mandelbrot.
See also Mathematical finance § Criticism, Financial economics § Challenges and criticism and Financial engineering § Criticisms.
== Competitive modeling ==
Several financial modeling competitions exist, emphasizing speed and accuracy in modeling. The Microsoft-sponsored ModelOff Financial Modeling World Championships were held annually from 2012 to 2019, with competitions throughout the year and a finals championship in New York or London. After its end in 2020, several other modeling championships have been started, including the Financial Modeling World Cup and Microsoft Excel Collegiate Challenge, also sponsored by Microsoft.
== Philosophy of financial modeling ==
Philosophy of financial modeling is a branch of philosophy concerned with the foundations, methods, and implications of modeling science.
In the philosophy of financial modeling, scholars have more recently begun to question the generally-held assumption that financial modelers seek to represent any "real-world" or actually ongoing investment situation. Instead, it has been suggested that the task of the financial modeler resides in demonstrating the possibility of a transaction in a prospective investment scenario, from a limited base of possibility conditions initially assumed in the model.
== See also ==
== References ==
== Bibliography == | Wikipedia/Financial_modeling |
ReScience C is a journal created in 2015 by Nicolas Rougier and Konrad Hinsen with the aim of publishing researchers' attempts to replicate computations made by other authors, using independently written, free and open-source software (FOSS), with an open process of peer review. The journal states that requiring the replication software to be free and open-source ensures the reproducibility of the original research.
== Creation ==
ReScience C was created in 2015 by Nicolas Rougier and Konrad Hinsen in the context of the replication crisis of the early 2010s, in which concern about difficulty in replicating (different data or details of method) or reproducing (same data, same method) peer-reviewed, published research papers was widely discussed. ReScience C's scope is computational research, with the motivation that journals rarely require the provision of source code, and when source code is provided, it is rarely checked against the results claimed in the research article.
== Policies and methods ==
The scope of ReScience C is mainly focussed on researchers' attempts to replicate computations made by other authors, using independently written, free and open-source software (FOSS). Articles are submitted using the "issues" feature of a git repository run by GitHub, together with other online archiving services, including Zenodo and Software Heritage. Peer review takes place publicly in the same "issues" online format.
In 2020, Nature reported on the results of ReScience C's "Ten Years' Reproducibility Challenge", in which scientists were asked to try reproducing the results from peer-reviewed articles that they had published at least ten years earlier, using the same data and software if possible, updated to a modern software environment and free licensing. As of 24 August 2020, out of 35 researchers who had proposed to reproduce the results of 43 of their old articles, 28 reports had been written, 13 had been accepted after peer review and published, among which 11 documented successful reproductions.
== References ==
== External links ==
free-licensed images by Nicolas Rougier, co-editor of ReScience C | Wikipedia/ReScience_C |
Optical projection tomography is a form of tomography involving optical microscopy. The OPT technique is sometimes referred to as optical computed tomography (optical-CT) and optical emission computed tomography (optical-ECT) in the literature, to address the fact that the technique bears similarity to X-ray computed tomography (CT) and single-photon emission computed tomography (SPECT).
It is in many ways the optical equivalent of X-ray computed tomography or the medical CT scan. OPT differs in the way that it often uses ultraviolet, visible, and near-infrared photons as opposed to X-ray photons. However, essential mathematics and reconstruction algorithms used for CT and OPT are similar; for example, radon transform or iterative reconstruction based on projection data are used in both medical CT scan and OPT for 3D reconstruction.
Both medical CT and OPT compute 3D volumes based on transmission of the photon through the material of interest. Given that the tissue is typically opaque in the ultraviolet, visible, and near-infrared spectrum, the tissue must first be made clear with an optical clearing agent, so that the light can pass through. Common optical clearing agents include BABB and methyl salicylate (wintergreen).
OPT can assume two primary forms – transmission mode and emission mode. In transmission mode, where light is passed through an optically cleared sample, one can obtain structural information about the sample of interest. In emission mode, where the sample is exposed to excitation light, one can obtain functional information about the sample of interest. In tandem with organs harvested from genetically modified mouse that express fluorescent proteins such as green fluorescent proteins, the emission mode of OPT can yield 3D genetic expression images of the mouse organ.
The technique has already contributed to a large number of studies aimed at addressing a broad range of biological questions in diverse systems such as human, mice, chicken, fly, zebrafish, and plants. More recent adaptations have further enabled the use of the technique for studies of specimens on the adult mouse organ scale, individual cell nuclei, and longitudinal assessments of organ cultures.
Fluorescence optical projection tomography visualises the distribution of dyes in the specimen.
== See also ==
Diffuse optical imaging
Optical coherence tomography
Optical tomography
== References ==
== External links ==
https://web.archive.org/web/20101105182544/http://genex.hgu.mrc.ac.uk/OPT_Microscopy/optwebsite/frontpage/index.htm
Video I: Optical Projection Tomography of a mouse left lateral liver lobe.
Video II: Optical Projection Tomography of an embryonic stomach, intestine and pancreas of a mouse.
Inner World of carnivorous plants from the John Innes Centre Archived 2020-06-10 at the Wayback Machine | Wikipedia/Optical_projection_tomography |
Computational Engineering is an emerging discipline that deals with the development and application of computational models for engineering, known as Computational Engineering Models or CEM. Computational engineering uses computers to solve engineering design problems important to a variety of industries. At this time, various different approaches are summarized under the term Computational Engineering, including using computational geometry and virtual design for engineering tasks, often coupled with a simulation-driven approach In Computational Engineering, algorithms solve mathematical and logical models that describe engineering challenges, sometimes coupled with some aspect of AI
In Computational Engineering the engineer encodes their knowledge in a computer program. The result is an algorithm, the Computational Engineering Model, that can produce many different variants of engineering designs, based on varied input requirements. The results can then be analyzed through additional mathematical models to create algorithmic feedback loops.
Simulations of physical behaviors relevant to the field, often coupled with high-performance computing, to solve complex physical problems arising in engineering analysis and design (as well as natural phenomena (computational science). It is therefore related to Computational Science and Engineering, which has been described as the "third mode of discovery" (next to theory and experimentation).
In Computational Engineering, computer simulation provides the capability to create feedback that would be inaccessible to traditional experimentation or where carrying out traditional empirical inquiries is prohibitively expensive.
Computational Engineering should neither be confused with pure computer science, nor with computer engineering, although a wide domain in the former is used in Computational Engineering (e.g., certain algorithms, data structures, parallel programming, high performance computing) and some problems in the latter can be modeled and solved with Computational Engineering methods (as an application area).
== Methods ==
Computational Engineering methods and frameworks include:
High performance computing and techniques to gain efficiency (through change in computer architecture, parallel algorithms etc.)
Modeling and simulation
Algorithms for solving discrete and continuous problems
Analysis and visualization of data
Mathematical foundations: Numerical and applied linear algebra, initial & boundary value problems, Fourier analysis, optimization
Data Science for developing methods and algorithms to handle and extract knowledge from large scientific data
With regard to computing, computer programming, algorithms, and parallel computing play a major role in Computational Engineering. The most widely used programming language in the scientific community is FORTRAN. Recently, C++ and C have increased in popularity over FORTRAN. Due to the wealth of legacy code in FORTRAN and its simpler syntax, the scientific computing community has been slow in completely adopting C++ as the lingua franca. Because of its very natural way of expressing mathematical computations, and its built-in visualization capacities, the proprietary language/environment MATLAB is also widely used, especially for rapid application development and model verification. Python along with external libraries (such as NumPy, SciPy, Matplotlib) has gained some popularity as a free and Copycenter alternative to MATLAB.
== Open Source Movement ==
There are a number of Free and Open-Source Software (FOSS) tools that support Computational Engineering.
OpenSCAD was released in 2010 and allows the scripted generation of CAD models, which can form the basis for Computational Engineering Models.
CadQuery uses Python to generate CAD models and is based on the OpenCascade framework. It is released under the Apache 2.0 Open-Source License.
PicoGKis an open-source framework for Computational Engineering which was released under the Apache 2.0 Open-Source License.
== Applications ==
Computational Engineering finds diverse applications, including in:
Aerospace Engineering and Mechanical Engineering: combustion simulations, structural dynamics, computational fluid dynamics, computational thermodynamics, computational solid mechanics, vehicle crash simulation, biomechanics, trajectory calculation of satellites
Astrophysical systems
Battlefield simulations and military gaming, homeland security, emergency response
Biology and Medicine: protein folding simulations (and other macromolecules), bioinformatics, genomics, computational neurological modeling, modeling of biological systems (e.g., ecological systems), 3D CT ultrasound, MRI imaging, molecular bionetworks, cancer and seizure control
Chemistry: calculating the structures and properties of chemical compounds/molecules and solids, computational chemistry/cheminformatics, molecular mechanics simulations, computational chemical methods in solid state physics, chemical pollution transport
Civil Engineering: finite element analysis, structures with random loads, construction engineering, water supply systems, transportation/vehicle modeling
Computer Engineering, Electrical Engineering, and Telecommunications: VLSI, computational electromagnetics, semiconductor modeling, simulation of microelectronics, energy infrastructure, RF simulation, networks
Epidemiology: influenza spread
Environmental Engineering and Numerical weather prediction: climate research, Computational geophysics (seismic processing), modeling of natural disasters
Finance: derivative pricing, risk management
Industrial Engineering: discrete event and Monte-Carlo simulations (for logistics and manufacturing systems for example), queueing networks, mathematical optimization
Material Science: glass manufacturing, polymers, and crystals
Nuclear Engineering: nuclear reactor modeling, radiation shielding simulations, fusion simulations
Petroleum engineering: petroleum reservoir modeling, oil and gas exploration
Physics: Computational particle physics, automatic calculation of particle interaction or decay, plasma modeling, cosmological simulations
Transportation
== See also ==
Applied mathematics
Computational science
Computational mathematics
Computational fluid dynamics
Computational electromagnetics
Engineering mathematics
High-performance computing
Grand Challenges
List of computer-aided engineering software
List of open-source engineering software
Numerical analysis
Modeling and simulation
Multiphysics
== References ==
== External links ==
Oden Institute for Computational Engineering and Sciences
Scope of Computational engineering
Society of Industrial and Applied Mathematics
International Centre for Computational Engineering (IC2E)
Georgia Institute of Technology, USA, MS/PhD Programme Computational Science & Engineering
The graduate program for the University of Tennessee at Chattanooga
Master and PhD Program in Computational Modeling at Rio de Janeiro State University
Computational Science and Engineering with Scilab
Internacional Center for Numerical Methods in Engineering (CIMNE) | Wikipedia/Computational_science_and_engineering |
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter.
A definite integral computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an antiderivative, a function whose derivative is the given function; in this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides a method to compute the definite integral of a function when its antiderivative is known; differentiation and integration are inverse operations.
Although methods of calculating areas and volumes dated from ancient Greek mathematics, the principles of integration were formulated independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, who thought of the area under a curve as an infinite sum of rectangles of infinitesimal width. Bernhard Riemann later gave a rigorous definition of integrals, which is based on a limiting procedure that approximates the area of a curvilinear region by breaking the region into infinitesimally thin vertical slabs. In the early 20th century, Henri Lebesgue generalized Riemann's formulation by introducing what is now referred to as the Lebesgue integral; it is more general than Riemann's in the sense that a wider class of functions are Lebesgue-integrable.
Integrals may be generalized depending on the type of the function as well as the domain over which the integration is performed. For example, a line integral is defined for functions of two or more variables, and the interval of integration is replaced by a curve connecting two points in space. In a surface integral, the curve is replaced by a piece of a surface in three-dimensional space.
== History ==
=== Pre-calculus integration ===
The first documented systematic technique capable of determining integrals is the method of exhaustion of the ancient Greek astronomer Eudoxus and philosopher Democritus (ca. 370 BC), which sought to find areas and volumes by breaking them up into an infinite number of divisions for which the area or volume was known. This method was further developed and employed by Archimedes in the 3rd century BC and used to calculate the area of a circle, the surface area and volume of a sphere, area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.
A similar method was independently developed in China around the 3rd century AD by Liu Hui, who used it to find the area of the circle. This method was later used in the 5th century by Chinese father-and-son mathematicians Zu Chongzhi and Zu Geng to find the volume of a sphere.
In the Middle East, Hasan Ibn al-Haytham, Latinized as Alhazen (c. 965 – c. 1040 AD) derived a formula for the sum of fourth powers. Alhazen determined the equations to calculate the area enclosed by the curve represented by
y
=
x
k
{\displaystyle y=x^{k}}
(which translates to the integral
∫
x
k
d
x
{\displaystyle \int x^{k}\,dx}
in contemporary notation), for any given non-negative integer value of
k
{\displaystyle k}
. He used the results to carry out what would now be called an integration of this function, where the formulae for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid.
The next significant advances in integral calculus did not begin to appear until the 17th century. At this time, the work of Cavalieri with his method of indivisibles, and work by Fermat, began to lay the foundations of modern calculus, with Cavalieri computing the integrals of xn up to degree n = 9 in Cavalieri's quadrature formula. The case n = −1 required the invention of a function, the hyperbolic logarithm, achieved by quadrature of the hyperbola in 1647.
Further steps were made in the early 17th century by Barrow and Torricelli, who provided the first hints of a connection between integration and differentiation. Barrow provided the first proof of the fundamental theorem of calculus. Wallis generalized Cavalieri's method, computing integrals of x to a general power, including negative powers and fractional powers.
=== Leibniz and Newton ===
The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton. The theorem demonstrates a connection between integration and differentiation. This connection, combined with the comparative ease of differentiation, can be exploited to calculate integrals. In particular, the fundamental theorem of calculus allows one to solve a much broader class of problems. Equal in importance is the comprehensive mathematical framework that both Leibniz and Newton developed. Given the name infinitesimal calculus, it allowed for precise analysis of functions with continuous domains. This framework eventually became modern calculus, whose notation for integrals is drawn directly from the work of Leibniz.
=== Formalization ===
While Newton and Leibniz provided a systematic approach to integration, their work lacked a degree of rigour. Bishop Berkeley memorably attacked the vanishing increments used by Newton, calling them "ghosts of departed quantities". Calculus acquired a firmer footing with the development of limits. Integration was first rigorously formalized, using limits, by Riemann. Although all bounded piecewise continuous functions are Riemann-integrable on a bounded interval, subsequently more general functions were considered—particularly in the context of Fourier analysis—to which Riemann's definition does not apply, and Lebesgue formulated a different definition of integral, founded in measure theory (a subfield of real analysis). Other definitions of integral, extending Riemann's and Lebesgue's approaches, were proposed. These approaches based on the real number system are the ones most common today, but alternative approaches exist, such as a definition of integral as the standard part of an infinite Riemann sum, based on the hyperreal number system.
=== Historical notation ===
The notation for the indefinite integral was introduced by Gottfried Wilhelm Leibniz in 1675. He adapted the integral symbol, ∫, from the letter ſ (long s), standing for summa (written as ſumma; Latin for "sum" or "total"). The modern notation for the definite integral, with limits above and below the integral sign, was first used by Joseph Fourier in Mémoires of the French Academy around 1819–1820, reprinted in his book of 1822.
Isaac Newton used a small vertical bar above a variable to indicate integration, or placed the variable inside a box. The vertical bar was easily confused with .x or x′, which are used to indicate differentiation, and the box notation was difficult for printers to reproduce, so these notations were not widely adopted.
=== First use of the term ===
The term was first printed in Latin by Jacob Bernoulli in 1690: "Ergo et horum Integralia aequantur".
== Terminology and notation ==
In general, the integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is written as
∫
a
b
f
(
x
)
d
x
.
{\displaystyle \int _{a}^{b}f(x)\,dx.}
The integral sign ∫ represents integration. The symbol dx, called the differential of the variable x, indicates that the variable of integration is x. The function f(x) is called the integrand, the points a and b are called the limits (or bounds) of integration, and the integral is said to be over the interval [a, b], called the interval of integration.
A function is said to be integrable if its integral over its domain is finite. If limits are specified, the integral is called a definite integral.
When the limits are omitted, as in
∫
f
(
x
)
d
x
,
{\displaystyle \int f(x)\,dx,}
the integral is called an indefinite integral, which represents a class of functions (the antiderivative) whose derivative is the integrand. The fundamental theorem of calculus relates the evaluation of definite integrals to indefinite integrals. There are several extensions of the notation for integrals to encompass integration on unbounded domains and/or in multiple dimensions (see later sections of this article).
In advanced settings, it is not uncommon to leave out dx when only the simple Riemann integral is being used, or the exact type of integral is immaterial. For instance, one might write
∫
a
b
(
c
1
f
+
c
2
g
)
=
c
1
∫
a
b
f
+
c
2
∫
a
b
g
{\textstyle \int _{a}^{b}(c_{1}f+c_{2}g)=c_{1}\int _{a}^{b}f+c_{2}\int _{a}^{b}g}
to express the linearity of the integral, a property shared by the Riemann integral and all generalizations thereof.
== Interpretations ==
Integrals appear in many practical situations. For instance, from the length, width and depth of a swimming pool which is rectangular with a flat bottom, one can determine the volume of water it can contain, the area of its surface, and the length of its edge. But if it is oval with a rounded bottom, integrals are required to find exact and rigorous values for these quantities. In each case, one may divide the sought quantity into infinitely many infinitesimal pieces, then sum the pieces to achieve an accurate approximation.
As another example, to find the area of the region bounded by the graph of the function f(x) =
x
{\textstyle {\sqrt {x}}}
between x = 0 and x = 1, one can divide the interval into five pieces (0, 1/5, 2/5, ..., 1), then construct rectangles using the right end height of each piece (thus √0, √1/5, √2/5, ..., √1) and sum their areas to get the approximation
1
5
(
1
5
−
0
)
+
2
5
(
2
5
−
1
5
)
+
⋯
+
5
5
(
5
5
−
4
5
)
≈
0.7497
,
{\displaystyle \textstyle {\sqrt {\frac {1}{5}}}\left({\frac {1}{5}}-0\right)+{\sqrt {\frac {2}{5}}}\left({\frac {2}{5}}-{\frac {1}{5}}\right)+\cdots +{\sqrt {\frac {5}{5}}}\left({\frac {5}{5}}-{\frac {4}{5}}\right)\approx 0.7497,}
which is larger than the exact value. Alternatively, when replacing these subintervals by ones with the left end height of each piece, the approximation one gets is too low: with twelve such subintervals the approximated area is only 0.6203. However, when the number of pieces increases to infinity, it will reach a limit which is the exact value of the area sought (in this case, 2/3). One writes
∫
0
1
x
d
x
=
2
3
,
{\displaystyle \int _{0}^{1}{\sqrt {x}}\,dx={\frac {2}{3}},}
which means 2/3 is the result of a weighted sum of function values, √x, multiplied by the infinitesimal step widths, denoted by dx, on the interval [0, 1].
== Formal definitions ==
There are many ways of formally defining an integral, not all of which are equivalent. The differences exist mostly to deal with differing special cases which may not be integrable under other definitions, but are also occasionally for pedagogical reasons. The most commonly used definitions are Riemann integrals and Lebesgue integrals.
=== Riemann integral ===
The Riemann integral is defined in terms of Riemann sums of functions with respect to tagged partitions of an interval. A tagged partition of a closed interval [a, b] on the real line is a finite sequence
a
=
x
0
≤
t
1
≤
x
1
≤
t
2
≤
x
2
≤
⋯
≤
x
n
−
1
≤
t
n
≤
x
n
=
b
.
{\displaystyle a=x_{0}\leq t_{1}\leq x_{1}\leq t_{2}\leq x_{2}\leq \cdots \leq x_{n-1}\leq t_{n}\leq x_{n}=b.\,\!}
This partitions the interval [a, b] into n sub-intervals [xi−1, xi] indexed by i, each of which is "tagged" with a specific point ti ∈ [xi−1, xi]. A Riemann sum of a function f with respect to such a tagged partition is defined as
∑
i
=
1
n
f
(
t
i
)
Δ
i
;
{\displaystyle \sum _{i=1}^{n}f(t_{i})\,\Delta _{i};}
thus each term of the sum is the area of a rectangle with height equal to the function value at the chosen point of the given sub-interval, and width the same as the width of sub-interval, Δi = xi−xi−1. The mesh of such a tagged partition is the width of the largest sub-interval formed by the partition, maxi=1...n Δi. The Riemann integral of a function f over the interval [a, b] is equal to S if:
For all
ε
>
0
{\displaystyle \varepsilon >0}
there exists
δ
>
0
{\displaystyle \delta >0}
such that, for any tagged partition
[
a
,
b
]
{\displaystyle [a,b]}
with mesh less than
δ
{\displaystyle \delta }
,
|
S
−
∑
i
=
1
n
f
(
t
i
)
Δ
i
|
<
ε
.
{\displaystyle \left|S-\sum _{i=1}^{n}f(t_{i})\,\Delta _{i}\right|<\varepsilon .}
When the chosen tags are the maximum (respectively, minimum) value of the function in each interval, the Riemann sum becomes an upper (respectively, lower) Darboux sum, suggesting the close connection between the Riemann integral and the Darboux integral.
=== Lebesgue integral ===
It is often of interest, both in theory and applications, to be able to pass to the limit under the integral. For instance, a sequence of functions can frequently be constructed that approximate, in a suitable sense, the solution to a problem. Then the integral of the solution function should be the limit of the integrals of the approximations. However, many functions that can be obtained as limits are not Riemann-integrable, and so such limit theorems do not hold with the Riemann integral. Therefore, it is of great importance to have a definition of the integral that allows a wider class of functions to be integrated.
Such an integral is the Lebesgue integral, that exploits the following fact to enlarge the class of integrable functions: if the values of a function are rearranged over the domain, the integral of a function should remain the same. Thus Henri Lebesgue introduced the integral bearing his name, explaining this integral thus in a letter to Paul Montel:
I have to pay a certain sum, which I have collected in my pocket. I take the bills and coins out of my pocket and give them to the creditor in the order I find them until I have reached the total sum. This is the Riemann integral. But I can proceed differently. After I have taken all the money out of my pocket I order the bills and coins according to identical values and then I pay the several heaps one after the other to the creditor. This is my integral.
As Folland puts it, "To compute the Riemann integral of f, one partitions the domain [a, b] into subintervals", while in the Lebesgue integral, "one is in effect partitioning the range of f ". The definition of the Lebesgue integral thus begins with a measure, μ. In the simplest case, the Lebesgue measure μ(A) of an interval A = [a, b] is its width, b − a, so that the Lebesgue integral agrees with the (proper) Riemann integral when both exist. In more complicated cases, the sets being measured can be highly fragmented, with no continuity and no resemblance to intervals.
Using the "partitioning the range of f " philosophy, the integral of a non-negative function f : R → R should be the sum over t of the areas between a thin horizontal strip between y = t and y = t + dt. This area is just μ{ x : f(x) > t} dt. Let f∗(t) = μ{ x : f(x) > t }. The Lebesgue integral of f is then defined by
∫
f
=
∫
0
∞
f
∗
(
t
)
d
t
{\displaystyle \int f=\int _{0}^{\infty }f^{*}(t)\,dt}
where the integral on the right is an ordinary improper Riemann integral (f∗ is a strictly decreasing positive function, and therefore has a well-defined improper Riemann integral). For a suitable class of functions (the measurable functions) this defines the Lebesgue integral.
A general measurable function f is Lebesgue-integrable if the sum of the absolute values of the areas of the regions between the graph of f and the x-axis is finite:
∫
E
|
f
|
d
μ
<
+
∞
.
{\displaystyle \int _{E}|f|\,d\mu <+\infty .}
In that case, the integral is, as in the Riemannian case, the difference between the area above the x-axis and the area below the x-axis:
∫
E
f
d
μ
=
∫
E
f
+
d
μ
−
∫
E
f
−
d
μ
{\displaystyle \int _{E}f\,d\mu =\int _{E}f^{+}\,d\mu -\int _{E}f^{-}\,d\mu }
where
f
+
(
x
)
=
max
{
f
(
x
)
,
0
}
=
{
f
(
x
)
,
if
f
(
x
)
>
0
,
0
,
otherwise,
f
−
(
x
)
=
max
{
−
f
(
x
)
,
0
}
=
{
−
f
(
x
)
,
if
f
(
x
)
<
0
,
0
,
otherwise.
{\displaystyle {\begin{alignedat}{3}&f^{+}(x)&&{}={}\max\{f(x),0\}&&{}={}{\begin{cases}f(x),&{\text{if }}f(x)>0,\\0,&{\text{otherwise,}}\end{cases}}\\&f^{-}(x)&&{}={}\max\{-f(x),0\}&&{}={}{\begin{cases}-f(x),&{\text{if }}f(x)<0,\\0,&{\text{otherwise.}}\end{cases}}\end{alignedat}}}
=== Other integrals ===
Although the Riemann and Lebesgue integrals are the most widely used definitions of the integral, a number of others exist, including:
The Darboux integral, which is defined by Darboux sums (restricted Riemann sums) yet is equivalent to the Riemann integral. A function is Darboux-integrable if and only if it is Riemann-integrable. Darboux integrals have the advantage of being easier to define than Riemann integrals.
The Riemann–Stieltjes integral, an extension of the Riemann integral which integrates with respect to a function as opposed to a variable.
The Lebesgue–Stieltjes integral, further developed by Johann Radon, which generalizes both the Riemann–Stieltjes and Lebesgue integrals.
The Daniell integral, which subsumes the Lebesgue integral and Lebesgue–Stieltjes integral without depending on measures.
The Haar integral, used for integration on locally compact topological groups, introduced by Alfréd Haar in 1933.
The Henstock–Kurzweil integral, variously defined by Arnaud Denjoy, Oskar Perron, and (most elegantly, as the gauge integral) Jaroslav Kurzweil, and developed by Ralph Henstock.
The Khinchin integral, named after Aleksandr Khinchin.
The Itô integral and Stratonovich integral, which define integration with respect to semimartingales such as Brownian motion.
The Young integral, which is a kind of Riemann–Stieltjes integral with respect to certain functions of unbounded variation.
The rough path integral, which is defined for functions equipped with some additional "rough path" structure and generalizes stochastic integration against both semimartingales and processes such as the fractional Brownian motion.
The Choquet integral, a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953.
The Bochner integral, a generalization of the Lebesgue integral to functions that take values in a Banach space.
== Properties ==
=== Linearity ===
The collection of Riemann-integrable functions on a closed interval [a, b] forms a vector space under the operations of pointwise addition and multiplication by a scalar, and the operation of integration
f
↦
∫
a
b
f
(
x
)
d
x
{\displaystyle f\mapsto \int _{a}^{b}f(x)\;dx}
is a linear functional on this vector space. Thus, the collection of integrable functions is closed under taking linear combinations, and the integral of a linear combination is the linear combination of the integrals:
∫
a
b
(
α
f
+
β
g
)
(
x
)
d
x
=
α
∫
a
b
f
(
x
)
d
x
+
β
∫
a
b
g
(
x
)
d
x
.
{\displaystyle \int _{a}^{b}(\alpha f+\beta g)(x)\,dx=\alpha \int _{a}^{b}f(x)\,dx+\beta \int _{a}^{b}g(x)\,dx.\,}
Similarly, the set of real-valued Lebesgue-integrable functions on a given measure space E with measure μ is closed under taking linear combinations and hence form a vector space, and the Lebesgue integral
f
↦
∫
E
f
d
μ
{\displaystyle f\mapsto \int _{E}f\,d\mu }
is a linear functional on this vector space, so that:
∫
E
(
α
f
+
β
g
)
d
μ
=
α
∫
E
f
d
μ
+
β
∫
E
g
d
μ
.
{\displaystyle \int _{E}(\alpha f+\beta g)\,d\mu =\alpha \int _{E}f\,d\mu +\beta \int _{E}g\,d\mu .}
More generally, consider the vector space of all measurable functions on a measure space (E,μ), taking values in a locally compact complete topological vector space V over a locally compact topological field K, f : E → V. Then one may define an abstract integration map assigning to each function f an element of V or the symbol ∞,
f
↦
∫
E
f
d
μ
,
{\displaystyle f\mapsto \int _{E}f\,d\mu ,\,}
that is compatible with linear combinations. In this situation, the linearity holds for the subspace of functions whose integral is an element of V (i.e. "finite"). The most important special cases arise when K is R, C, or a finite extension of the field Qp of p-adic numbers, and V is a finite-dimensional vector space over K, and when K = C and V is a complex Hilbert space.
Linearity, together with some natural continuity properties and normalization for a certain class of "simple" functions, may be used to give an alternative definition of the integral. This is the approach of Daniell for the case of real-valued functions on a set X, generalized by Nicolas Bourbaki to functions with values in a locally compact topological vector space. See Hildebrandt 1953 for an axiomatic characterization of the integral.
=== Inequalities ===
A number of general inequalities hold for Riemann-integrable functions defined on a closed and bounded interval [a, b] and can be generalized to other notions of integral (Lebesgue and Daniell).
Upper and lower bounds. An integrable function f on [a, b], is necessarily bounded on that interval. Thus there are real numbers m and M so that m ≤ f (x) ≤ M for all x in [a, b]. Since the lower and upper sums of f over [a, b] are therefore bounded by, respectively, m(b − a) and M(b − a), it follows that
m
(
b
−
a
)
≤
∫
a
b
f
(
x
)
d
x
≤
M
(
b
−
a
)
.
{\displaystyle m(b-a)\leq \int _{a}^{b}f(x)\,dx\leq M(b-a).}
Inequalities between functions. If f(x) ≤ g(x) for each x in [a, b] then each of the upper and lower sums of f is bounded above by the upper and lower sums, respectively, of g. Thus
∫
a
b
f
(
x
)
d
x
≤
∫
a
b
g
(
x
)
d
x
.
{\displaystyle \int _{a}^{b}f(x)\,dx\leq \int _{a}^{b}g(x)\,dx.}
This is a generalization of the above inequalities, as M(b − a) is the integral of the constant function with value M over [a, b]. In addition, if the inequality between functions is strict, then the inequality between integrals is also strict. That is, if f(x) < g(x) for each x in [a, b], then
∫
a
b
f
(
x
)
d
x
<
∫
a
b
g
(
x
)
d
x
.
{\displaystyle \int _{a}^{b}f(x)\,dx<\int _{a}^{b}g(x)\,dx.}
Subintervals. If [c, d] is a subinterval of [a, b] and f (x) is non-negative for all x, then
∫
c
d
f
(
x
)
d
x
≤
∫
a
b
f
(
x
)
d
x
.
{\displaystyle \int _{c}^{d}f(x)\,dx\leq \int _{a}^{b}f(x)\,dx.}
Products and absolute values of functions. If f and g are two functions, then we may consider their pointwise products and powers, and absolute values:
(
f
g
)
(
x
)
=
f
(
x
)
g
(
x
)
,
f
2
(
x
)
=
(
f
(
x
)
)
2
,
|
f
|
(
x
)
=
|
f
(
x
)
|
.
{\displaystyle (fg)(x)=f(x)g(x),\;f^{2}(x)=(f(x))^{2},\;|f|(x)=|f(x)|.}
If f is Riemann-integrable on [a, b] then the same is true for |f|, and
|
∫
a
b
f
(
x
)
d
x
|
≤
∫
a
b
|
f
(
x
)
|
d
x
.
{\displaystyle \left|\int _{a}^{b}f(x)\,dx\right|\leq \int _{a}^{b}|f(x)|\,dx.}
Moreover, if f and g are both Riemann-integrable then fg is also Riemann-integrable, and
(
∫
a
b
(
f
g
)
(
x
)
d
x
)
2
≤
(
∫
a
b
f
(
x
)
2
d
x
)
(
∫
a
b
g
(
x
)
2
d
x
)
.
{\displaystyle \left(\int _{a}^{b}(fg)(x)\,dx\right)^{2}\leq \left(\int _{a}^{b}f(x)^{2}\,dx\right)\left(\int _{a}^{b}g(x)^{2}\,dx\right).}
This inequality, known as the Cauchy–Schwarz inequality, plays a prominent role in Hilbert space theory, where the left hand side is interpreted as the inner product of two square-integrable functions f and g on the interval [a, b].
Hölder's inequality. Suppose that p and q are two real numbers, 1 ≤ p, q ≤ ∞ with 1/p + 1/q = 1, and f and g are two Riemann-integrable functions. Then the functions |f|p and |g|q are also integrable and the following Hölder's inequality holds:
|
∫
f
(
x
)
g
(
x
)
d
x
|
≤
(
∫
|
f
(
x
)
|
p
d
x
)
1
/
p
(
∫
|
g
(
x
)
|
q
d
x
)
1
/
q
.
{\displaystyle \left|\int f(x)g(x)\,dx\right|\leq \left(\int \left|f(x)\right|^{p}\,dx\right)^{1/p}\left(\int \left|g(x)\right|^{q}\,dx\right)^{1/q}.}
For p = q = 2, Hölder's inequality becomes the Cauchy–Schwarz inequality.
Minkowski inequality. Suppose that p ≥ 1 is a real number and f and g are Riemann-integrable functions. Then | f |p, | g |p and | f + g |p are also Riemann-integrable and the following Minkowski inequality holds:
(
∫
|
f
(
x
)
+
g
(
x
)
|
p
d
x
)
1
/
p
≤
(
∫
|
f
(
x
)
|
p
d
x
)
1
/
p
+
(
∫
|
g
(
x
)
|
p
d
x
)
1
/
p
.
{\displaystyle \left(\int \left|f(x)+g(x)\right|^{p}\,dx\right)^{1/p}\leq \left(\int \left|f(x)\right|^{p}\,dx\right)^{1/p}+\left(\int \left|g(x)\right|^{p}\,dx\right)^{1/p}.}
An analogue of this inequality for Lebesgue integral is used in construction of Lp spaces.
=== Conventions ===
In this section, f is a real-valued Riemann-integrable function. The integral
∫
a
b
f
(
x
)
d
x
{\displaystyle \int _{a}^{b}f(x)\,dx}
over an interval [a, b] is defined if a < b. This means that the upper and lower sums of the function f are evaluated on a partition a = x0 ≤ x1 ≤ . . . ≤ xn = b whose values xi are increasing. Geometrically, this signifies that integration takes place "left to right", evaluating f within intervals [x i , x i +1] where an interval with a higher index lies to the right of one with a lower index. The values a and b, the end-points of the interval, are called the limits of integration of f. Integrals can also be defined if a > b:
∫
a
b
f
(
x
)
d
x
=
−
∫
b
a
f
(
x
)
d
x
.
{\displaystyle \int _{a}^{b}f(x)\,dx=-\int _{b}^{a}f(x)\,dx.}
With a = b, this implies:
∫
a
a
f
(
x
)
d
x
=
0.
{\displaystyle \int _{a}^{a}f(x)\,dx=0.}
The first convention is necessary in consideration of taking integrals over subintervals of [a, b]; the second says that an integral taken over a degenerate interval, or a point, should be zero. One reason for the first convention is that the integrability of f on an interval [a, b] implies that f is integrable on any subinterval [c, d], but in particular integrals have the property that if c is any element of [a, b], then:
∫
a
b
f
(
x
)
d
x
=
∫
a
c
f
(
x
)
d
x
+
∫
c
b
f
(
x
)
d
x
.
{\displaystyle \int _{a}^{b}f(x)\,dx=\int _{a}^{c}f(x)\,dx+\int _{c}^{b}f(x)\,dx.}
With the first convention, the resulting relation
∫
a
c
f
(
x
)
d
x
=
∫
a
b
f
(
x
)
d
x
−
∫
c
b
f
(
x
)
d
x
=
∫
a
b
f
(
x
)
d
x
+
∫
b
c
f
(
x
)
d
x
{\displaystyle {\begin{aligned}\int _{a}^{c}f(x)\,dx&{}=\int _{a}^{b}f(x)\,dx-\int _{c}^{b}f(x)\,dx\\&{}=\int _{a}^{b}f(x)\,dx+\int _{b}^{c}f(x)\,dx\end{aligned}}}
is then well-defined for any cyclic permutation of a, b, and c.
== Fundamental theorem of calculus ==
The fundamental theorem of calculus is the statement that differentiation and integration are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieved. An important consequence, sometimes called the second fundamental theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated.
=== First theorem ===
Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for all x in [a, b], by
F
(
x
)
=
∫
a
x
f
(
t
)
d
t
.
{\displaystyle F(x)=\int _{a}^{x}f(t)\,dt.}
Then, F is continuous on [a, b], differentiable on the open interval (a, b), and
F
′
(
x
)
=
f
(
x
)
{\displaystyle F'(x)=f(x)}
for all x in (a, b).
=== Second theorem ===
Let f be a real-valued function defined on a closed interval [a, b] that admits an antiderivative F on [a, b]. That is, f and F are functions such that for all x in [a, b],
f
(
x
)
=
F
′
(
x
)
.
{\displaystyle f(x)=F'(x).}
If f is integrable on [a, b] then
∫
a
b
f
(
x
)
d
x
=
F
(
b
)
−
F
(
a
)
.
{\displaystyle \int _{a}^{b}f(x)\,dx=F(b)-F(a).}
== Extensions ==
=== Improper integrals ===
A "proper" Riemann integral assumes the integrand is defined and finite on a closed and bounded interval, bracketed by the limits of integration. An improper integral occurs when one or more of these conditions is not satisfied. In some cases such integrals may be defined by considering the limit of a sequence of proper Riemann integrals on progressively larger intervals.
If the interval is unbounded, for instance at its upper end, then the improper integral is the limit as that endpoint goes to infinity:
∫
a
∞
f
(
x
)
d
x
=
lim
b
→
∞
∫
a
b
f
(
x
)
d
x
.
{\displaystyle \int _{a}^{\infty }f(x)\,dx=\lim _{b\to \infty }\int _{a}^{b}f(x)\,dx.}
If the integrand is only defined or finite on a half-open interval, for instance (a, b], then again a limit may provide a finite result:
∫
a
b
f
(
x
)
d
x
=
lim
ε
→
0
∫
a
+
ϵ
b
f
(
x
)
d
x
.
{\displaystyle \int _{a}^{b}f(x)\,dx=\lim _{\varepsilon \to 0}\int _{a+\epsilon }^{b}f(x)\,dx.}
That is, the improper integral is the limit of proper integrals as one endpoint of the interval of integration approaches either a specified real number, or ∞, or −∞. In more complicated cases, limits are required at both endpoints, or at interior points.
=== Multiple integration ===
Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function and the plane that contains its domain. For example, a function in two dimensions depends on two real variables, x and y, and the integral of a function f over the rectangle R given as the Cartesian product of two intervals
R
=
[
a
,
b
]
×
[
c
,
d
]
{\displaystyle R=[a,b]\times [c,d]}
can be written
∫
R
f
(
x
,
y
)
d
A
{\displaystyle \int _{R}f(x,y)\,dA}
where the differential dA indicates that integration is taken with respect to area. This double integral can be defined using Riemann sums, and represents the (signed) volume under the graph of z = f(x,y) over the domain R. Under suitable conditions (e.g., if f is continuous), Fubini's theorem states that this integral can be expressed as an equivalent iterated integral
∫
a
b
[
∫
c
d
f
(
x
,
y
)
d
y
]
d
x
.
{\displaystyle \int _{a}^{b}\left[\int _{c}^{d}f(x,y)\,dy\right]\,dx.}
This reduces the problem of computing a double integral to computing one-dimensional integrals. Because of this, another notation for the integral over R uses a double integral sign:
∬
R
f
(
x
,
y
)
d
A
.
{\displaystyle \iint _{R}f(x,y)\,dA.}
Integration over more general domains is possible. The integral of a function f, with respect to volume, over an n-dimensional region D of
R
n
{\displaystyle \mathbb {R} ^{n}}
is denoted by symbols such as:
∫
D
f
(
x
)
d
n
x
=
∫
D
f
d
V
.
{\displaystyle \int _{D}f(\mathbf {x} )d^{n}\mathbf {x} \ =\int _{D}f\,dV.}
=== Line integrals and surface integrals ===
The concept of an integral can be extended to more general domains of integration, such as curved lines and surfaces inside higher-dimensional spaces. Such integrals are known as line integrals and surface integrals respectively. These have important applications in physics, as when dealing with vector fields.
A line integral (sometimes called a path integral) is an integral where the function to be integrated is evaluated along a curve. Various different line integrals are in use. In the case of a closed curve it is also called a contour integral.
The function to be integrated may be a scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes the line integral from simpler integrals defined on intervals. Many simple formulas in physics have natural continuous analogs in terms of line integrals; for example, the fact that work is equal to force, F, multiplied by displacement, s, may be expressed (in terms of vector quantities) as:
W
=
F
⋅
s
.
{\displaystyle W=\mathbf {F} \cdot \mathbf {s} .}
For an object moving along a path C in a vector field F such as an electric field or gravitational field, the total work done by the field on the object is obtained by summing up the differential work done in moving from s to s + ds. This gives the line integral
W
=
∫
C
F
⋅
d
s
.
{\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {s} .}
A surface integral generalizes double integrals to integration over a surface (which may be a curved set in space); it can be thought of as the double integral analog of the line integral. The function to be integrated may be a scalar field or a vector field. The value of the surface integral is the sum of the field at all points on the surface. This can be achieved by splitting the surface into surface elements, which provide the partitioning for Riemann sums.
For an example of applications of surface integrals, consider a vector field v on a surface S; that is, for each point x in S, v(x) is a vector. Imagine that a fluid flows through S, such that v(x) determines the velocity of the fluid at x. The flux is defined as the quantity of fluid flowing through S in unit amount of time. To find the flux, one need to take the dot product of v with the unit surface normal to S at each point, which will give a scalar field, which is integrated over the surface:
∫
S
v
⋅
d
S
.
{\displaystyle \int _{S}{\mathbf {v} }\cdot \,d{\mathbf {S} }.}
The fluid flux in this example may be from a physical fluid such as water or air, or from electrical or magnetic flux. Thus surface integrals have applications in physics, particularly with the classical theory of electromagnetism.
=== Contour integrals ===
In complex analysis, the integrand is a complex-valued function of a complex variable z instead of a real function of a real variable x. When a complex function is integrated along a curve
γ
{\displaystyle \gamma }
in the complex plane, the integral is denoted as follows
∫
γ
f
(
z
)
d
z
.
{\displaystyle \int _{\gamma }f(z)\,dz.}
This is known as a contour integral.
=== Integrals of differential forms ===
A differential form is a mathematical concept in the fields of multivariable calculus, differential topology, and tensors. Differential forms are organized by degree. For example, a one-form is a weighted sum of the differentials of the coordinates, such as:
E
(
x
,
y
,
z
)
d
x
+
F
(
x
,
y
,
z
)
d
y
+
G
(
x
,
y
,
z
)
d
z
{\displaystyle E(x,y,z)\,dx+F(x,y,z)\,dy+G(x,y,z)\,dz}
where E, F, G are functions in three dimensions. A differential one-form can be integrated over an oriented path, and the resulting integral is just another way of writing a line integral. Here the basic differentials dx, dy, dz measure infinitesimal oriented lengths parallel to the three coordinate axes.
A differential two-form is a sum of the form
G
(
x
,
y
,
z
)
d
x
∧
d
y
+
E
(
x
,
y
,
z
)
d
y
∧
d
z
+
F
(
x
,
y
,
z
)
d
z
∧
d
x
.
{\displaystyle G(x,y,z)\,dx\wedge dy+E(x,y,z)\,dy\wedge dz+F(x,y,z)\,dz\wedge dx.}
Here the basic two-forms
d
x
∧
d
y
,
d
z
∧
d
x
,
d
y
∧
d
z
{\displaystyle dx\wedge dy,dz\wedge dx,dy\wedge dz}
measure oriented areas parallel to the coordinate two-planes. The symbol
∧
{\displaystyle \wedge }
denotes the wedge product, which is similar to the cross product in the sense that the wedge product of two forms representing oriented lengths represents an oriented area. A two-form can be integrated over an oriented surface, and the resulting integral is equivalent to the surface integral giving the flux of
E
i
+
F
j
+
G
k
{\displaystyle E\mathbf {i} +F\mathbf {j} +G\mathbf {k} }
.
Unlike the cross product, and the three-dimensional vector calculus, the wedge product and the calculus of differential forms makes sense in arbitrary dimension and on more general manifolds (curves, surfaces, and their higher-dimensional analogs). The exterior derivative plays the role of the gradient and curl of vector calculus, and Stokes' theorem simultaneously generalizes the three theorems of vector calculus: the divergence theorem, Green's theorem, and the Kelvin-Stokes theorem.
=== Summations ===
The discrete equivalent of integration is summation. Summations and integrals can be put on the same foundations using the theory of Lebesgue integrals or time-scale calculus.
=== Functional integrals ===
An integration that is performed not over a variable (or, in physics, over a space or time dimension), but over a space of functions, is referred to as a functional integral.
== Applications ==
Integrals are used extensively in many areas. For example, in probability theory, integrals are used to determine the probability of some random variable falling within a certain range. Moreover, the integral under an entire probability density function must equal 1, which provides a test of whether a function with no negative values could be a density function or not.
Integrals can be used for computing the area of a two-dimensional region that has a curved boundary, as well as computing the volume of a three-dimensional object that has a curved boundary. The area of a two-dimensional region can be calculated using the aforementioned definite integral. The volume of a three-dimensional object such as a disc or washer can be computed by disc integration using the equation for the volume of a cylinder,
π
r
2
h
{\displaystyle \pi r^{2}h}
, where
r
{\displaystyle r}
is the radius. In the case of a simple disc created by rotating a curve about the x-axis, the radius is given by f(x), and its height is the differential dx. Using an integral with bounds a and b, the volume of the disc is equal to:
π
∫
a
b
f
2
(
x
)
d
x
.
{\displaystyle \pi \int _{a}^{b}f^{2}(x)\,dx.}
Integrals are also used in physics, in areas like kinematics to find quantities like displacement, time, and velocity. For example, in rectilinear motion, the displacement of an object over the time interval
[
a
,
b
]
{\displaystyle [a,b]}
is given by
x
(
b
)
−
x
(
a
)
=
∫
a
b
v
(
t
)
d
t
,
{\displaystyle x(b)-x(a)=\int _{a}^{b}v(t)\,dt,}
where
v
(
t
)
{\displaystyle v(t)}
is the velocity expressed as a function of time. The work done by a force
F
(
x
)
{\displaystyle F(x)}
(given as a function of position) from an initial position
A
{\displaystyle A}
to a final position
B
{\displaystyle B}
is:
W
A
→
B
=
∫
A
B
F
(
x
)
d
x
.
{\displaystyle W_{A\rightarrow B}=\int _{A}^{B}F(x)\,dx.}
Integrals are also used in thermodynamics, where thermodynamic integration is used to calculate the difference in free energy between two given states.
== Computation ==
=== Analytical ===
The most basic technique for computing definite integrals of one real variable is based on the fundamental theorem of calculus. Let f(x) be the function of x to be integrated over a given interval [a, b]. Then, find an antiderivative of f; that is, a function F such that F′ = f on the interval. Provided the integrand and integral have no singularities on the path of integration, by the fundamental theorem of calculus,
∫
a
b
f
(
x
)
d
x
=
F
(
b
)
−
F
(
a
)
.
{\displaystyle \int _{a}^{b}f(x)\,dx=F(b)-F(a).}
Sometimes it is necessary to use one of the many techniques that have been developed to evaluate integrals. Most of these techniques rewrite one integral as a different one which is hopefully more tractable. Techniques include integration by substitution, integration by parts, integration by trigonometric substitution, and integration by partial fractions.
Alternative methods exist to compute more complex integrals. Many nonelementary integrals can be expanded in a Taylor series and integrated term by term. Occasionally, the resulting infinite series can be summed analytically. The method of convolution using Meijer G-functions can also be used, assuming that the integrand can be written as a product of Meijer G-functions. There are also many less common ways of calculating definite integrals; for instance, Parseval's identity can be used to transform an integral over a rectangular region into an infinite sum. Occasionally, an integral can be evaluated by a trick; for an example of this, see Gaussian integral.
Computations of volumes of solids of revolution can usually be done with disk integration or shell integration.
Specific results which have been worked out by various techniques are collected in the list of integrals.
=== Symbolic ===
Many problems in mathematics, physics, and engineering involve integration where an explicit formula for the integral is desired. Extensive tables of integrals have been compiled and published over the years for this purpose. With the spread of computers, many professionals, educators, and students have turned to computer algebra systems that are specifically designed to perform difficult or tedious tasks, including integration. Symbolic integration has been one of the motivations for the development of the first such systems, like Macsyma and Maple.
A major mathematical difficulty in symbolic integration is that in many cases, a relatively simple function does not have integrals that can be expressed in closed form involving only elementary functions, include rational and exponential functions, logarithm, trigonometric functions and inverse trigonometric functions, and the operations of multiplication and composition. The Risch algorithm provides a general criterion to determine whether the antiderivative of an elementary function is elementary and to compute the integral if is elementary. However, functions with closed expressions of antiderivatives are the exception, and consequently, computerized algebra systems have no hope of being able to find an antiderivative for a randomly constructed elementary function. On the positive side, if the 'building blocks' for antiderivatives are fixed in advance, it may still be possible to decide whether the antiderivative of a given function can be expressed using these blocks and operations of multiplication and composition and to find the symbolic answer whenever it exists. The Risch algorithm, implemented in Mathematica, Maple and other computer algebra systems, does just that for functions and antiderivatives built from rational functions, radicals, logarithm, and exponential functions.
Some special integrands occur often enough to warrant special study. In particular, it may be useful to have, in the set of antiderivatives, the special functions (like the Legendre functions, the hypergeometric function, the gamma function, the incomplete gamma function and so on). Extending Risch's algorithm to include such functions is possible but challenging and has been an active research subject.
More recently a new approach has emerged, using D-finite functions, which are the solutions of linear differential equations with polynomial coefficients. Most of the elementary and special functions are D-finite, and the integral of a D-finite function is also a D-finite function. This provides an algorithm to express the antiderivative of a D-finite function as the solution of a differential equation. This theory also allows one to compute the definite integral of a D-function as the sum of a series given by the first coefficients and provides an algorithm to compute any coefficient.
Rule-based integration systems facilitate integration. Rubi, a computer algebra system rule-based integrator, pattern matches an extensive system of symbolic integration rules to integrate a wide variety of integrands. This system uses over 6600 integration rules to compute integrals. The method of brackets is a generalization of Ramanujan's master theorem that can be applied to a wide range of univariate and multivariate integrals. A set of rules are applied to the coefficients and exponential terms of the integrand's power series expansion to determine the integral. The method is closely related to the Mellin transform.
=== Numerical ===
Definite integrals may be approximated using several methods of numerical integration. The rectangle method relies on dividing the region under the function into a series of rectangles corresponding to function values and multiplies by the step width to find the sum. A better approach, the trapezoidal rule, replaces the rectangles used in a Riemann sum with trapezoids. The trapezoidal rule weights the first and last values by one half, then multiplies by the step width to obtain a better approximation. The idea behind the trapezoidal rule, that more accurate approximations to the function yield better approximations to the integral, can be carried further: Simpson's rule approximates the integrand by a piecewise quadratic function.
Riemann sums, the trapezoidal rule, and Simpson's rule are examples of a family of quadrature rules called the Newton–Cotes formulas. The degree n Newton–Cotes quadrature rule approximates the polynomial on each subinterval by a degree n polynomial. This polynomial is chosen to interpolate the values of the function on the interval. Higher degree Newton–Cotes approximations can be more accurate, but they require more function evaluations, and they can suffer from numerical inaccuracy due to Runge's phenomenon. One solution to this problem is Clenshaw–Curtis quadrature, in which the integrand is approximated by expanding it in terms of Chebyshev polynomials.
Romberg's method halves the step widths incrementally, giving trapezoid approximations denoted by T(h0), T(h1), and so on, where hk+1 is half of hk. For each new step size, only half the new function values need to be computed; the others carry over from the previous size. It then interpolate a polynomial through the approximations, and extrapolate to T(0). Gaussian quadrature evaluates the function at the roots of a set of orthogonal polynomials. An n-point Gaussian method is exact for polynomials of degree up to 2n − 1.
The computation of higher-dimensional integrals (for example, volume calculations) makes important use of such alternatives as Monte Carlo integration.
=== Mechanical ===
The area of an arbitrary two-dimensional shape can be determined using a measuring instrument called planimeter. The volume of irregular objects can be measured with precision by the fluid displaced as the object is submerged.
=== Geometrical ===
Area can sometimes be found via geometrical compass-and-straightedge constructions of an equivalent square.
=== Integration by differentiation ===
Kempf, Jackson and Morales demonstrated mathematical relations that allow an integral to be calculated by means of differentiation. Their calculus involves the Dirac delta function and the partial derivative operator
∂
x
{\displaystyle \partial _{x}}
. This can also be applied to functional integrals, allowing them to be computed by functional differentiation.
== Examples ==
=== Using the fundamental theorem of calculus ===
The fundamental theorem of calculus allows straightforward calculations of basic functions:
∫
0
π
sin
(
x
)
d
x
=
−
cos
(
x
)
|
x
=
0
x
=
π
=
−
cos
(
π
)
−
(
−
cos
(
0
)
)
=
2.
{\displaystyle \int _{0}^{\pi }\sin(x)\,dx=-\cos(x){\big |}_{x=0}^{x=\pi }=-\cos(\pi )-{\big (}-\cos(0){\big )}=2.}
== See also ==
Integral equation – Equations with an unknown function under an integral sign
Integral symbol – Mathematical symbol used to denote integrals and antiderivatives
Lists of integrals
== Notes ==
== References ==
== Bibliography ==
== External links ==
"Integral", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
Online Integral Calculator, Wolfram Alpha.
=== Online books ===
Keisler, H. Jerome, Elementary Calculus: An Approach Using Infinitesimals, University of Wisconsin
Stroyan, K. D., A Brief Introduction to Infinitesimal Calculus, University of Iowa
Mauch, Sean, Sean's Applied Math Book, CIT, an online textbook that includes a complete introduction to calculus
Crowell, Benjamin, Calculus, Fullerton College, an online textbook
Garrett, Paul, Notes on First-Year Calculus
Hussain, Faraz, Understanding Calculus, an online textbook
Johnson, William Woolsey (1909) Elementary Treatise on Integral Calculus, link from HathiTrust.
Kowalk, W. P., Integration Theory, University of Oldenburg. A new concept to an old problem. Online textbook
Sloughter, Dan, Difference Equations to Differential Equations, an introduction to calculus
Numerical Methods of Integration at Holistic Numerical Methods Institute
P. S. Wang, Evaluation of Definite Integrals by Symbolic Manipulation (1972) — a cookbook of definite integral techniques | Wikipedia/Methods_of_integration |
ATL (ATLAS Transformation Language) is a model transformation language and toolkit developed and maintained by OBEO and AtlanMod. It was initiated by the AtlanMod team (previously called ATLAS Group). In the field of Model-Driven Engineering (MDE), ATL provides ways to produce a set of target models from a set of source models.
Released under the terms of the Eclipse Public License, ATL is an M2M (Eclipse) component, inside of the Eclipse Modeling Project (EMP).
== Overview ==
ATL is a model transformation language (MTL) developed by OBEO and INRIA to answer the QVT Request For Proposal. QVT is an Object Management Group standard for performing model transformations. It can be used to do syntactic or semantic translation. ATL is built on top of a model transformation Virtual Machine.
ATL is the ATLAS INRIA & LINA research group answer to the OMG MOF/QVT RFP. It is a model transformation language specified both as a metamodel and as a textual concrete syntax. It is a hybrid of declarative and imperative. The preferred style of transformation writing is declarative, which means simple mappings can be expressed simply. However, imperative constructs are provided so that some mappings too complex to be declaratively handled can still be specified.
An ATL transformation program is composed of rules that define how source model elements are matched and navigated to create and initialize the elements of the target models.
== Architecture ==
A model-transformation-oriented virtual machine has been defined and implemented to provide execution support for ATL while maintaining a certain level of flexibility. As a matter of fact, ATL becomes executable simply because a specific transformation from its metamodel to the virtual machine bytecode exists. Extending ATL is therefore mainly a matter of specifying the new language features execution semantics in terms of simple instructions: basic actions on models (elements creations and properties assignments).
== Example ==
An ATL program (T1.atl here) will take model Ma.xmi as input and will produce model Mb.xmi as output. Both models may be expressed in the OMG XMI standard. The model Ma conforms to metamodel MMa.km3. Model Mb conforms to metamodel MMb.km3. The KM3 notation is a simple and neutral metamodel specification language.
The ATL program itself (T1.atl here) is also a model, so it conforms to a metamodel (the ATL metamodel) not presented here.
An ATL program is composed of a header, of a set of side-effect free functions called helpers and of a set of rules.
== Implementations ==
There is an associated ATL Development Toolkit plugin available in open source
from the ATL Eclipse Modeling Project (EMP) that implements the ATL transformation language which is inspired by the MOF Query/View/Transformation language QVT. A large library of transformations is available. MOF QVT is a Domain Specific Language for Model Transformation. It supports models conforming to Ecore, EMOF, KM3 (a specific Domain Specific Language for metamodel specification), etc. ATL is also running on MDR/NetBeans.
== See also ==
Model Driven Engineering (MDE)
Domain-specific modelling (DSM)
Model Transformation Language (MTL)
MOF Queries/Views/Transformations (QVT)
== References ==
== Further reading ==
Bohlen, M: QVT and multi metamodel transformation in MDA. Webpublished
Wagelaar, D: MDE Case Study: Using Model Transformations for UML and DSLs. Webpublished
Czarnecki, K, and Helsen, S : Classification of Model Transformation Approaches. In: Proceedings of the OOPSLA'03 Workshop on the Generative Techniques in the Context Of Model-Driven Architecture. Anaheim (CA, USA). Webpublished
ModelBaset.net. MDA Tools
SoftwareMag.com. MDA Tools. Webpublished
=== Articles ===
Model-Driven Architecture: Vision, Standards And Emerging Technologies at OMG.org
An Introduction to Model Driven Architecture at IBM.com
From Object Composition to Model Transformation with the MDA at OMG.org
Jouault, F and Kurtev, I: On the Architectural Alignment of ATL and QVT. In: Proceedings of ACM Symposium on Applied Computing (SAC 06), Model Transformation Track. Dijon (Bourgogne, FRA), April 2006. Webpublished
=== ATL Atlas model transformation language ===
Eclipse/M2M newsgroup: ATL discussion group.
Jouault, F and Kurtev, I:On the Architectural Alignment of ATL and QVT. In: Proceedings of ACM Symposium on Applied Computing (SAC 06), Model Transformation Track. Dijon (Bourgogne, FRA), April 2006. Webpublished
Eclipse : M2M/ATL is part of the new Top Level Modeling Project
=== UMT UML model transformation tool ===
Grønmo, R, and Oldevik, J : An Empirical Study of the UML Model Transformation Tool (UMT). In: INTEROP-ESA'05, Feb. 2005. Webpublished
=== Related model-driven development approaches ===
Voelter, M: Model Driven Software Development. Webpublished
Portal site MDA and Model Transformation:
== External links ==
Official website | Wikipedia/ATLAS_Transformation_Language |
Generic Eclipse Modeling System (GEMS) is a configurable toolkit for creating domain-specific modeling and program synthesis environments for Eclipse. The project aims to bridge the gap between the communities experienced with visual metamodeling tools like those built around the Eclipse modeling technologies, such as the Eclipse Modeling Framework (EMF) and Graphical Modeling Framework (GMF). GEMS helps developers rapidly create a graphical modeling tool from a visual language description or metamodel without any coding in third-generation languages. Graphical modeling tools created with GEMS automatically support complex capabilities, such as remote updating and querying, template creation, styling with Cascading Style Sheets (CSS), and model linking.
The configuration is accomplished through metamodels specifying the modeling paradigm of the application domain, i.e. a domain-specific modeling language (DSML). The modeling paradigm contains all the syntactic, semantic, and presentation information regarding the domain; which concepts will be used to construct models, what relationships may exist among those concepts, how the concepts may be organized and viewed by the modeler, and rules governing the construction of models. The modeling paradigm defines the family of models that can be created using the resultant modeling environment.
The built-in metamodeling language is based on the UML class diagram notation. Metamodels in other eCore readable formats can be used as well. Metamodel constraints can be specified in declarative languages (e.g. OCL, Prolog) or, alternatively, in Java. Once a metamodel has been created, GEMS plug-in generator can be invoked to create the modeling tool. The generated plug-in uses Eclipse's Graphical Editing Framework (GEF) and Draw2D plug-in to visualize the DSML as a diagram. GEMS extension points can be used to create an interpreter which traverses the domain-specific model and generates code. Interpreters can also interpret the model to provide executable semantics and perform complex analyses.
== References ==
== Related tools ==
GEMS EMF Intelligence Framework
== External links ==
GEMS Homepage | Wikipedia/Generic_Eclipse_Modeling_System |
Application lifecycle management (ALM) is the product lifecycle management (governance, development, and maintenance) of computer programs. It encompasses requirements management, software architecture, computer programming, software testing, software maintenance, change management, continuous integration, project management, and release management.
== ALM vs. Software Development Life Cycle ==
ALM is a broader perspective than the Software Development Life Cycle (SDLC), which is limited to the phases of software development such as requirements, design, coding, testing, configuration, project management, and change management. ALM continues after development until the application is no longer used, and may span many SDLCs.
== Integrated ALM ==
Modern software development processes are not restricted to the discrete ALM/SDLC steps managed by different teams using multiple tools from different locations. Real-time collaboration, access to the centralized data repository, cross-tool and cross-project visibility, better project monitoring and reporting are the key to developing quality software in less time.
This has given rise to the practice of integrated application lifecycle management, or integrated ALM, where all the tools and tools' users are synchronized with each other throughout the application development stages. This integration ensures that every team member knows Who, What, When, and Why of any changes made during the development process and there is no last minute surprise causing delivery delays or project failure.
Today's application management vendors focus more on API management capabilities for third party best-of-breed tool integration which ensures that organizations are well-equipped with an internal software development system that can easily integrate with any IT or ALM tools needed in a project.
A research director with research firm Gartner proposed changing the term ALM to ADLM (Application Development Life-cycle Management) to include DevOps, the software engineering culture and practice that aims at unifying software development (Dev) and software operation (Ops).
== ALM software suites ==
Some specialized software suites for ALM are:
== See also ==
Application Lifecycle Framework
Business transaction management
Open Services for Lifecycle Collaboration
Systems development life-cycle
Software project management
Comparison of project management software
Bug tracking system
Forge (software)
== References ==
== Further reading ==
Keuper, Frank; Oecking, Christian; Degenhardt, Andreas; Verlag, Gabler (2011). Application Management: Challenges - Service Creation - Strategies. ISBN 978-3-8349-1667-9.
Linnartz, Walter; Kohlhoff, Barbara; Heck, Gertrud; Schmidt, Benedikt (2004). Application Management Services und Support. Publicis Corporate Publishing. ISBN 3-89578-224-6.
"Gartner Market Scope for ALM 2010".
Hüttermann, Michael (2011). Agile Application Lifecycle Management. Manning. ISBN 978-1-935182-63-4.
== External links ==
Chappell, David, What is Application Lifecycle Management? (PDF), archived from the original (PDF) on December 7, 2014
Gartner Analyst Sean Kenefick, Market Profile: Application Life Cycle Management (ALM) Tools, 2012
Margaret Rouse, application lifecycle management (ALM)
Dave West, Integrated ALM Tools Are Fundamental to Success
Dominic Tavassoli, Integrating application lifecycle management (ALM) processes provides additional benefits
Zane Galviņa1, Darja Šmite, Software Development Processes in Globally Distributed Environment | Wikipedia/Application_lifecycle_management |
The Graphical Modeling Framework (GMF) is a framework within the Eclipse platform. It provides a generative component and runtime infrastructure for developing graphical editors based on the Eclipse Modeling Framework (EMF) and Graphical Editing Framework (GEF). The project aims to provide these components, in addition to exemplary tools for select domain models which illustrate its capabilities.
GMF was first released as part of the Eclipse 3.2 Callisto release in June 2006.
== See also ==
Connected Data Objects (CDO), a free implementation of a Distributed Shared Model on top of EMF
Model-driven architecture
Generic Eclipse Modeling System (GEMS)
Eclipse Modeling Framework (EMF)
List of EMF based software
ATL (A Model Transformation Language)
Service-Oriented Modeling Framework (SOMF)
== References ==
Rubel, Dan; Wren, Jaime; Clayberg, Eric (2012). The Eclipse Graphical Editing Framework (GEF). Addison-Wesley Professional. ISBN 978-0-321-71838-9. Retrieved 1 April 2025.
== External links ==
GMF project page | Wikipedia/Graphical_Modeling_Framework |
Model-driven architecture (MDA) is a software design approach for the development of software systems. It provides a set of guidelines for the structuring of specifications, which are expressed as models. Model Driven Architecture is a kind of domain engineering, and supports model-driven engineering of software systems. It was launched by the Object Management Group (OMG) in 2001.
== Overview ==
Model Driven Architecture® (MDA®) "provides an approach for deriving value from models and architecture in support of the full life cycle of physical, organizational and I.T. systems". A model is a (representation of) an abstraction of a system. MDA® provides value by producing models at varying levels of abstraction, from a conceptual view down to the smallest implementation detail. OMG literature speaks of three such levels of abstraction, or architectural viewpoints: the Computation-independent Model (CIM), the Platform-independent model (PIM), and the Platform-specific model (PSM). The CIM describes a system conceptually, the PIM describes the computational aspects of a system without reference to the technologies that may be used to implement it, and the PSM provides the technical details necessary to implement the system. The OMG Guide notes, though, that these three architectural viewpoints are useful, but are just three of many possible viewpoints.
The OMG organization provides specifications rather than implementations, often as answers to Requests for Proposals (RFPs). Implementations come from private companies or open source groups.
=== Related standards ===
The MDA model is related to multiple standards, including the Unified Modeling Language (UML), the Meta-Object Facility (MOF), XML Metadata Interchange (XMI), Enterprise Distributed Object Computing (EDOC), the Software Process Engineering Metamodel (SPEM), and the Common Warehouse Metamodel (CWM). Note that the term “architecture” in Model Driven Architecture does not refer to the architecture of the system being modeled, but rather to the architecture of the various standards and model forms that serve as the technology basis for MDA.
Executable UML was the UML profile used when MDA was born. Now, the OMG is promoting fUML, instead. (The action language for fUML is ALF.)
=== Trademark ===
The Object Management Group holds registered trademarks on the term Model Driven Architecture and its acronym MDA, as well as trademarks for terms such as: Model Based Application Development, Model Driven Application Development, Model Based Application Development, Model Based Programming, Model Driven Systems, and others.
== Model Driven Architecture topics ==
=== MDA approach ===
OMG focuses Model Driven Architecture® on forward engineering, i.e. producing code from abstract, human-elaborated modeling diagrams (e.g. class diagrams). OMG's ADTF (Analysis and Design Task Force) group leads this effort. With some humour, the group chose ADM (MDA backwards) to name the study of reverse engineering. ADM decodes to Architecture-Driven Modernization. The objective of ADM is to produce standards for model-based reverse engineering of legacy systems. Knowledge Discovery Metamodel (KDM) is the furthest along of these efforts, and describes information systems in terms of various assets (programs, specifications, data, test files, database schemas, etc.).
As the concepts and technologies used to realize designs and the concepts and technologies used to realize architectures have changed at their own pace, decoupling them allows system developers to choose from the best and most fitting in both domains. The design addresses the functional (use case) requirements while architecture provides the infrastructure through which non-functional requirements like scalability, reliability and performance are realized. MDA envisages that the platform independent model (PIM), which represents a conceptual design realizing the functional requirements, will survive changes in realization technologies and software architectures.
Of particular importance to Model Driven Architecture is the notion of model transformation. A specific standard language for model transformation has been defined by OMG called QVT.
=== MDA tools ===
The OMG organization provides rough specifications rather than implementations, often as answers to Requests for Proposals (RFPs). The OMG documents the overall process in a document called the MDA Guide.
Basically, an MDA tool is a tool used to develop, interpret, compare, align, measure, verify, transform, etc. models or metamodels. In the following section "model" is interpreted as meaning any kind of model (e.g. a UML model) or metamodel (e.g. the CWM metamodel). In any MDA approach we have essentially two kinds of models: initial models are created manually by human agents while derived models are created automatically by programs. For example, an analyst may create a UML initial model from its observation of some loose business situation while a Java model may be automatically derived from this UML model by a Model transformation operation.
An MDA tool may be a tool used to check models for completeness, inconsistencies, or error and warning conditions.
Some tools perform more than one of the functions listed above. For example, some creation tools may also have transformation and test capabilities. There are other tools that are solely for creation, solely for graphical presentation, solely for transformation, etc.
Implementations of the OMG specifications come from private companies or open source groups. One important source of implementations for OMG specifications is the Eclipse Foundation (EF). Many implementations of OMG modeling standards may be found in the Eclipse Modeling Framework (EMF) or Graphical Modeling Framework (GMF), the Eclipse foundation is also developing other tools of various profiles as GMT. Eclipse's compliance to OMG specifications is often not strict. This is true for example for OMG's EMOF standard, which EMF approximates with its Ecore implementation. More examples may be found in the M2M project implementing the QVT standard or in the M2T project implementing the MOF2Text standard.
One should be careful not to confuse the List of MDA Tools and the List of UML tools, the former being much broader. This distinction can be made more general by distinguishing 'variable metamodel tools' and 'fixed metamodel tools'. A UML CASE tool is typically a 'fixed metamodel tool' since it has been hard-wired to work only with a given version of the UML metamodel (e.g. UML 2.1). On the contrary, other tools have internal generic capabilities allowing them to adapt to arbitrary metamodels or to a particular kind of metamodels.
Usually MDA tools focus rudimentary architecture specification, although in some cases the tools are architecture-independent (or platform independent).
Simple examples of architecture specifications include:
Selecting one of a number of supported reference architectures like Java EE or Microsoft .NET,
Specifying the architecture at a finer level including the choice of presentation layer technology, business logic layer technology, persistence technology and persistence mapping technology (e.g. object-relational mapper).
Metadata: information about data.
=== MDA concerns ===
Some key concepts that underpin the MDA approach (launched in 2001) were first elucidated by the Shlaer–Mellor method during the late 1980s. Indeed, a key absent technical standard of the MDA approach (that of an action language syntax for Executable UML) has been bridged by some vendors by adapting the original Shlaer–Mellor Action Language (modified for UML). However, during this period the MDA approach has not gained mainstream industry acceptance; with the Gartner Group still identifying MDA as an "on the rise" technology in its 2006 "Hype Cycle", and Forrester Research declaring MDA to be "D.O.A." in 2006. Potential concerns that have been raised with the OMG MDA approach include:
Incomplete Standards: The MDA approach is underpinned by a variety of technical standards, some of which are yet to be specified (e.g. an action semantic language for xtUML), or are yet to be implemented in a standard manner (e.g. a QVT transformation engine or a PIM with a virtual execution environment).
Vendor Lock-in: Although MDA was conceived as an approach for achieving (technical) platform independence, current MDA vendors have been reluctant to engineer their MDA toolsets to be interoperable. Such an outcome could result in vendor lock-in for those pursuing an MDA approach.
Idealistic: MDA is conceived as a forward engineering approach in which models that incorporate Action Language programming are transformed into implementation artifacts (e.g. executable code, database schema) in one direction via a fully or partially automated "generation" step. This aligns with OMG's vision that MDA should allow modelling of a problem domain's full complexity in UML (and related standards) with subsequent transformation to a complete (executable) application. This approach does, however, imply that changes to implementation artifacts (e.g. database schema tuning) are not supported . This constitutes a problem in situations where such post-transformation "adapting" of implementation artifacts is seen to be necessary. Evidence that the full MDA approach may be too idealistic for some real world deployments has been seen in the rise of so-called "pragmatic MDA". Pragmatic MDA blends the literal standards from OMG's MDA with more traditional model driven approaches such as round-trip engineering that provides support for adapting implementation artifacts (though not without substantial disadvantages).
Specialised Skillsets: Practitioners of MDA based software engineering are (as with other toolsets) required to have a high level of expertise in their field. Current expert MDA practitioners (often referred to as Modeller/Architects) are scarce relative to the availability of traditional developers.
OMG Track Record: The OMG consortium who sponsor the MDA approach (and own the MDA trademark) also introduced and sponsored the CORBA standard which itself failed to materialise as a widely utilised standard.
Uncertain Value Proposition (UVP): As discussed, the vision of MDA allows for the specification of a system as an abstract model, which may be realized as a concrete implementation (program) for a particular computing platform (e.g. .NET). Thus an application that has been successfully developed via a pure MDA approach could theoretically be ported to a newer release .NET platform (or even a Java platform) in a deterministic manner – although significant questions remain as to real-world practicalities during translation (such as user interface implementation). Whether this capability represents a significant value proposition remains a question for particular adopters. Regardless, adopters of MDA who are seeking value via an "alternative to programming" should be very careful when assessing this approach. The complexity of any given problem domain will always remain, and the programming of business logic needs to be undertaken in MDA as with any other approach. The difference with MDA is that the programming language used (e.g. xtUML) is more abstract (than, say, Java or C#) and exists interwoven with traditional UML artifacts (e.g. class diagrams). Whether programming in a language that is more abstract than mainstream 3GL languages will result in systems of better quality, cheaper cost or faster delivery, is a question that has yet to be adequately answered.
MDA was recognized as a possible way to bring various independently developed standardized solutions together. For the simulation community, it was recommended as a business and industry based alternative to yet another US DoD mandated standard.
== See also ==
== References ==
== Further reading ==
Kevin Lano. "Model-Driven Software Development With UML and Java". CENGAGE Learning, ISBN 978-1-84480-952-3
David S. Frankel. Model Driven Architecture: Applying MDA to Enterprise Computing. John Wiley & Sons, ISBN 0-471-31920-1
Meghan Kiffer The MDA Journal: Model Driven Architecture Straight From The Masters. ISBN 0-929652-25-8
Anneke Kleppe (2003). MDA Explained, The Model Driven Architecture: Practice and Promise. Addison-Wesley. ISBN 0-321-19442-X
Stephen J. Mellor (2004). MDA Distilled, Principles of Model Driven Architecture. Addison-Wesley Professional. ISBN 0-201-78891-8
Chris Raistrick. Model Driven Architecture With Executable UML. Cambridge University Press, ISBN 0-521-53771-1
Marco Brambilla, Jordi Cabot, Manuel Wimmer, Model Driven Software Engineering in Practice, foreword by Richard Soley (OMG Chairman), Morgan & Claypool, USA, 2012, Synthesis Lectures on Software Engineering #1. 182 pages. ISBN 9781608458820 (paperback), ISBN 9781608458837 (ebook). http://www.mdse-book.com
Stanley J. Sewall. Executive Justification for MDA
Soylu A., De Causmaecker Patrick. Merging model driven and ontology driven system development approaches pervasive computing perspective, in Proc 24th Intl Symposium on Computer and Information Sciences. 2009, pp 730–735.
== External links ==
OMG's MDA Web site
Model-Driven Software Development Course, B. Tekinerdogan, Bilkent University | Wikipedia/Model-Driven_Architecture |
Modeling Maturity Levels is a classification system defined by Anneke Kleppe and Jos Warmer in their book MDA Explained (published by Addison-Wesley). The levels characterize the role of modeling in a software project.
The concept shows resemblance to the way software processes are rated with the Capability Maturity Model.
There are 6 levels:
Level 0
No Specification: the specification of software is not written down. It is kept in the minds of the developers
Level 1
Textual Specification: the software is specified by a natural language text (be it English or Chinese or something else), written down in one or more documents
Level 2
Text with Models: a textual specification is enhanced with several models to show some of the main structures of the system
Level 3
Models with Text: the specification of software is written down in one or more models. In addition to these models, natural language text is used to explain details, the background, and the motivation of the models, but the core of the specifications lies in the models.
Level 4
Precise Models: the specification of the software is written down in one or more models. Natural language can still be used to explain the background and motivation of the models, but it takes on the same role as comments in source code.
Level 5
Models only: the models are precise and detailed enough to allow complete code generation. The code generators at this level have become as trustworthy as compilers, therefore no developer needs to even look at the generated code.
== References ==
T. Mettler, Thinking in terms of design decisions when developing maturity models, International Journal of Strategic Decision Sciences, 1(4), 2010, pp. 76-87.
T. Mettler, P. Rohner, and R. Winter, Towards a Classification of Maturity Models in Information Systems, Management of the Interconnected World, in: A. D'Atri, M. De Marco, A.M. Braccini, and F. Cabiddu (Eds.), Berlin, Heidelberg: Physica, 2010, pp. 333-340.
Anneke Kleppe and Jos Warmer in their book MDA Explained Addison-Wesley
Book: MDA Explained: The Model Driven Architecture : Practice and Promise" by Anneke G. Kleppe, Jos B. Warmer, Wim Bast, Publisher: Addison-Wesley Professional, Release Date: April 2003, ISBN 0-321-19442-X
== External links ==
Getting Started with Modeling Maturity Levels | Wikipedia/Modeling_Maturity_Level |
Sparx Systems is an Australian software company founded by Geoffrey Sparks in 1996 in Creswick, Victoria in Australia, known for the development of the Unified Modeling Language tool Enterprise Architect.
Sparx Systems specializes in the development of visual tools for planning, design and development of software intensive systems. This company is known for the development of Enterprise Architect released in 2000, which is nowadays considered one of the more advanced tool sets for UML. In 2006 the company was among the first manufacturers to support the OMG Systems Modeling Language (SysML).
Sparx Systems is a member of the Object Management Group (OMG).
== References == | Wikipedia/Sparx_Systems |
Grady Booch (born February 27, 1955) is an American software engineer, best known for developing the Unified Modeling Language (UML) with Ivar Jacobson and James Rumbaugh. He is recognized internationally for his innovative work in software architecture, software engineering, and collaborative development environments.
== Education ==
Booch earned his bachelor's degree in 1977 from the United States Air Force Academy and a master's degree in electrical engineering in 1979 from the University of California, Santa Barbara.
== Career and research ==
Booch worked at Vandenberg Air Force Base after he graduated. He started as a project engineer and later managed ground-support missions for the space shuttle and other projects. After he gained his master's degree he became an instructor at the Air Force Academy.
Booch served as Chief Scientist of Rational Software Corporation from its founding in 1981 through its acquisition by IBM in 2003, where he continued to work until March 2008. After this he became Chief Scientist, Software Engineering in IBM Research and series editor for Benjamin Cummings.
Booch has devoted his life's work to improving the art and the science of software development. In the 1980s, he wrote one of the more popular books on programming in Ada. He is best known for developing the Unified Modeling Language with Ivar Jacobson and James Rumbaugh in the 1990s.
=== IBM 1130 ===
Booch got his first exposure to programming on an IBM 1130.
... I pounded the doors at the local IBM sales office until a salesman took pity on me. After we chatted for a while, he handed me a Fortran [manual]. I'm sure he gave it to me thinking, "I'll never hear from this kid again." I returned the following week saying, "This is really cool. I've read the whole thing and have written a small program. Where can I find a computer?" The fellow, to my delight, found me programming time on an IBM 1130 on weekends and late-evening hours. That was my first programming experience, and I must thank that anonymous IBM salesman for launching my career. Thank you, IBM.
=== Booch method ===
Booch developed the 'Booch method' of software development, which he presents in his 1991/94 book, Object Oriented Analysis and Design With Applications. The method was authored by Booch when he was working for Rational Software (acquired by IBM), published in 1992 and revised in 1994.
The method is composed of an object modeling language, an iterative object-oriented development process, and a set of recommended practices. The recommended practices include adding more classes to simplify complex code. The methodology was widely used in software engineering for object-oriented analysis and design and benefited from ample documentation and support tools.
The Booch notation is characterized by cloud shapes to represent classes and distinguishes the following diagrams:
The process is organized around a macro and a micro process.
The macro process identifies the following activities cycle:
Conceptualization : establish core requirements
Analysis : develop a model of the desired behavior
Design : create an architecture
Evolution: for the implementation
Maintenance : for evolution after the delivery
The micro process is applied to new classes, structures or behaviors that emerge during the macro process. It is made of the following cycle:
Identification of classes and objects
Identification of their semantics
Identification of their relationships
Specification of their interfaces and implementation
The notation aspect of the Booch method has now been superseded by the Unified Modeling Language (UML), which features graphical elements from the Booch method along with elements from the object-modeling technique (OMT) and object-oriented software engineering (OOSE).
Methodological aspects of the Booch method have been incorporated into several methodologies and processes, the primary such methodology being the Rational Unified Process (RUP).
=== Design patterns ===
Booch is also an advocate of design patterns. For instance, he wrote the foreword to Design Patterns, an early and highly influential book in the field.
=== IBM Research - Almaden ===
He now is part of IBM Research - Almaden, serving as Chief Scientist for Software Engineering, where he continues his work on the "Handbook of Software Architecture" and also leads several long-term projects in software engineering. Grady has served as architect and architectural mentor for numerous complex software-intensive systems around the world.
=== Publications ===
Grady Booch published several articles and books. A selection:
== Awards and honors ==
In 1995, Booch was inducted as a Fellow of the Association for Computing Machinery. He was named an IBM Fellow in 2003, soon after his entry into IBM, and assumed his current role on March 18, 2008. He was recognized as an IEEE Fellow in 2010. In 2012, Booch was awarded the Lovelace Medal for 2012 by the British Computer Society and gave the 2013 Lovelace Lecture. He gave the Turing Lecture in 2007. He was awarded the IEEE Computer Society Computer Pioneer award in 2016 for his pioneering work in Object Modeling that led to the creation of the Unified Modeling Language (UML).
== References ==
== External links ==
Media related to Grady Booch at Wikimedia Commons
Quotations related to Grady Booch at Wikiquote
Class diagrams, Object diagrams, State Event diagrams and Module diagrams.
The Booch Method of Object-Oriented Analysis & Design | Wikipedia/Booch_method |
In software engineering, a domain model is a conceptual model of the domain that incorporates both behavior and data. In ontology engineering, a domain model is a formal representation of a knowledge domain with concepts, roles, datatypes, individuals, and rules, typically grounded in a description logic.
== Overview ==
In the field of computer science a conceptual model aims to express the meaning of terms and concepts used by domain experts to discuss the problem, and to find the correct relationships between different concepts. The conceptual model is explicitly chosen to be independent of design or implementation concerns, for example, concurrency or data storage. Conceptual modeling in computer science should not be confused with other modeling disciplines within the broader field of conceptual models such as data modelling, logical modelling and physical modelling.
The conceptual model attempts to clarify the meaning of various, usually ambiguous terms, and ensure that confusion caused by different interpretations of the terms and concepts cannot occur. Such differing interpretations could easily cause confusion amongst stakeholders, especially those responsible for designing and implementing a solution, where the conceptual model provides a key artifact of business understanding and clarity. Once the domain concepts have been modeled, the model becomes a stable basis for subsequent development of applications in the domain. The concepts of the conceptual model can be mapped into physical design or implementation constructs using either manual or automated code generation approaches. The realization of conceptual models of many domains can be combined to a coherent platform.
A conceptual model can be described using various notations, such as UML, ORM or OMT for object modelling, ITE, or IDEF1X for Entity Relationship Modelling. In UML notation, the conceptual model is often described with a class diagram in which classes represent concepts, associations represent relationships between concepts and role types of an association represent role types taken by instances of the modelled concepts in various situations. In ER notation, the conceptual model is described with an ER Diagram in which entities represent concepts, cardinality and optionality represent relationships between concepts. Regardless of the notation used, it is important not to compromise the richness and clarity of the business meaning depicted in the conceptual model by expressing it directly in a form influenced by design or implementation concerns.
This is often used for defining different processes in a particular company or institute.
A domain model is a system of abstractions that describes selected aspects of a sphere of knowledge, influence or activity (a domain). The model can then be used to solve problems related to that domain.
The domain model is a representation of meaningful real-world concepts pertinent to the domain that need to be modeled in software. The concepts include the data involved in the business and rules the business uses in relation to that data. A domain model leverages natural language of the domain.
A domain model generally uses the vocabulary of the domain, thus allowing a representation of the model to be communicated to non-technical stakeholders. It should not refer to any technical implementations such as databases or software components that are being designed.
== Usage ==
A domain model is generally implemented as an object model within a layer that uses a lower-level layer for persistence and "publishes" an API to a higher-level layer to gain access to the data and behavior of the model.
In the Unified Modeling Language (UML), a class diagram is used to represent the domain model.
== See also ==
Domain-driven design (DDD)
Domain layer
Information model
Feature-driven development
Logical data model
Mental model
OntoUML
== References ==
== Further reading ==
Halpin T, Morgan T: Information Modeling and Relational Databases, Morgan Kaufmann, 2008. ISBN 978-0-12-373568-3.
Fowler, Martin: Analysis Patterns, Reusable object models, Addison-Wesley Longman, 1997. ISBN 0-201-89542-0.
Stewart Robinson, Roger Brooks, Kathy Kotiadis, and Durk-Jouke Van Der Zee (Eds.): Conceptual Modeling for Discrete-Event Simulation, 2010. ISBN 978-1-4398-1037-8
David W. Embley, Bernhard Thalheim (Eds.): Handbook of Conceptual Modeling, 2011. ISBN 978-3-642-15864-3. | Wikipedia/Domain_model |
Real-Time Object-Oriented Modeling (ROOM) is a domain-specific language.
ROOM was developed in the early 1990s for modeling real-time systems. The initial focus was on telecommunications, even though ROOM can be applied to any event-driven real-time system.
ROOM was supported by ObjecTime Developer (commercial) and is now implemented by the official Eclipse project eTrice
When UML2 was defined (version 2 of UML with real time extensions), many elements of ROOM were adopted.
== Concepts and key notions of ROOM ==
ROOM is a modeling language for the definition of software systems. It allows the complete code generation for the whole system from the model. ROOM comes with a textual as well as with a graphical notation.
Typically the generated code is accompanied with manually written code, e.g. for graphical user interfaces (GUI).
The code is compiled and linked against a runtime library which provides base classes and basic services (e.g. messaging).
ROOM describes a software system along three dimensions: structure, behavior and inheritance. The following sections will explain these three aspects in more detail.
=== Structure ===
The structural view in ROOM is composed of actors or capsules. Actors can communicate with each other using ports. Those ports are connected by bindings. Actors do exchange messages asynchronously via ports and bindings. To each port a unique protocol is assigned. A protocol in ROOM defines a set of outgoing and a set of incoming messages. Ports can be connected with a binding if they belong to the same protocol and are conjugate to each other. That means that one port is sending the outgoing messages of the protocol and receiving the incoming ones. This port is called the regular port. Its peer port, the conjugated port, receives the outgoing messages and sends the incoming ones of the protocol. In other words, a port is the combination of a required and a provided interface in a role (since one and the same protocol can be used by several ports of an actor).
An actor can contain other actors (as a composition). In ROOM these are called actor references or actor refs for short. This allows to create structural hierarchies of arbitrary depth.
The actor's ports can be part of its interface (visible from the exterior) or part of its structure (used by itself) or both. Ports that are part of the interface only are called relay ports. They are directly connected to a port of a sub actor (they are delegating to the sub actor). Ports that are part of the structure only are called internal end ports. Ports that belong to both, structure and interface, are called external end ports.
=== Behavior ===
Each actor in ROOM has a behavior which is defined by means of a hierarchical finite-state machine, or just state machine for short. A state machine is a directed graph consisting of nodes called states and edges called transitions. State transitions are triggered by incoming messages from an internal or external end port. In this context the messages sometimes are also called events or signals. If a transition specifies a certain trigger then it is said to fire if the state machine is in the source state of the transition and a message of the type specified by the trigger arrives. Afterwards the state is changed to the target state of the transition.
During the state change certain pieces of code are executed. The programmer (or modeler) can attach them to the states and transitions. In ROOM this code is written in the so called detail level language, usually the target language of the code generation. A state can have entry code and exit code. During a state change first the exit code of the source state is executed. Then the action code of the firing transition is executed and finally the entry code of the target state. A typical part of those codes is the sending of messages through ports of the actor.
State machines in ROOM also have a graphical notation similar to the UML state charts. An example is shown in the diagram in this section.
A state machine can also have a hierarchy in the sense that states can have sub state machines. Similar to the structure this can be extended to arbitrary depth. For details of the semantics of hierarchical state machines we refer to the original book.
An important concept in the context of state machines is the execution model of run-to-completion. That means that an actor is processing a message completely before it accepts the next message. Since the run-to-completion semantics is guaranteed by the execution environment, the programmer/modeler doesn't have to deal with classical thread synchronization. And this despite the fact that typical ROOM systems are highly concurrent because of the asynchronous communication. And maybe its worth to stress that the asynchronous nature of ROOM systems is not by accident but reflects the inherent asynchronicity of e.g. the machine being controlled by the software. Definitely this requires another mind set than the one that is needed for functional programming of synchronous systems.
But after a short while of getting accustomed it will be evident that asynchronously communicating state machines are perfectly suited for control software.
=== Inheritance ===
Like other object-oriented programming languages ROOM uses the concept of classes. Actors are classes which can be instantiated as objects several times in the system. Of course each instance of an actor class tracks its own state and can communicate with other instances of the same (and other) classes.
Similar to other modern programming languages ROOM allows inheritance of actor classes. It is a single inheritance as an actor class can be derived from another actor class (its base class).
It inherits all features of the base class like ports and actor refs, but also the state machine.
The derived actor class can add further states and transitions to the inherited one.
=== Layering ===
A last powerful concept of ROOM is layering. This notion refers to the vertical layers of a software system consisting of services and their clients. ROOM introduces the notions of service access point (SAP) for the client side and service provision point (SPP) for the server side. From the point of view of an actor implementation the SAPs and SPPs work like ports. Like ports they are associated with a protocol. But other than ports they don't have to (and even cannot) be bound explicitly. Rather, an actor is bound to a concrete service by a layer connection and this binding of a service is propagated recursively to all sub actors of this actor.
This concept is very similar to dependency injection.
== Literature ==
Bran Selic, Garth Gullekson, Paul T. Ward: "Real-Time Object-Oriented Modeling", New York, John Wiley & Sons Inc, 1994, ISBN 978-0-471-59917-3
New edition: Bran Selic, Garth Gullekson, Paul T. Ward: "Real-Time Object-Oriented Modeling", Hamburg, MBSE4U, 2023, ISBN 978-3911081016
== References ==
== External links ==
Media related to Real-Time Object-Oriented Modeling at Wikimedia Commons | Wikipedia/Real-Time_Object-Oriented_Modeling |
Open ModelSphere was a data, process and UML modeling tool written in Java and distributed as free software under the GPL License. It provided support for forward and reverse engineering between UML and relational schemas.
== History ==
Open ModelSphere has SILVERRUN PerfectO for an ancestor, proprietary software developed by Computer Systems Advisers and released in 1996. PerfectO was part of the SILVERRUN suite of modeling tools, known in the modeling community since the 1990s; PerfectO was used to support object-oriented modeling (limited to class modeling at that time) and object-relational modeling.
In 1998, PerfectO was translated into Java resulting in SILVERRUN-JD (Java Designer). With the addition of relational data modeling, the product was renamed to SILVERRUN ModelSphere and released in 2002. Later on, more features were added including support for business process modeling, conceptual data modeling, and UML diagramming.
In September 2008, Grandite released ModelSphere's core application as an open source product based on the GNU General Public License version 3. Its development environment was hosted on JavaForge which shut down March 31, 2016. An empty project is hosted on SourceForge which was registered on Sep 16th, 2008 and last updated on Mar 27th, 2013.
No releases, files, or source code are available anymore from Grandite as of Oct 18th, 2016. The remaining publicly available forks of the 3.0 codeline are based on Java 7, out of free support itself since 2015.
== Database support ==
Open ModelSphere works with
Oracle
Informix
Microsoft SQL Server
Sybase
DB2
PostgreSQL
== Releases ==
January 6, 2016: Open ModelSphere 3.2.2
No release notes provided
November 2009: Open ModelSphere 3.1, featuring
Core application based on Java 6
New look & feel
Interface to forward / reverse engineer Java code
New mechanism to facilitate the use of plug-ins
September 2008: Open ModelSphere 3.0
First open source release
July 2002: SILVERRUN ModelSphere 2.0
Addition of business process modeling
February 2002: SILVERRUN ModelSphere 1.0
Addition of relational modeling
== See also ==
List of UML tools
Entity-relationship model
== References ==
== External links ==
Official website
Mirror of the source code from Sep 28, 2013 (it corresponds to the version 3.0 from 2008) on GitHub | Wikipedia/Open_ModelSphere |
The Shlaer–Mellor method, also known as object-oriented systems analysis (OOSA) or object-oriented analysis (OOA) is an object-oriented software development methodology introduced by Sally Shlaer and Stephen Mellor in 1988. The method makes the documented analysis so precise that it is possible to implement the analysis model directly by translation to the target architecture, rather than by elaborating model changes through a series of more platform-specific models. In the new millennium the Shlaer–Mellor method has migrated to the UML notation, becoming Executable UML.
== Overview ==
The Shlaer–Mellor method is one of a number of software development methodologies which arrived in the late 1980s. Most familiar were object-oriented analysis and design (OOAD) by Grady Booch, object modeling technique (OMT) by James Rumbaugh, object-oriented software engineering by Ivar Jacobson and object-oriented analysis (OOA) by Shlaer and Mellor. These methods had adopted a new object-oriented paradigm to overcome the established weaknesses in the existing structured analysis and structured design (SASD) methods of the 1960s and 1970s. Of these well-known problems, Shlaer and Mellor chose to address:
The complexity of designs generated through the use of structured analysis and structured design (SASD) methods.
The problem of maintaining analysis and design documentation over time.
Before publication of their second book in 1991 Shlaer and Mellor had stopped naming their method "Object-Oriented Systems Analysis" in favor of just "Object-Oriented Analysis". The method started focusing on the concept of Recursive Design (RD), which enabled the automated translation aspect of the method.
What makes Shlaer–Mellor unique among the object-oriented methods is:
the degree to which object-oriented semantic decomposition is taken,
the precision of the Shlaer–Mellor Notation used to express the analysis, and
the defined behavior of that analysis model at run-time.
The general solution taken by the object-oriented analysis and design methods to these particular problems with structured analysis and design, was to switch from functional decomposition to semantic decomposition. For example, one can describe the control of a passenger train as:
load passengers, close doors, start train, stop train, open doors, unload passengers.
Then a design becomes focused on the behavior of doors, brakes, and passengers, and how those objects (doors, brakes, etc.) are related and behave within the passenger train domain. Other objects, that provide services used by the passenger train domain, are modeled in other domains connected to the passenger train domain.
== Shlaer–Mellor method topics ==
=== Translation v. elaboration ===
The goal of the Shlaer–Mellor method is to make the documented analysis so precise that it is possible to implement the analysis model directly by translation rather than by elaboration. In Shlaer–Mellor terminology this is called recursive design. In current (2011) terminology, we would say the Shlaer–Mellor method uses a form of model-driven architecture (MDA) normally associated with the Unified Modeling Language (UML).
By taking this translative approach, the implementation is always generated (either manually, or more typically, automatically) directly from the analysis. This is not to say that there is no design in Shlaer–Mellor, rather that there is considered to be a virtual machine that can execute any Shlaer–Mellor analysis model for any particular hardware/software platform combination.
This is similar in concept to the virtual machines at the heart of the Java programming language and the Ada programming language, but existing at analysis level rather than at programming level. Once designed and implemented, such a virtual machine is re-usable across a range of applications. Shlaer–Mellor virtual machines are available commercially from a number of tool vendors, notably Abstract Solutions, Mentor Graphics and Pathfinder Solutions.
=== Semantic decomposition ===
Shlaer–Mellor proposes a semantic decomposition in multiple (problem) domains.
The split between analysis and design models: The analysis domain expresses precisely what the system must do, the design domain is a model of how the Shlaer–Mellor virtual machine operates for a particular hardware and software platform. These models are disjoint, the only connection being the notation used to express the models.
Decomposition within the analysis domain where system requirements are modelled, and grouped, around specific, disjoint, subject matters. To return to the earlier passenger train example, individual semantic models may be created based on door actuators, motor controls, and braking systems. Each grouping is considered, and modelled, independently. The only defined relationship between the groupings are dependencies e.g. a passenger train application may depend on both door actuation and motor control. Braking systems may depend upon motor control.
Domain models of door actuators, motor controls, and braking systems would typically be considered as generic re-usable service domains whereas the passenger train controller domain is likely to be a very product-specific application domain.
A particular system is composed of domains and the defined bridges between the domains. A bridge is described in the terms of the assumptions held by the domain acting as a client bridged to a domain acting as a server.
=== Precise action language ===
One of the requirements for automated code generation is to precisely model the actions within the finite-state machines used to express dynamic behaviour of Shlaer–Mellor objects.
Shlaer–Mellor is unique amongst object-oriented analysis methods in expressing such sequential behavior graphically as Action Data Flow Diagrams (ADFDs). In practice the tools that supported Shlaer–Mellor, provided a precise action language. The action languages superseded the ADFD approach, so all actions are written in textual form.
=== Test and simulation ===
The translative approach of the Shlaer–Mellor method lends itself to automated test and simulation environments (by switching the target platform during code generation), and this may partly explain the popularity of Shlaer–Mellor and other MDA-based methods when developing embedded systems, where testing on target systems e.g. mobile phones or engine management systems, is particularly difficult.
What makes such testing useful and productive is the concept of the Shlaer–Mellor virtual machine. As with most OOA/OOD methods, Shlaer–Mellor is an event-driven, message-passing environment. Onto this generic view, the Shlaer–Mellor virtual machine mandates a prioritised event mechanism built around State Models, which allows for concurrent execution of actions in different state machines.
Since any implementation of Shlaer–Mellor requires this model to be fully supported, testing under simulation can be a very close model of testing on target platform. Whilst functionality heavily dependent upon timing constraints may be difficult to test, the majority of system behaviour is highly predictable due to the prioritized execution model.
== Criticisms ==
There has never been a universally agreed textual language to express actions within the Shlaer–Mellor community. Tool vendors have defined their own copyrighted and controlled action languages.
Graham (1994) described Shlaer–Mellor method as early example of object-oriented analysis, that could not really be regarded as object-oriented. According to Graham the method lacks "notion of inheritance. As described in their book it was little more than an object-based extension of data modelling." In line with comment Capretz (1996) argues that the Shlaer–Mellor method "fails to account for the vast majority of object-oriented ideas and an ordinary graphical notation is prescribed", which is primarily taken "from entity–relationship diagrams and data flow diagrams found in other structured methods".
== See also ==
Embedded system
Executable UML
Finite-state machine (FSM)
Functional decomposition
I-OOA
Massive parallelism
Model-driven architecture (MDA)
Structured analysis
Unified Modeling Language (UML)
== Bibliography ==
Stephen Mellor (2002) Make Models Be Assets, Communications of the ACM Volume 45, 11:76-87 (November 2002), 2002
Rodney C. Montrose (2001) Object-Oriented Development Using The Shlaer–Mellor Method. Project Technology, Inc.
Sally Shlaer, Stephen Mellor (1988) Object-Oriented Systems Analysis: Modeling the World in Data, Yourdon Press. ISBN 0-13-629023-X
Sally Shlaer, Stephen Mellor (1991) Object Lifecycles: Modeling the World in States, Yourdon Press. ISBN 0-13-629940-7
Leon Starr (1996) How to Build Shlaer–Mellor Object Models. Prentice Hall. ISBN 0-13-207663-2
== References ==
== External links ==
Shlaer–Mellor and Executable UML Portal, blog 2008-2011
Shlaer–Mellor and Executable UML References, 2008
Shlaer-Mellor Metamodel Blog, 2011 | Wikipedia/Shlaer–Mellor_method |
Software Ideas Modeler is a CASE and an UML tool. The modeler supports all 14 diagram types specified in UML 2.5. It also supports among others the following diagrams and standards:
ER diagrams
BPMN 2.0
CMMN
SysML 1.5
ArchiMate 3
JSD
CRC
flowcharts
data flow diagram
Infographics
Wireframes
Mind maps
User Stories
Roadmaps
ORM (Object-role_modeling)
Decision Model and Notation
Gantt chart
Nassi–Shneiderman diagram
C4 model
Feature_model
Software Ideas Modeler is the work of Slovak software developer Dušan Rodina. The software is written in C#.
== Exports ==
There is an export to raster image formats (BMP, GIF, JPG, PNG, TIFF), vector image formats (Windows Metafile, SVG) and PDF.
There is also export to XMI.
== Imports ==
There is an import from XMI.
== Supported programming languages ==
There is an export to:
ActionScript
C#
C++
Dart
Object Pascal (Delphi)
Java
JavaScript
JSON
JSON Schema
PHP
Protobuf
Python
Ruby
Rust
SQL
TypeScript
Visual Basic
Visual Basic .NET
XML Schema
There is an import from:
C#
C++
Dart
Java
JavaScript
Object Pascal (Delphi)
PHP
Python
Ruby
Rust
SQL
TypeScript
Visual Basic .NET
== See also ==
List of UML tools
== References ==
== External links ==
Official website
Review
Download software at CNet | Wikipedia/Software_Ideas_Modeler |
SAP PowerDesigner (or PowerDesigner) is a collaborative enterprise modelling tool produced by Sybase, currently owned by SAP. It can run either under Microsoft Windows as a native application or in an Eclipse environment through a plugin. It supports model-driven architecture software design, and stores models using a variety of file extensions, such as .bpm, .cdm and .pdm. The internal file structure can be either XML or a compressed binary file format. It can also store models in a database repository.
The PowerDesigner data modeling tool's market share in 2002 was 39%. It is priced from US$3,000 to $7,500 per developer seat.
== Features ==
PowerDesigner includes support for:
Business Process Modeling (ProcessAnalyst) supporting BPMN
Code generation (Java, C#, VB .NET, Hibernate, EJB3, NHibernate, JSF, WinForm (.NET and .NET CF), PowerBuilder, ...)
Data modeling (works with most major RDBMS systems)
Data Warehouse Modeling (WarehouseArchitect)
Eclipse plugin
Object modeling (UML 2.0 diagrams)
Report generation
Supports Simul8 to add simulation functions to the BPM module to enhance business processes design.
Repository It refers to a repository of models (enterprise, information, data).
Requirements analysis
XML Modeling supporting XML Schema and DTD standards
Visual Studio 2005 / 2008 addin
== History ==
PowerDesigner started life as AMC*Designor in France and S-Designor internationally, which was written by Xiao-Yun Wang of SDP Technologies. The "or" in the product name refers to "Oracle", since initially the product was developed to design Oracle databases, but very quickly evolved to support all major RDBMS in the market. SDP Technologies was a French company that was started in 1983. Powersoft purchased SDP in 1995, and Sybase had purchased Powersoft earlier in 1994. Shortly after the acquisition, the product was renamed to be consistent with the Powersoft brand. Sybase currently owns all rights to PowerDesigner and PowerAMC (the French version of PowerDesigner). In May 2010, SAP announced that it would be acquiring Sybase for $5.8 billion.
The data modeling features of the French and English editions were originally following 2 different methodologies: Merise for PowerAMC and information technology engineering (based on Yourdon / DeMarco works) for PowerDesigner. Since version 7, both editions support all methodologies and only differ from their user language. From v16.6 onwards, both editions are called PowerDesigner and are delivered in a single installer.
=== Version History ===
1989 - The first commercial release of AMC*Designor (version 2.0) in France
1992 - The first commercial release of S-Designer in the US.
1994 - ProcessAnalyst was added to the suite in 1994.
1995 - S-Designer becomes PowerDesigner, AMC*Designor becomes PowerAMC
1997 - PowerDesigner 6.0 releases.
1998 - WarehouseArchitect was added.
1999 - PowerDesigner 7.0 was rewritten to take advantage of newer technologies and to provide an interface more consistent with other Sybase products.
December 2001 - PowerDesigner 9.5 was initially released, with maintenance releases through 2003.
December 2004 - Version 10.0 (Minerva release)
2005 - Version 11.0
January 2006 - PowerDesigner 12.0 released with metadata mappings and reporting features
August 2006 - PowerDesigner 12.1 released with enhanced support for Microsoft Visual Studio and SQL Server
July 2007 - PowerDesigner 12.5 released with new ETL (Extract, transform, load) and EII (Enterprise Information Integration) modeling and full UML 2.0 diagrams support
October 2008 - PowerDesigner 15.0 released with new Enterprise Architecture Model, customizable frameworks support (Zachman Framework, FEAF, ...), Impact and Lineage Analysis Diagram, logical data model, Barker's Notation, Project support and lot more
November 2011 - PowerDesigner 16.0 released with new Shell, Role-based UI, Glossary, Impact analysis on the repository, Sybase IQ reference architecture wizard, New database support, Web portal enhancements
January 2013 - PowerDesigner 16.5 released with new features supporting SAP Platform: SAP HANA, SAP BusinessObjects, SAP Netweaver and SAP Solution Manager
March 2016 - PowerDesigner 16.6 released with Support for SAP HANA Calculation Views and SAP HANA Core Data Services (CDS). PowerDesigner Web can now edit Enterprise Architecture and Requirements Models.
April 2020 - PowerDesigner 16.7 released with new features supporting: Export from Web privilege, Limit the choice of model types offered in New Model dialog, New models added, Customize link symbol labels, Generate Models using the CSN notation, OAuth 2.0 Client Credentials authentication
== Standards ==
PowerDesigner supports the following standards:
BPEL4WS
Business Process Modeling Notation (BPMN)
Document Type Definition (DTD)
ebXML
IDEF
IE/Information engineering
Merise
RDBMS
Rich Text Format (RTF)
UML 2.0 diagrams
XML
XML Schema
== See also ==
Comparison of data modeling tools
== References ==
== External links ==
SAP PowerDesigner webpage
Novalys PowerDesigner | Wikipedia/PowerDesigner |
ModelCenter, developed by Phoenix Integration, is a software package that aids in the design and optimization of systems. It enables users to conduct trade studies, as well as optimize designs. It interacts with other common modeling tools, including Systems Tool Kit, PTC Integrity Modeler, IBM Rhapsody, No Magic, Matlab, Nastran, Microsoft Excel, and Wolfram SystemModeler. ModelCenter also has tools to enable collaboration among design team members.
== Modules and Packs ==
RSM Toolkit 3.0 gives users a mathematical model based on source data from simulations or actual experiments. This new model can then be integrated as a component within another model within ModelCenter.
QuickWrap 3.0 automates batch mode programs.
The Enhanced Workflow Module allows workflows to be graphically constructed and executed.
The Visualization Pak helps users to visualize the design space and perform trade studies.
The Optimization Pak includes various tools to allow users to optimize designs after integrating the components of the model. Tools within this pack include the Design of Experiments Tool, Variable Influence Profiler, Gradient Based Optimization, and Prediction Profiler. The Optimization pack has over 30 optimization algorithms.
The CAD Fusion Pak allows users to incorporate work from popular CAD packages into the analysis on designs within ModelCenter.
== Applications ==
ModelCenter is used in a variety of applications, primarily system design and optimization in the aerospace and defense industry. It is also used for process design and optimization in the automotive, manufacturing, electronics, building design, and consumer products industries.
== Examples of use ==
ModelCenter served as the environment in which to integrate the Life-Cycle Cost Analysis Model into the Integrated Program Model for NASA's Constellation Program.
ModelCenter was used in pre-concept design work of an unmanned combat aerial vehicle. Engineers integrated various analysis modules within ModelCenter, and also used ModelCenter for design of experiments.
Volvo used ModelCenter in its MDO Process Workflow Integration.
Airbus selected ModelCenter to run engineering studies, including design of experiments and optimization. ModelCenter was one of several commercial software packages integrated into Airbus's integrated aerodynamic framework.
== See also ==
Multidisciplinary design optimization
Phoenix Integration
Simulink
== External links ==
ModelCenter Website
== References == | Wikipedia/ModelCenter |
The common warehouse metamodel (CWM) defines a specification for modeling metadata for relational, non-relational, multi-dimensional, and most other objects found in a data warehousing environment. The specification is released and owned by the Object Management Group, which also claims a trademark in the use of "CWM".
== Overview ==
The CWM specifies interfaces that can be used to enable interchange of warehouse and business intelligence metadata between warehouse tools, warehouse platforms and warehouse metadata repositories in distributed heterogeneous environments. CWM is based on three standards:
UML – Unified Modeling Language, an OMG modeling standard
MOF – Meta Object Facility, an OMG metamodeling and metadata repository standard
XMI – XML Metadata Interchange, an OMG metadata interchange standard
CWM models enable users to trace the lineage of data – CWM provides objects that describe where the data came from and when and how the data was created. Instances of the metamodel are exchanged via XML Metadata Interchange (XMI) documents.
Initially, CWM contained a local definition for a data translation facility. It is not clear how the QVT final adopted specification will affect CWM.
== Support for the CWM ==
=== Submitters of CWM specification ===
While the Object Management Group owns the standard for CWM, some companies are considered co-submitters of the CWM specification. The following companies were listed as co-submitters to the v1.1 specification:
International Business Machines Corporation
Unisys Corporation
NCR Corporation
Hyperion Solutions Corporation
Oracle Corporation
UBS AG
Genesis Development Corporation
Dimension EDI
=== Compliance with the CWM specification ===
Software vendors claiming CWM support differ in the degree to which they comply with CWM. Some were co-submitters of the specification, and are actively using the OMG trademark in marketing literature. Other vendors have expressed support for CWM or claim they have products that are "CWM-compliant."
Questions about compliance are addressed within the specification itself. Chapter 18 in both the 1.0 and 1.1 specification list required and optional compliance points.
The Object Management Group has a list of CWM implementations, but it is unclear how this list is maintained.
=== Interoperability of CWM tools ===
Compliance with the CWM specification does not guarantee tools from different vendors will integrate well, even when they are "CWM-compliant". The OMG addressed some of these issues by releasing patterns and best practices to correct these problems in a supplementary specification, CWM Metadata Interchange Patterns
== Vendors supporting CWM ==
=== CWM implementations identified by OMG ===
These vendors have been identified as having a CWM implementation or have active projects to support CWM.
IBM
Informatica produces Intelligence Data Platform with PowerCenter, a data integration tool with a metadata extension Enterprise Data Catalog (EDC) (metadata manager formerly known as SuperGlue is replacing by EDC). Informatica is one of the members of the OMG
Oracle Corporation Oracle Warehouse Builder and Oracle SQL Developer Data Modeler (formerly known as IKAN CWM4ALL)
Pentaho
prudsys AG – XELOPES library for embedded data mining
SAS SAS adheres to the Object Management Group's CWM as the interoperability and interchange standard. An alliance between SAS and Meta Integration Technology Inc. (MITI) enables SAS to provide bridges for sharing and exchanging metadata with more than 40 design tool and repository vendors
=== Other vendors supporting CWM ===
The following products or companies have claimed CWM support, but are not listed by OMG as having a CWM implementation. In some cases, the vendor may have implemented the v1.0 specification, which was replaced by the v1.1 specification. Refer to the software vendor to determine if the product is compliant with CWM or merely supports a subset of the required portions of the specification.
Cognos, now a division of IBM, is listed as a supporter of CWM in the v1.1 specification. Cognos product literature claims support for "Common Warehouse Model (CWM)" but never mentions an actual OMG specification.
Hyperion Solutions, now a division of Oracle Corporation
InQuisient fully supports version 1.1 in its data repository.
Pentaho Pentaho Open Source Business Intelligence Project has recently added "Pentaho Metadata" which supports CWM
== See also ==
Data Warehouse
Metadata
Metadata registry
Metadata standards
Extensible Markup Language (XML)
XML Metadata Interchange (XMI)
Domain Specific Language (DSL)
Domain-specific modeling (DSM)
Model-based testing (MBT)
Meta-modeling
Unified Modeling Language (UML)
ATLAS Transformation Language (ATL)
Visual Automated Model Transformations (VIATRA) framework
Object Constraint Language (OCL)
Model Transformation Language (MTL)
Meta-Object Facility (MOF)
Query/View/Transformation (QVT) languages
== References ==
== Further reading ==
John Poole, Dan Chang, Douglas Tolbert, and David Mellor (2002). The Common Warehouse Metamodel: An Introduction to the standard for Data Warehouse Integration. OMG Press (John Wiley & Sons), 2002 ISBN 0-471-20052-2
John Poole, Dan Chang, Douglas Tolbert, and David Mellor (2003). Common Warehouse Metamodel Developer's Guide. OMG Press (John Wiley & Sons), 2003 ISBN 978-0-471-20243-1
== External links ==
CWM Forum website
OMG CWM Technology
OMG CWM Specification | Wikipedia/Common_Warehouse_Metamodel |
Domain-specific multimodeling is a software development paradigm where each view is made explicit as a separate domain-specific language (DSL).
Successful development of a modern enterprise system requires the convergence of multiple views. Business analysts, domain experts, interaction designers, database experts, and developers with different kinds of expertise all take part in the process of building such a system. Their different work products must be managed, aligned, and integrated to produce a running system. Every participant of the development process has a particular language tailored to solve problems specific to its view on the system. The challenge of integrating these different views and avoiding the potential cacophony of multiple different languages is the coordination problem.
Domain-specific multimodeling is promising when compared to more traditional development paradigms such as single-language programming and general-purpose modeling. To reap the benefits of this new paradigm, we must solve the coordination problem. This problem is also known as the fragmentation problem in the context of Global Model Management.
One proposal to solve this problem is the coordination method. This is a three-step method to overcome the obstacles of integrating different views and coordinating multiple languages. The method prescribes how to (1) identify and (2) specify the references across language boundaries, that is the overlaps between different languages. Finally, the method offers concrete proposals on how to (3) apply this knowledge in actual development in the form of consistency, navigation, and guidance.
== Motivating example ==
Enterprise systems based on multiple domain-specific languages are abundant. Languages with a metamodel defined in the Extensible Markup Language (XML) enjoy particularly widespread adoption. To illustrate development with multiple languages, we will draw an example from a case study: The Apache Open For Business (OFBiz) system. Briefly stated, OFBiz is an enterprise resource planning system that includes standard components such as inventory, accounting, e-commerce etc. These components are implemented by a mixture of XML-based languages and regular Java code. As an example, let us focus on the content management component, particularly a use case in which the administrative user creates an online web survey as shown in the screenshot below. We will refer to this example as the create survey example.
The figure shows a screenshot of the administrative interface of the content management application in a running OFBiz instance. To create a survey, the user fills out the fields of the input form and hits the update button. This creates a new survey which can be edited and later published on a frontend website in OFBiz. Behind the scenes, this use case involves several artifacts written in different languages. In this example, let us focus on only three of these languages: the Entity, the Service, and the Form DSL.
These three languages correspond roughly to the structural, the behavioural, and the user interface concern in OFBiz. The Entity DSL is used to describe the underlying data model and hence the way the created survey will be saved. The Service DSL is used to describe the interface of the service that is invoked when the user hits the update button. Finally, the Form DSL is used to describe the visual appearance of the form. Although the three languages are tailored for different things, they can not be separated entirely. The user interface invokes a certain application logic and this application logic manipulates the data of the application. This is an example of non-orthogonal concerns. The languages overlap because the concerns that they represent cannot be separated entirely. Let us examine these three languages in a bottom-up manner and point out their overlaps.
=== Entity DSL ===
The Entity DSL defines the structure of data in OFBiz. The listing below shows the definition of the Survey entity which is the business object that represents the concept of a survey. The code in the Listing is self-explanatory: An entity called Survey is defined with 10 fields. Each field has a name and a type. The field surveyId is used as the primary key. This definition is loaded by a central component in OFBiz called the entity engine. The entity engine instantiates a corresponding business object. The purpose of the entity engine is to manage transactional properties of all business objects and interact with various persistence mechanisms such as Java Database Connectivity, Enterprise JavaBeans or even some legacy system.
=== Service DSL ===
The Service DSL specifies the interface of the services in OFBiz. Each service encapsulates part of the application logic of the system. The purpose of this language is to have a uniform abstraction over various implementing mechanisms. Individual services can be implemented in Java, a scripting language, or using a rule engine. The listing below shows the interface of the createSurvey service.
Apart from the name, the service element specifies the location and invocation command of the implementation for this service. The default-entity-name attribute specifies that this service refers to the Survey entity which was defined in the previous listing. This is an overlap between the two languages, specifically a so-called soft reference. A model in the Service DSL refers to a model in the Entity DSL. This reference is used in the two auto-attributes elements below which specify the input and output of the service in the form of typed attributes. As input, the service accepts attributes corresponding to all non-primary key (nonpk) fields of the Survey entity and these attributes are optional. As output, the service returns attributes corresponding to the primary key (pk) fields of Survey, i.e., in this case the surveyId field, and these attributes are mandatory. The purpose of the reference across languages is in this case to reduce redundancy. The attributes of the createSurvey service corresponds to the fields of the Survey entity and it is therefore only necessary to specify them once.
=== Form DSL ===
The Form DSL is used to describe the layout and visual appearance of input forms in the user interface. The language consists of domain concepts such as Form and Field. The listing below shows the implementation of the EditSurvey form. This time the Form DSL overlaps with the Service DSL. The target attribute of the form and the alt-target elements specify that the input from the submission of this form should be directed to either the updateSurvey or createSurvey services. The auto-fields-service element specifies that the form should include a field corresponding to each of the attributes of the updateSurvey service (which are similar to the attributes of the createSurvey service). This produces a similar effect of importing definitions from another model as in the case of the auto-attributes elements in the previous listing. Further down, we can see that it is possible to customize the appearance of these imported fields such as isAnonymous. Finally, a submitButton is added with a localized title such that the user can submit his data to the referenced service.
The create survey example, as described here, is implemented using models in three different languages. The complete implementation actually involves even more languages such as a Screen DSL to specify the layout of the screen where the form is placed, and a Minilang DSL which is a data-manipulation language used to implement the service. However, these three languages do illustrate the main idea of making each concern concrete. The example also shows a simple way of reducing redundancy by letting the languages overlap slightly.
=== Multi-level customization ===
Domain-specific languages, like those described above, have limited expressiveness. It is often necessary to add code snippets in a general-purpose language like Java to implement specialized functionality that is beyond the scope of the languages. This method is called multi-level customization.
Since this method is very commonly used in setups with multiple languages, we will illustrate it by a continuation of the example. Let us call this the build PDF example.
Suppose we want to build a PDF file for each survey response to the online surveys that users create. Building a PDF file is outside the scope of our languages so we need to write some Java code that can invoke a third-party PDF library to perform this specialized functionality. Two artifacts are required:
First, an additional service model, as shown below, in the Service DSL that defines the interface of the concrete service such that it can be accessed on the modeling level. The service model describes the location of the implementation and what the input and output attributes are.
Second, we need a code snippet, as shown below, that contains the actual implementation of this service. A service can have multiple inputs and outputs so input to the Java method is a map, called context, from argument names to argument values and returns output in the form of another map, called results.
This multi-level customization method uses soft references similar to the create survey example. The main difference is that the reference here is between model and code rather than between model and model. The advantage, in this case, is that a third-party Java library for building PDFs can be leveraged. Another typical application is to use Java code snippets to invoke external webservices and import results in a suitable format.
== Coordination problem ==
The example illustrates some of the advantages of using multiple languages in development. There are, however, also difficulties associated with this kind of development. These difficulties stem from the observation that the more kinds of artifacts we introduce into our process, the more coordination between developer efforts is needed. We will refer to these difficulties as the Coordination Problem. The Coordination Problem has a conceptual and a technical aspect. Conceptually, the main problem is to understand the different languages and their interaction. To properly design and coordinate models in multiple languages, developers must have a sufficient understanding of how languages interact. Technically, the main problem is to enforce consistency. Tools must be provided to detect inconsistencies early, i.e., at modeling time, and assist developers in resolving these inconsistencies. In the following, we will examine these two aspects in greater detail.
=== Coordination as a conceptual challenge ===
The first problem that developers encounter when starting on development with multiple languages is language cacophony. Learning the different languages and understanding their interaction is necessary to make sense of the complex composition of artifacts. The OFBiz framework for instance has seventeen different languages and more than 200 000 lines of domain-specific language code so the complexity can be quite overwhelming! There is currently no established method of characterizing different languages such that developers quickly can reach an operational understanding. Tools are important here as an ad hoc mechanism for learning and exploration because developers typically use tools to learn by experiments. There are especially three areas where tools for domain-specific models are helpful:
Understanding a language
Understanding language interactions
Understanding how to use languages
First, understanding a language can be difficult and in the case of XML-based domain-specific languages a frequent and intuitive objection is the syntax matters objection. This argument can be stated in the following way: “The different languages are hard to understand and only add to the confusion because their XML-based syntax is particularly verbose and unintelligible. Using a single general-purpose language like Java would be better because then developers could rely on a syntax that they already know”. While this objection is certainly important, it misses a central point. XML or a similar representation format may not be the syntax that developers actually work with. One of the advantages of using XML-based domain-specific languages is that we can then provide domain-specific editors. The figure below shows what a hypothetical editor for the Entity DSL might look like. This editor presents the domain in a simple and visually appealing manner but may very well use the XML representation (and perhaps a layout configuration) underneath.
Just as we may complain that XML is a bad choice, we could also object that a general-purpose language like Java is a poor choice for some tasks. Furthermore, developers may feel less intimidated by the editor in figure than by code Listings in XML or Java. If we accept that syntax matters then the use of different languages with tailored editors becomes a reasonable strategy. The simplicity of the editor makes the language easier to understand and hence easier to use. In other words, the syntax matters objection may be the very reason why we explore the field of Domain-specific languages.
Second, language interactions reveal relations between languages. Developers should be able to jump between related elements in different artifacts. Ease of navigation between different software artifacts is an important criterion for tools in traditional development environments. Although we have performed no empirical studies in this area, we hypothesize that proper navigation facilities increase productivity. This claim is supported by the observation that all major development environments today offer quite sophisticated navigation facilities such as type hierarchy browser or the ability to quickly locate and jump to references to a method definition. The development environments can provide these navigation facilities because they maintain a continuously updated model of the sourcefiles in the form of an abstract syntax tree.
In a development environment with multiple languages, navigation is much more difficult. Existing environments are not geared to parsing and representing DSL models as abstract syntax trees for arbitrary and perhaps even application-specific languages such as the languages from the previous example. Furthermore without this internal representation, existing environments cannot resolve neither intra- nor inter-language references for such languages and hence cannot provide useful navigation. This means that developers must maintain a conceptual model of how the parts of their system are related. New tools with navigation facilities geared to multiple languages would on the other hand be very helpful in understanding the relations between languages. In terms of the create survey example such tools should display the relations between the three languages by using the soft references as navigation points.
Third, to understand language use we must be able to distinguish correct editing operations from wrong ones in our development environment. Traditional development environments have long provided guidance during the writing of a program. Incremental compilation allows the environment to offer detailed suggestions to the developer such as how to complete a statement. More intrusive kinds of guidance also exist such as syntax-oriented editors where only input conforming to the grammar can be entered. Generic text-editors that can be parameterized with the grammar of a language have existed for a long time.
Existing editors do not take inter-language consistency relations into account when providing guidance. In the previous example, an ideal editor should for instance be able to suggest the createSurvey service as a valid value when the developer edits the target attribute in the Form definition. An environment which could reason about artifacts from different languages would also be able to help the developer identify program states where there was local but not global consistency. Such a situation can arise when a model is well-formed and hence locally consistent but at the same time violates an inter-language constraint. Guidance or intelligent assistance in the form of proposals on how to complete a model would be useful for setups with multiple languages and complex consistency constraints. Tool-suggested editing operations could make it easier for the developer to get started on the process of learning how to use the languages.
=== Coordination as a technical challenge ===
The technical aspect of the coordination problem is essentially a matter of enforcing consistency. How can we detect inconsistencies across models from multiple languages at modeling time? To fully understand the complexity of the consistency requirements of a system based on multiple languages, it is useful to refine our concept of consistency.
Consistency can be either intra- or inter-consistency. Intra-consistency concerns the consistency of elements within a single model. The requirements here are that the model must conform to its metamodel, i.e., be syntactically well-formed. In terms of the create survey example, the entity model must for instance conform to the XSD schema of the Entity DSL. This schema is the metamodel of the Entity DSL and it specifies how elements can be composed and what are, to some extent, the valid domains of attributes.
Inter-consistency is achieved when references across language boundaries can be resolved. This kind of consistency can be further subdivided into (1) model-to-model consistency and (2) model-to-code consistency. Model-to-model consistency concerns the referential integrity as well as high-level constraints of the system. In the create survey example, the default-entity-name attribute from the Service listing refers to the name attribute from Entity listing. If we change one of these values without updating the other, we break the reference. More high-level consistency constraints across different models also exist as discussed later. A project can have certain patterns or conventions for naming and relating model elements. Current development environments must be tailored to specific languages with handwritten plugins or similar mechanisms in order to enforce consistency between languages such as those from the previous example.
Model-to-code consistency is an essential requirement in multi-level customization. When models are supplemented with code snippets as in the build PDF example, it is necessary to check that models and code actually fit. This partly a matter of making sure that soft references between models and code are not broken, similar to referential integrity in model-to-model consistency. But it is also a matter of making sure that the code does not violate expectations set up in the model. In the build PDF example, the model specifies that outByteWrapper will always be part of the output, i.e., the outByteWrapper key is put in the results map. An analysis of the code shows that outByteWrapper will only be part of the output if no exceptions are thrown before line 10. In other words, some possible executions of the code will violate a specification on the modeling level. More generally, we can state that multi-level customization imposes very fine-grained constraints on the involved models and code snippets.
=== Solving the coordination problem ===
The coordination problem arises from the fact that multiple languages are used in a single system. The two previous Subsections illustrate that this problem has both a conceptual side as well as a low-level technical side. The challenges that we have described are real rather than hypothetical challenges. Specifically, we have faced these challenges in two concrete and representative case studies: an enterprise resource planning system, OFBiz, and a health care system, the District Health Information System (DHIS). Both cases are medium-sized systems that are in actual industrial use. Our solution to the practical problems we have encountered during our work with these systems are a set of guidelines and prototypes. In the following, we will introduce an overall conceptual framework which incorporates the guidelines and prototypes into a coherent method: the coordination method.
== Coordination method ==
The goal of the coordination method is to solve the coordination problem and thereby provide better support for development with multiple languages. To properly appreciate the method, it is important to understand that it does not prescribe the design of individual languages. Plenty of methods and tools have already been proposed for this. This method assumes the existence of a setup with multiple domain-specific languages. Given such a setup, one can apply the method. The method consists of three steps as shown in the diagram below. Each step consist of a couple of parts which are shown as little boxes in the diagram. Boxes with dotted lines represent automatic processes and boxes with solid lines represent manual ones. In the following, we will explain these steps in a bit more detail.
=== Step 1: identification ===
The goal of the identification step is to identify language overlaps. As described in the example, an overlap is an area where the concerns of two languages intersect. The soft references from Form DSL to Service DSL and from Service DSL to Entity DSL in the create survey use case are examples of such overlaps. Another example is the case where a customized code snippet is used to extend a model. Such overlaps are frequent when the expressiveness of general-purpose languages is needed to implement specialized requirements that are beyond the scope of the model. The identification step can either be a manual or an automatic process depending on the complexity of the overlaps. When the overlaps have been identified and made explicit, this information is used as input to the second step in the method: the specification step.
=== Step 2: specification ===
The goal of the specification step is to create a coordination model which specifies how languages interact. The references across language boundaries in a system constitute the coordination model for that particular system. It is created by mapping the main software artifacts into a common representation. Additional information such as domain- or application-specific constraints may also be encoded to provide a rich representation. The coordination model is based on generic information such as language grammars and constraints as well as application-specific information such as concrete models and application-specific constraints. This means that even though the same languages are used across several products, each product has a specification of its own unique coordination model. The coordination model is used as basis for various forms of reasoning in the final step of the method: the application step.
=== Step 3: application ===
The goal of the application step is to take advantage of the coordination model. The coordination model allows tools to derive three layers of useful information. First, the coordination model can be used to enforce consistency across multiple languages. The coordination model specifies consistency relations such as how elements from different languages can refer to each other. Tools can enforce referential integrity and perform static checks of the final system before deployment. Second, the consistency relations are used to navigate, visualize and map the web of different languages in a development setup. This information is used to quickly link and relate elements from different languages and to provide traceability among different models. Third, based on consistency relations and navigational information about how elements are related, tools can provide guidance, specifically completion or assistance. Model completion can for instance be provided in a generic manner across domain-specific tools.
=== Evaluation of the coordination method ===
The coordination method can best be seen as a conceptual framework that prescribes a certain workflow when working with multiple languages. The three successive steps that constitute this workflow are not supported by an integrated workbench or development environment. The focus is rather on extending the developer's existing environments to add support for (1) identification, (2) specification, and (3) application. The main advantage of this approach has been that developers have actually tested our work and given us feedback. This kind of evaluation of the method is valuable because it reduces the risk of solving a purely hypothetical problem. Several papers introduce the different steps of the coordination method, report on this evaluation, and elaborates on the technical aspects of each individual experiment. Overall, the results have been promising: a significant number of errors have been found in production systems and given rise to a constructive dialog with developers on future tool requirements. A development process based on these guidelines and supported by tools constitutes a serious attempt to solve the coordination problem and make domain-specific multimodeling a practical proposition.
== See also ==
Domain-specific language
Domain-specific modeling
Model-driven engineering
== References == | Wikipedia/Domain-specific_multimodeling |
Eclipse Modeling Framework (EMF) is an Eclipse-based modeling framework and code generation facility for building tools and other applications based on a structured data model.
From a model specification described in XML Metadata Interchange (XMI), EMF provides tools and runtime support to produce a set of Java classes for the model, a set of adapter classes that enable viewing and command-based editing of the model, and a basic editor. Models can be specified using annotated Java, UML, XML documents, or modeling tools, then imported into EMF. Most important of all, EMF provides the foundation for interoperability with other EMF-based tools and applications.
== Ecore ==
Ecore is the core (meta-)model at the heart of EMF. It allows expressing other models by leveraging its constructs. Ecore is also its own metamodel (i.e.: Ecore is defined in terms of itself).
According to Ed Merks, EMF project lead, "Ecore is the defacto reference implementation of OMG's EMOF" (Essential Meta-Object Facility). Still according to Merks, EMOF was actually defined by OMG as a simplified version of the more comprehensive 'C'MOF by drawing on the experience of the successful simplification of Ecore's original implementation.
Using Ecore as a foundational meta-model allows a modeler to take advantage of the entire EMF ecosystem and tooling - in as much as it's then reasonably easy to map application-level models back to Ecore. This isn't to say that it's best practice for applications to directly leverage Ecore as their metamodel; rather they might consider defining their own metamodels based on Ecore.
== See also ==
Acceleo, a code generator using EMF models in input
ATL, a model transformation language
Connected Data Objects (CDO), a free implementation of a Distributed Shared Model on top of EMF
Generic Eclipse Modeling System (GEMS)
Graphical Modeling Framework (GMF)
List of EMF based software
Model-driven architecture
Xtext
== References ==
== External links ==
EMF project page | Wikipedia/Eclipse_Modeling_Framework |
Story-driven modeling is an object-oriented modeling technique. Other forms of object-oriented modeling focus on class diagrams.
Class diagrams describe the static structure of a program, i.e. the building blocks of a program and how they relate to each other.
Class diagrams also model data structures, but with an emphasis on rather abstract concepts like types and type features.
Instead of abstract static structures, story-driven modeling focuses on concrete example scenarios and on how the steps of the example scenarios
may be represented as object diagrams and how these object diagrams evolve during scenario execution.
== Software development approach ==
Story-driven modeling proposes the following software development approach:
Textual scenarios: For the feature you want to implement, develop a textual scenario description for the most common case. Look on only one example at a time. Try to use specific terms and individual names instead of general terms and e.g. role names:
Scenario Go-Dutch barbecue
Start: This Sunday Peter, Putri, and Peng meet at the park for a go-Dutch barbecue. They use the Group Account app to do the accounting.
Step 1: Peter brings the meat for $12. Peter adds this item to the Group Account app.
Step 2: Putri brings salad for $9. Peter adds this item, too. The app shows that by now the average share is $7 and that Peng still have to bring these $7 while Peter gets $5 out and Putri gets $2 out.
Step 3: ...
GUI mock-ups: To illustrate the graphical user interface (GUI) for the desired feature, you may add some wireframe models or GUI mock-ups to your scenario:
Scenario Go-Dutch barbecue
Start: This Sunday Peter, Putri, and Peng meet at the park for a go-Dutch barbecue. They use the Group Account app to do the accounting.
Step 1: Peter brings the meat for $12. Peter adds this item to the Group Account app.
Step 2: Putri brings salad for $9. Peter adds this item, too. The app shows that by now the average share is $7 and that Peng still have to bring these $7 while Peter gets $5 out and Putri gets $2 out:
Step 3: ...
Storyboarding: Next, you think about how a certain situation, i.e. a certain step of a scenario may be represented within a computer by a runtime object structure. This is done by adding object diagrams to the scenario. In story driven modeling, a scenario with object diagrams is also called a storyboard.
Scenario Go-Dutch barbecue
Start: This Sunday Peter, Putri, and Peng meet at the park for a go-Dutch barbecue. They use the Group Account app to do the accounting.
Step 1: Peter brings the meat for $12. Peter adds this item to the Group Account app.
Step 2: Putri brings salad for $9. Peter adds this item, too. The app shows that by now the average share is $7 and that Peng still have to bring these $7 while Peter gets $5 out and Putri gets $2 out:
Step 3: ...
Class diagram derivation: Now it is fairly straightforward to derive a class diagram from the object diagrams used in the storyboards.Note, the class diagram serves as a common reference for all object diagrams. This ensures that overall the same types and attributes are used. Using a UML tool, you may generate a first implementation from this class diagram.
Algorithm design: So far you have modeled and implemented that object structures that are deployed in your application. Now you need to add behavior, i.e. algorithms and method bodies. Programming the behavior of an application is a demanding task. To facilitate it, you should first outline the behavior in pseudocode notation. You might do this, e.g. with an object game. For example, to update the saldo attributes of all persons you look at our object structure and from the point of view of the GroupAccount object you do the following:
Update the saldo of all persons:
visit each item
for each item add the value to the total value and add 1 to the number of items
compute the average share of each person by dividing the total value by the number of persons
visit each person
for each person reset the saldo
for each person visit each item bought by this person
for each item add the value to the saldo of the current person
for each person subtract the share from the saldo
Behavior implementation: Once you have refined your algorithm pseudocode down to the level of operations on object structures it is straightforward to derive source code that executes the same operations on your object model implementation.
Testing: Finally, the scenarios may be used to derive automatic JUnit tests. The pseudocode for a test for our example might look like:
Test update the saldo of all persons:
create a group account object
add a person object with name Peter and a person object with name Putri and a person object with name Peng to the group account object
add an item object with buyer Peter, description Meat, and value $12 to the group account object
add an item object with buyer Putri, description Salad, and value $9 to the group account object
call method update the saldo of all persons on the group account object
ensure that the saldo of the Peter object is $5
ensure that the saldo of the Putri object is $2
ensure that the saldo of the Peter object is -$7
ensure that the sum of all saldos is $0
Such automatic tests ensure that in the example situation the behavior implementation actually does what is outlined in the storyboard. While these tests are pretty simple and may not identify all kinds of bugs, these tests are very useful to document the desired behavior and the usage of the new features and these tests ensure that the corresponding functionality is not lost due to future changes.
== Summary ==
Story driven modeling has proven to work very well for the cooperation with non IT experts. People from other domains usually have difficulties to describe their needs in general terms (i.e. classes) and general rules (pseudocode). Similarly, normal people have problems to understand pseudocode or to judge, whether their needs are properly addressed or not. However, these people know their business very well and with the help of concrete examples and scenarios it is very easy for normal people to spot problematic cases and to judge whether their needs have been addressed properly.
Story Driven Modeling has matured since its beginning in 1997. In 2013 it is used for teaching e.g. in Kassel University, Paderborn University, Tartu University, Antwerp University, Nazarbayev University Astana, Hasso Platner Institute Potsdam, University of Victoria, ...
== See also ==
Agile modeling
Entity–control–boundary
Agile software development
Class-responsibility-collaboration card
Object-oriented analysis and design
Object-oriented modeling
Test-driven development
Unified Modeling Language
== References == | Wikipedia/Story-driven_modeling |
In cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output. The transformation is "one-way", meaning that it is difficult given a particular output to compute inputs which compress to that output. One-way compression functions are not related to conventional data compression algorithms, which instead can be inverted exactly (lossless compression) or approximately (lossy compression) to the original data.
One-way compression functions are for instance used in the Merkle–Damgård construction inside cryptographic hash functions.
One-way compression functions are often built from block ciphers.
Some methods to turn any normal block cipher into a one-way compression function are Davies–Meyer, Matyas–Meyer–Oseas, Miyaguchi–Preneel (single-block-length compression functions) and MDC-2/Meyer–Schilling, MDC-4, Hirose (double-block-length compression functions). These methods are described in detail further down. (MDC-2 is also the name of a hash function patented by IBM.)
Another method is 2BOW (or NBOW in general), which is a "high-rate multi-block-length hash function based on block ciphers" and typically achieves (asymptotic) rates between 1 and 2 independent of the hash size (only with small constant overhead). This method has not yet seen any serious security analysis, so should be handled with care.
== Compression ==
A compression function mixes two fixed length inputs and produces a single fixed length output of the same size as one of the inputs. This can also be seen as that the compression function transforms one large fixed-length input into a shorter, fixed-length output.
For instance, input A might be 128 bits, input B 128 bits and they are compressed together to a single output of 128 bits. This is equivalent to having a single 256-bit input compressed to a single output of 128 bits.
Some compression functions do not compress by half, but instead by some other factor. For example, input A might be 256 bits, and input B 128 bits, which are compressed to a single output of 128 bits. That is, a total of 384 input bits are compressed together to 128 output bits.
The mixing is done in such a way that full avalanche effect is achieved. That is, every output bit depends on every input bit.
== One-way ==
A one-way function is a function that is easy to compute but hard to invert. A one-way compression function (also called hash function) should have the following properties:
Easy to compute: If you have some input(s), it is easy to calculate the output.
Preimage-resistance: If an attacker only knows the output it should be infeasible to calculate an input. In other words, given an output
h
{\displaystyle h}
, it should be unfeasible to calculate an input
m
{\displaystyle m}
such that
hash
(
m
)
=
h
{\displaystyle \operatorname {hash} (m)=h}
.
Second preimage-resistance: Given an input
m
1
{\displaystyle m_{1}}
whose output is
h
{\displaystyle h}
, it should be infeasible to find another input
m
2
{\displaystyle m_{2}}
that has the same output
h
{\displaystyle h}
, i.e.
hash
(
m
1
)
=
hash
(
m
2
)
{\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}
.
Collision-resistance: It should be hard to find any two different inputs that compress to the same output i.e. an attacker should not be able to find a pair of messages
m
1
≠
m
2
{\displaystyle m_{1}\neq m_{2}}
such that
hash
(
m
1
)
=
hash
(
m
2
)
{\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}
. Due to the birthday paradox (see also birthday attack) there is a 50% chance a collision can be found in time of about
2
n
/
2
{\displaystyle 2^{n/2}}
where
n
{\displaystyle n}
is the number of bits in the hash function's output. An attack on the hash function thus should not be able to find a collision with less than about
2
n
/
2
{\displaystyle 2^{n/2}}
work.
Ideally one would like the "infeasibility" in preimage-resistance and second preimage-resistance to mean a work of about
2
n
{\displaystyle 2^{n}}
where
n
{\displaystyle n}
is the number of bits in the hash function's output. However, particularly for second preimage-resistance this is a difficult problem.
== The Merkle–Damgård construction ==
A common use of one-way compression functions is in the Merkle–Damgård construction inside cryptographic hash functions. Most widely used hash functions, including MD5, SHA-1 (which is deprecated) and SHA-2 use this construction.
A hash function must be able to process an arbitrary-length message into a fixed-length output. This can be achieved by breaking the input up into a series of equal-sized blocks, and operating on them in sequence using a one-way compression function. The compression function can either be specially designed for hashing or be built from a block cipher. The last block processed should also be length padded, which is crucial to the security of this construction.
When length padding (also called MD-strengthening) is applied, attacks cannot find collisions faster than the birthday paradox (
2
n
/
2
{\displaystyle 2^{n/2}}
,
n
{\displaystyle n}
being the block size in bits) if the used function
f
{\displaystyle f}
is collision-resistant. Hence, the Merkle–Damgård hash construction reduces the problem of finding a proper hash function to finding a proper compression function.
A second preimage attack (given a message
m
1
{\displaystyle m_{1}}
an attacker finds another message
m
2
{\displaystyle m_{2}}
to satisfy
hash
(
m
1
)
=
hash
(
m
2
)
{\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}
can be done according to Kelsey and Schneier for a
2
k
{\displaystyle 2^{k}}
-message-block message in time
k
×
2
n
/
2
+
1
+
2
n
−
k
+
1
{\displaystyle k\times 2^{n/2+1}+2^{n-k+1}}
. The complexity of this attack reaches a minimum of
2
3
n
/
4
+
2
{\displaystyle 2^{3n/4+2}}
for long messages when
k
=
2
n
/
4
{\displaystyle k=2^{n/4}}
and approaches
2
n
{\displaystyle 2^{n}}
when messages are short.
== Construction from block ciphers ==
One-way compression functions are often built from block ciphers.
Block ciphers take (like one-way compression functions) two fixed size inputs (the key and the plaintext) and return one single output (the ciphertext) which is the same size as the input plaintext.
However, modern block ciphers are only partially one-way. That is, given a plaintext and a ciphertext it is infeasible to find a key that encrypts the plaintext to the ciphertext. But, given a ciphertext and a key a matching plaintext can be found simply by using the block cipher's decryption function. Thus, to turn a block cipher into a one-way compression function some extra operations have to be added.
Some methods to turn any normal block cipher into a one-way compression function are Davies–Meyer, Matyas–Meyer–Oseas, Miyaguchi–Preneel (single-block-length compression functions) and MDC-2, MDC-4, Hirose (double-block-length compressions functions).
Single-block-length compression functions output the same number of bits as processed by the underlying block cipher. Consequently, double-block-length compression functions output twice the number of bits.
If a block cipher has a block size of say 128 bits single-block-length methods create a hash function that has the block size of 128 bits and produces a hash of 128 bits. Double-block-length methods make hashes with double the hash size compared to the block size of the block cipher used. So a 128-bit block cipher can be turned into a 256-bit hash function.
These methods are then used inside the Merkle–Damgård construction to build the actual hash function. These methods are described in detail further down.
Using a block cipher to build the one-way compression function for a hash function is usually somewhat slower than using a specially designed one-way compression function in the hash function. This is because all known secure constructions do the key scheduling for each block of the message. Black, Cochran and Shrimpton have shown that it is impossible to construct a one-way compression function that makes only one call to a block cipher with a fixed key. In practice reasonable speeds are achieved provided the key scheduling of the selected block cipher is not a too heavy operation.
But, in some cases it is easier because a single implementation of a block cipher can be used for both a block cipher and a hash function. It can also save code space in very tiny embedded systems like for instance smart cards or nodes in cars or other machines.
Therefore, the hash-rate or rate gives a glimpse of the efficiency of a hash function based on a certain compression function. The rate of an iterated hash function outlines the ratio between the number of block cipher operations and the output. More precisely, the rate represents the ratio between the number of processed bits of input
m
{\displaystyle m}
, the output bit-length
n
{\displaystyle n}
of the block cipher, and the necessary block cipher operations
s
{\displaystyle s}
to produce these
n
{\displaystyle n}
output bits. Generally, the usage of fewer block cipher operations results in a better overall performance of the entire hash function, but it also leads to a smaller hash-value which could be undesirable. The rate is expressed by the formula:
R
h
=
|
m
i
|
s
⋅
n
{\displaystyle R_{h}={\frac {\left|m_{i}\right|}{s\cdot n}}}
The hash function can only be considered secure if at least the following conditions are met:
The block cipher has no special properties that distinguish it from ideal ciphers, such as weak keys or keys that lead to identical or related encryptions (fixed points or key-collisions).
The resulting hash size is big enough. According to the birthday attack a security level of 280 (generally assumed to be infeasible to compute today) is desirable thus the hash size should be at least 160 bits.
The last block is properly length padded prior to the hashing. (See Merkle–Damgård construction.) Length padding is normally implemented and handled internally in specialised hash functions like SHA-1 etc.
The constructions presented below: Davies–Meyer, Matyas–Meyer–Oseas, Miyaguchi–Preneel and Hirose have been shown to be secure under the black-box analysis. The goal is to show that any attack that can be found is at most as efficient as the birthday attack under certain assumptions. The black-box model assumes that a block cipher is used that is randomly chosen from a set containing all appropriate block ciphers. In this model an attacker may freely encrypt and decrypt any blocks, but does not have access to an implementation of the block cipher. The encryption and decryption function are represented by oracles that receive a pair of either a plaintext and a key or a ciphertext and a key. The oracles then respond with a randomly chosen plaintext or ciphertext, if the pair was asked for the first time. They both share a table for these triplets, a pair from the query and corresponding response, and return the record, if a query was received for the second time. For the proof there is a collision finding algorithm that makes randomly chosen queries to the oracles. The algorithm returns 1, if two responses result in a collision involving the hash function that is built from a compression function applying this block cipher (0 else). The probability that the algorithm returns 1 is dependent on the number of queries which determine the security level.
== Davies–Meyer ==
The Davies–Meyer single-block-length compression function feeds each block of the message (
m
i
{\displaystyle m_{i}}
) as the key to a block cipher. It feeds the previous hash value (
H
i
−
1
{\displaystyle H_{i-1}}
) as the plaintext to be encrypted. The output ciphertext is then also XORed (⊕) with the previous hash value (
H
i
−
1
{\displaystyle H_{i-1}}
) to produce the next hash value (
H
i
{\displaystyle H_{i}}
). In the first round when there is no previous hash value it uses a constant pre-specified initial value (
H
0
{\displaystyle H_{0}}
).
In mathematical notation Davies–Meyer can be described as:
H
i
=
E
m
i
(
H
i
−
1
)
⊕
H
i
−
1
{\displaystyle H_{i}=E_{m_{i}}{(H_{i-1})}\oplus {H_{i-1}}}
The scheme has the rate (k is the keysize):
R
D
M
=
k
1
⋅
n
=
k
n
{\displaystyle R_{DM}={\frac {k}{1\cdot n}}={\frac {k}{n}}}
If the block cipher uses for instance 256-bit keys then each message block (
m
i
{\displaystyle m_{i}}
) is a 256-bit chunk of the message. If the same block cipher uses a block size of 128 bits then the input and output hash values in each round is 128 bits.
Variations of this method replace XOR with any other group operation, such as addition on 32-bit unsigned integers.
A notable property of the Davies–Meyer construction is that even if the underlying block cipher is totally secure, it is possible to compute fixed points for the construction: for any
m
{\displaystyle m}
, one can find a value of
h
{\displaystyle h}
such that
E
m
(
h
)
⊕
h
=
h
{\displaystyle E_{m}(h)\oplus h=h}
: one just has to set
h
=
E
m
−
1
(
0
)
{\displaystyle h=E_{m}^{-1}(0)}
. This is a property that random functions certainly do not have. So far, no practical attack has been based on this property, but one should be aware of this "feature". The fixed-points can be used in a second preimage attack (given a message
m
1
{\displaystyle m_{1}}
, attacker finds another message
m
2
{\displaystyle m_{2}}
to satisfy
hash
(
m
1
)
=
hash
(
m
2
)
{\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}
) of Kelsey and Schneier for a
2
k
{\displaystyle 2^{k}}
-message-block message in time
3
×
2
n
/
2
+
1
+
2
n
−
k
+
1
{\displaystyle 3\times 2^{n/2+1}+2^{n-k+1}}
. If the construction does not allow easy creation of fixed points (like Matyas–Meyer–Oseas or Miyaguchi–Preneel) then this attack can be done in
k
×
2
n
/
2
+
1
+
2
n
−
k
+
1
{\displaystyle k\times 2^{n/2+1}+2^{n-k+1}}
time. In both cases the complexity is above
2
n
/
2
{\displaystyle 2^{n/2}}
but below
2
n
{\displaystyle 2^{n}}
when messages are long and that when messages get shorter the complexity of the attack approaches
2
n
{\displaystyle 2^{n}}
.
The security of the Davies–Meyer construction in the Ideal Cipher Model was first proven by R. Winternitz.
== Matyas–Meyer–Oseas ==
The Matyas–Meyer–Oseas single-block-length one-way compression function can be considered the dual (the opposite) of Davies–Meyer.
It feeds each block of the message (
m
i
{\displaystyle m_{i}}
) as the plaintext to be encrypted. The output ciphertext is then also XORed (⊕) with the same message block (
m
i
{\displaystyle m_{i}}
) to produce the next hash value (
H
i
{\displaystyle H_{i}}
). The previous hash value (
H
i
−
1
{\displaystyle H_{i-1}}
) is fed as the key to the block cipher. In the first round when there is no previous hash value it uses a constant pre-specified initial value (
H
0
{\displaystyle H_{0}}
).
If the block cipher has different block and key sizes the hash value (
H
i
−
1
{\displaystyle H_{i-1}}
) will have the wrong size for use as the key. The cipher might also have other special requirements on the key. Then the hash value is first fed through the function
g
{\displaystyle g}
to be converted/padded to fit as key for the cipher.
In mathematical notation Matyas–Meyer–Oseas can be described as:
H
i
=
E
g
(
H
i
−
1
)
(
m
i
)
⊕
m
i
{\displaystyle H_{i}=E_{g(H_{i-1})}(m_{i})\oplus m_{i}}
The scheme has the rate:
R
M
M
O
=
n
1
⋅
n
=
1
{\displaystyle R_{MMO}={\frac {n}{1\cdot n}}=1}
A second preimage attack (given a message
m
1
{\displaystyle m_{1}}
an attacker finds another message
m
2
{\displaystyle m_{2}}
to satisfy
hash
(
m
1
)
=
hash
(
m
2
)
{\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}
) can be done according to Kelsey and Schneier for a
2
k
{\displaystyle 2^{k}}
-message-block message in time
k
×
2
n
/
2
+
1
+
2
n
−
k
+
1
{\displaystyle k\times 2^{n/2+1}+2^{n-k+1}}
. The complexity is above
2
n
/
2
{\displaystyle 2^{n/2}}
but below
2
n
{\displaystyle 2^{n}}
when messages are long, and that when messages get shorter the complexity of the attack approaches
2
n
{\displaystyle 2^{n}}
.
== Miyaguchi–Preneel ==
The Miyaguchi–Preneel single-block-length one-way compression function is an extended variant of Matyas–Meyer–Oseas. It was independently proposed by Shoji Miyaguchi and Bart Preneel.
It feeds each block of the message (
m
i
{\displaystyle m_{i}}
) as the plaintext to be encrypted. The output ciphertext is then XORed (⊕) with the same message block (
m
i
{\displaystyle m_{i}}
) and then also XORed with the previous hash value (
H
i
−
1
{\displaystyle H_{i-1}}
) to produce the next hash value (
H
i
{\displaystyle H_{i}}
). The previous hash value (
H
i
−
1
{\displaystyle H_{i-1}}
) is fed as the key to the block cipher. In the first round when there is no previous hash value it uses a constant pre-specified initial value (
H
0
{\displaystyle H_{0}}
).
If the block cipher has different block and key sizes the hash value (
H
i
−
1
{\displaystyle H_{i-1}}
) will have the wrong size for use as the key. The cipher might also have other special requirements on the key. Then the hash value is first fed through the function
g
{\displaystyle g}
to be converted/padded to fit as key for the cipher.
In mathematical notation Miyaguchi–Preneel can be described as:
H
i
=
E
g
(
H
i
−
1
)
(
m
i
)
⊕
H
i
−
1
⊕
m
i
{\displaystyle H_{i}=E_{g(H_{i-1})}(m_{i})\oplus H_{i-1}\oplus m_{i}}
The scheme has the rate:
R
M
P
=
n
1
⋅
n
=
1
{\displaystyle R_{MP}={\frac {n}{1\cdot n}}=1}
The roles of
m
i
{\displaystyle m_{i}}
and
H
i
−
1
{\displaystyle H_{i-1}}
may be switched, so that
H
i
−
1
{\displaystyle H_{i-1}}
is encrypted under the key
m
i
{\displaystyle m_{i}}
, thus making this method an extension of Davies–Meyer instead.
A second preimage attack (given a message
m
1
{\displaystyle m_{1}}
an attacker finds another message
m
2
{\displaystyle m_{2}}
to satisfy
hash
(
m
1
)
=
hash
(
m
2
)
{\displaystyle \operatorname {hash} (m_{1})=\operatorname {hash} (m_{2})}
) can be done according to Kelsey and Schneier for a
2
k
{\displaystyle 2^{k}}
-message-block message in time
k
×
2
n
/
2
+
1
+
2
n
−
k
+
1
{\displaystyle k\times 2^{n/2+1}+2^{n-k+1}}
. The complexity is above
2
n
/
2
{\displaystyle 2^{n/2}}
but below
2
n
{\displaystyle 2^{n}}
when messages are long, and that when messages get shorter the complexity of the attack approaches
2
n
{\displaystyle 2^{n}}
.
== Hirose ==
The Hirose double-block-length one-way compression function consists of a block cipher plus a permutation
p
{\displaystyle p}
. It was proposed by Shoichi Hirose in 2006 and is based on a work by Mridul Nandi.
It uses a block cipher whose key length
k
{\displaystyle k}
is larger than the block length
n
{\displaystyle n}
, and produces a hash of size
2
n
{\displaystyle 2n}
. For example, any of the AES candidates with a 192- or 256-bit key (and 128-bit block).
Each round accepts a portion of the message
m
i
{\displaystyle m_{i}}
that is
k
−
n
{\displaystyle k-n}
bits long, and uses it to update two
n
{\displaystyle n}
-bit state values
G
{\displaystyle G}
and
H
{\displaystyle H}
.
First,
m
i
{\displaystyle m_{i}}
is concatenated with
H
i
−
1
{\displaystyle H_{i-1}}
to produce a key
K
i
{\displaystyle K_{i}}
. Then the two feedback values are updated according to:
G
i
=
E
K
i
(
G
i
−
1
)
⊕
G
i
−
1
{\displaystyle G_{i}=E_{K_{i}}(G_{i-1})\oplus G_{i-1}}
H
i
=
E
K
i
(
p
(
G
i
−
1
)
)
⊕
p
(
G
i
−
1
)
{\displaystyle H_{i}=E_{K_{i}}(p(G_{i-1}))\oplus p(G_{i-1})}
p
(
G
i
−
1
)
{\displaystyle p(G_{i-1})}
is an arbitrary fixed-point-free permutation on an
n
{\displaystyle n}
-bit value, typically defined as
p
(
x
)
=
x
⊕
c
{\displaystyle p(x)=x\oplus c}
for an arbitrary non-zero constant
c
{\displaystyle c}
(all ones may be a convenient choice).
Each encryption resembles the standard Davies–Meyer construction. The advantage of this scheme over other proposed double-block-length schemes is that both encryptions use the same key, and thus key scheduling effort may be shared.
The final output is
H
t
|
|
G
t
{\displaystyle H_{t}||G_{t}}
. The scheme has the rate
R
H
i
r
o
s
e
=
k
−
n
2
n
{\textstyle R_{Hirose}={\frac {k-n}{2n}}}
relative to encrypting the message with the cipher.
Hirose also provides a proof in the Ideal Cipher Model.
== Sponge construction ==
The sponge construction can be used to build one-way compression functions.
== See also ==
Whirlpool — A cryptographic hash function built using the Miyaguchi–Preneel construction and a block cipher similar to Square and AES.
CBC-MAC, OMAC, and PMAC — Methods to turn block ciphers into message authentication codes (MACs).
== References ==
=== Citations ===
=== Sources === | Wikipedia/One-way_compression_function |
In cryptography, cryptographic hash functions can be divided into two main categories. In the first category are those functions whose designs are based on mathematical problems, and whose security thus follows from rigorous mathematical proofs, complexity theory and formal reduction. These functions are called provably secure cryptographic hash functions. To construct these is very difficult, and few examples have been introduced. Their practical use is limited.
In the second category are functions which are not based on mathematical problems, but on an ad-hoc constructions, in which the bits of the message are mixed to produce the hash. These are then believed to be hard to break, but no formal proof is given. Almost all hash functions in widespread use reside in this category. Some of these functions are already broken, and are no longer in use. See Hash function security summary.
== Types of security of hash functions ==
Generally, the basic security of cryptographic hash functions can be seen from different angles: pre-image resistance, second pre-image resistance, collision resistance, and pseudo-randomness.
Pre-image resistance: given a hash h, it should be hard to find any message m such that h = hash(m). This concept is related to that of the one-way function. Functions that lack this property are vulnerable to pre-image attacks.
Second pre-image resistance: given an input m1, it should be hard to find another input m2 ≠ m1 such that hash(m1) = hash(m2). This property is sometimes referred to as weak collision resistance. Functions that lack this property are vulnerable to second pre-image attacks.
Collision resistance: it should be hard to find two different messages m1 and m2 such that hash(m1) = hash(m2). Such a pair is called a (cryptographic) hash collision. This property is sometimes referred to as strong collision resistance. It requires a hash value at least twice as long as what is required for pre-image resistance; otherwise, collisions may be found by a birthday attack.
Pseudo-randomness: it should be hard to distinguish a pseudo-random number generator based on the hash function from true random number generator; for example, it passes usual randomness tests.
=== The meaning of hard ===
The basic question is the meaning of hard. There are two approaches to answer this question. First is the intuitive/practical approach: "hard means that it is almost certainly beyond the reach of any adversary who must be prevented from breaking the system for as long as the security of the system is deemed important." The second approach is theoretical and is based on the computational complexity theory: if problem A is hard, then there exists a formal security reduction from a problem which is widely considered unsolvable in polynomial time, such as integer factorization or the discrete logarithm problem.
However, non-existence of a polynomial time algorithm does not automatically ensure that the system is secure. The difficulty of a problem also depends on its size. For example, RSA public-key cryptography (which relies on the difficulty of integer factorization) is considered secure only with keys that are at least 2048 bits long, whereas keys for the ElGamal cryptosystem (which relies on the difficulty of the discrete logarithm problem) are commonly in the range of 256–512 bits.
=== Password case ===
If the set of inputs to the hash is relatively small or is ordered by likelihood in some way, then a brute force search may be practical, regardless of theoretical security. The likelihood of recovering the preimage depends on the input set size and the speed or cost of computing the hash function. A common example is the use of hashes to store password validation data. Rather than store the plaintext of user passwords, an access control system typically stores a hash of the password. When a person requests access, the password they submit is hashed and compared with the stored value. If the stored validation data is stolen, then the thief will only have the hash values, not the passwords. However, most users choose passwords in predictable ways, and passwords are often short enough so that all possible combinations can be tested if fast hashes are used. Special hashes called key derivation functions have been created to slow searches. See Password cracking.
== Cryptographic hash functions ==
Most hash functions are built on an ad-hoc basis, where the bits of the message are nicely mixed to produce the hash. Various bitwise operations (e.g. rotations), modular additions, and compression functions are used in iterative mode to ensure high complexity and pseudo-randomness of the output. In this way, the security is very hard to prove and the proof is usually not done. Only a few years ago, one of the most popular hash functions, SHA-1, was shown to be less secure than its length suggested: collisions could be found in only 251 tests, rather than the brute-force number of 280.
In other words, most of the hash functions in use nowadays are not provably collision-resistant. These hashes are not based on purely mathematical functions. This approach results generally in more effective hashing functions, but with the risk that a weakness of such a function will be eventually used to find collisions. One famous case is MD5.
== Provably secure hash functions ==
In this approach, the security of a hash function is based on some hard mathematical problem, and it is proved that finding collisions of the hash function is as hard as breaking the underlying problem. This gives a somewhat stronger notion of security than just relying on complex mixing of bits as in the classical approach.
A cryptographic hash function has provable security against collision attacks if finding collisions is provably polynomial-time reducible from a problem P which is supposed to be unsolvable in polynomial time. The function is then called provably secure, or just provable.
It means that if finding collisions would be feasible in polynomial time by algorithm A, then one could find and use polynomial time algorithm R (reduction algorithm) that would use algorithm A to solve problem P, which is widely supposed to be unsolvable in polynomial time. That is a contradiction. This means that finding collisions cannot be easier than solving P.
However, this only indicates that finding collisions is difficult in some cases, as not all instances of a computationally hard problem are typically hard. Indeed, very large instances of NP-hard problems are routinely solved, while only the hardest are practically impossible to solve.
=== Hard problems ===
Examples of problems that are assumed to be not solvable in polynomial time include
Discrete logarithm
Modular square roots
Integer factorization
Subset sum
=== Downsides of the provable approach ===
Current collision-resistant hash algorithms that have provable security reductions are too inefficient to be used in practice. In comparison to classical hash functions, they tend to be relatively slow and do not always meet all of criteria traditionally expected of cryptographic hashes. Very smooth hash is an example.
Constructing a hash function with provable security is much more difficult than using a classical approach where one just hopes that the complex mixing of bits in the hashing algorithm is strong enough to prevent adversary from finding collisions.
The proof is often a reduction to a problem with asymptotically hard worst-case or average-case complexity. Worst-case complexity measures the difficulty of solving pathological cases rather than typical cases of the underlying problem. Even a reduction to a problem with hard average-case complexity offers only limited security, as there still can be an algorithm that easily solves the problem for a subset of the problem space. For example, early versions of Fast Syndrome Based Hash turned out to be insecure. This problem was solved in the latest version.
SWIFFT is an example of a hash function that circumvents these security problems. It can be shown that, for any algorithm that can break SWIFFT with probability p within an estimated time t, one can find an algorithm that solves the worst-case scenario of a certain difficult mathematical problem within time t′ depending on t and p.
=== Example of (impractical) provably secure hash function ===
Let hash(m) = xm mod n, where n is a hard-to-factor composite number, and x is some prespecified base value. A collision xm1 ≡ xm2 (mod n) reveals a multiple m1 − m2 of the multiplicative order of x modulo n. This information can be used to factor n in polynomial time, assuming certain properties of x.
But the algorithm is quite inefficient because it requires on average 1.5 multiplications modulo n per message-bit.
=== More practical provably secure hash functions ===
VSH—Very Smooth Hash—a provably secure collision-resistant hash function assuming the hardness of finding nontrivial modular square roots modulo composite number n (this is proven to be as hard as factoring n).
MuHASH
ECOH—Elliptic Curve Only hash function—based on the concept of elliptic curves, the subset sum problem, and summation of polynomials. The security proof of the collision resistance was based on weakened assumptionsm, and eventually a second pre-image attack was found.
FSB—Fast Syndrome-Based hash function—it can be proven that breaking FSB is at least as difficult as solving regular syndrome decoding, which is known to be NP-complete.
SWIFFT—SWIFFT is based on the fast Fourier transform and is provably collision resistant, under a relatively mild assumption about the worst-case difficulty of finding short vectors in cyclic/ideal lattices.
Chaum, van Heijst, Pfitzmann hash function—a compression function where finding collisions is as hard as solving the discrete logarithm problem in a finite group F2p+1.
Knapsack-based hash functions—a family of hash functions based on the knapsack problem.
The Zémor-Tillich hash function—a family of hash functions that relies on the arithmetic of the group of matrices SL2. Finding collisions is at least as difficult as finding factorization of certain elements in this group. This is supposed to be hard, at least PSPACE-complete. For this hash, an attack was eventually discovered with a time complexity close to 2n/2. This beat by far the birthday bound and ideal pre-image complexities, which are 23n/2 and 23n for the Zémor-Tillich hash function. As the attacks include a birthday search in a reduced set of size 2n, they indeed do not destroy the idea of provable security or invalidate the scheme but rather suggest that the initial parameters were too small.
Hash functions from Sigma Protocols—there exists a general way of constructing a provably secure hash, specifically from any (suitable) sigma protocol. A faster version of VSH (called VSH*) could be obtained in this way.
== References == | Wikipedia/Provably_secure_cryptographic_hash_function |
The non-cryptographic hash functions (NCHFs) are hash functions intended for applications that do not need the rigorous security requirements of the cryptographic hash functions (e.g., preimage resistance) and therefore can be faster and less resource-intensive. Typical examples of CPU-optimized non-cryptographic hashes include FNV-1a and Murmur3. Some non-cryptographic hash functions are used in cryptographic applications (usually in combination with other cryptographic primitives); in this case they are described as universal hash functions.
== Applications and requirements ==
Among the typical uses of non-cryptographic hash functions are bloom filters, hash tables, and count sketches. These applications require, in addition to speed, uniform distribution and avalanche properties. Collision resistance is an additional feature that can be useful against hash flooding attacks; simple NCHFs, like the cyclic redundancy check (CRC), have essentially no collision resistance and thus cannot be used with an input open to manipulation by an attacker.
NCHFs are used in diverse systems: lexical analyzers, compilers, databases, communication networks, video games, DNS servers, filesystems—anywhere in computing where there is a need to find the information very quickly (preferably in the O(1) time, which will also achieve perfect scalability).
Estébanez et al. list the "most important" NCHFs:
The Fowler–Noll–Vo hash function (FNV) was created by Glenn Fowler and Phong Vo in 1991 with contributions from Landon Curt Noll. FNV with its two variants, FNV-1 and FNV-1a, is very widely used in Linux, FreeBSD OSes, DNS servers, NFS, Twitter, PlayStation 2, and Xbox, among others.
lookup3 was created by Robert Jenkins. This hash is also widely used and can be found in PostgreSQL, Linux, Perl, Ruby, and Infoseek.
SuperFastHash was created by Paul Hsieh using ideas from FNV and lookup3, with one of the goals being a high degree of avalanche effect. The hash is used in WebKit (part of Safari and Google Chrome).
MurmurHash2 was created by Austin Appleby in 2008 and is used in libmemcached, Maatkit, and Apache Hadoop.
DJBX33A ("Daniel J. Bernstein, Times 33 with Addition"). This very simple multiplication-and-addition function was proposed by Daniel J. Bernstein. It is fast and efficient during initialization. Many programming environments based on PHP 5, Python, and ASP.NET use variants of this hash. The hash is easy to flood, exposing the servers.
BuzHash was created by Robert Uzgalis in 1992. It is designed around a substitution table and can tolerate extremely skewed distributions on the input.
DEK is an early multiplicative hash based on a proposal by Donald Knuth and is one of the oldest hashes that is still in use.
== Design ==
Non-cryptographic hash functions optimized for software frequently involve the multiplication operation. Since in-hardware multiplication is resource-intensive and frequency-limiting, ASIC-friendlier designs had been proposed, including SipHash (which has an additional benefit of being able to use a secret key for message authentication), NSGAhash, and XORhash. Although technically lightweight cryptography can be used for the same applications, the latency of its algorithms is usually too high due to a large number of rounds. Sateesan et al. propose using the reduced-round versions of lightweight hashes and ciphers as non-cryptographic hash functions.
Many NCHFs have a relatively small result size (e.g., 64 bits for SipHash or even less): large result size does not increase the performance of the target applications, but slows down the calculation, as more bits need to be generated.
== See also ==
A list of non-cryptographic hash functions
== References ==
== Sources ==
Sateesan, Arish; Biesmans, Jelle; Claesen, Thomas; Vliegen, Jo; Mentens, Nele (April 2023). "Optimized algorithms and architectures for fast non-cryptographic hash functions in hardware" (PDF). Microprocessors and Microsystems. 98: 104782. doi:10.1016/j.micpro.2023.104782. ISSN 0141-9331.
Estébanez, César; Saez, Yago; Recio, Gustavo; Isasi, Pedro (28 January 2013). "Performance of the most common non-cryptographic hash functions" (PDF). Software: Practice and Experience. 44 (6): 681–698. doi:10.1002/spe.2179. ISSN 0038-0644.
Stamp, Mark (8 November 2011). "Non-Cryptographic Hashes". Information Security: Principles and Practice (2 ed.). John Wiley & Sons. ISBN 978-1-118-02796-7. OCLC 1039294381.
Patgiri, Ripon; Nayak, Sabuzima; Muppalaneni, Naresh Babu (25 April 2023). Bloom Filter: A Data Structure for Computer Networking, Big Data, Cloud Computing, Internet of Things, Bioinformatics and Beyond. Academic Press. pp. 37–38. ISBN 978-0-12-823646-8. OCLC 1377693258.
Mittelbach, Arno; Fischlin, Marc (2021). "Non-cryptographic Hashing". The Theory of Hash Functions and Random Oracles. Cham: Springer International Publishing. pp. 303–334. doi:10.1007/978-3-030-63287-8_7. ISBN 978-3-030-63286-1. | Wikipedia/Non-cryptographic_hash_function |
In cryptography, cryptographic hash functions can be divided into two main categories. In the first category are those functions whose designs are based on mathematical problems, and whose security thus follows from rigorous mathematical proofs, complexity theory and formal reduction. These functions are called provably secure cryptographic hash functions. To construct these is very difficult, and few examples have been introduced. Their practical use is limited.
In the second category are functions which are not based on mathematical problems, but on an ad-hoc constructions, in which the bits of the message are mixed to produce the hash. These are then believed to be hard to break, but no formal proof is given. Almost all hash functions in widespread use reside in this category. Some of these functions are already broken, and are no longer in use. See Hash function security summary.
== Types of security of hash functions ==
Generally, the basic security of cryptographic hash functions can be seen from different angles: pre-image resistance, second pre-image resistance, collision resistance, and pseudo-randomness.
Pre-image resistance: given a hash h, it should be hard to find any message m such that h = hash(m). This concept is related to that of the one-way function. Functions that lack this property are vulnerable to pre-image attacks.
Second pre-image resistance: given an input m1, it should be hard to find another input m2 ≠ m1 such that hash(m1) = hash(m2). This property is sometimes referred to as weak collision resistance. Functions that lack this property are vulnerable to second pre-image attacks.
Collision resistance: it should be hard to find two different messages m1 and m2 such that hash(m1) = hash(m2). Such a pair is called a (cryptographic) hash collision. This property is sometimes referred to as strong collision resistance. It requires a hash value at least twice as long as what is required for pre-image resistance; otherwise, collisions may be found by a birthday attack.
Pseudo-randomness: it should be hard to distinguish a pseudo-random number generator based on the hash function from true random number generator; for example, it passes usual randomness tests.
=== The meaning of hard ===
The basic question is the meaning of hard. There are two approaches to answer this question. First is the intuitive/practical approach: "hard means that it is almost certainly beyond the reach of any adversary who must be prevented from breaking the system for as long as the security of the system is deemed important." The second approach is theoretical and is based on the computational complexity theory: if problem A is hard, then there exists a formal security reduction from a problem which is widely considered unsolvable in polynomial time, such as integer factorization or the discrete logarithm problem.
However, non-existence of a polynomial time algorithm does not automatically ensure that the system is secure. The difficulty of a problem also depends on its size. For example, RSA public-key cryptography (which relies on the difficulty of integer factorization) is considered secure only with keys that are at least 2048 bits long, whereas keys for the ElGamal cryptosystem (which relies on the difficulty of the discrete logarithm problem) are commonly in the range of 256–512 bits.
=== Password case ===
If the set of inputs to the hash is relatively small or is ordered by likelihood in some way, then a brute force search may be practical, regardless of theoretical security. The likelihood of recovering the preimage depends on the input set size and the speed or cost of computing the hash function. A common example is the use of hashes to store password validation data. Rather than store the plaintext of user passwords, an access control system typically stores a hash of the password. When a person requests access, the password they submit is hashed and compared with the stored value. If the stored validation data is stolen, then the thief will only have the hash values, not the passwords. However, most users choose passwords in predictable ways, and passwords are often short enough so that all possible combinations can be tested if fast hashes are used. Special hashes called key derivation functions have been created to slow searches. See Password cracking.
== Cryptographic hash functions ==
Most hash functions are built on an ad-hoc basis, where the bits of the message are nicely mixed to produce the hash. Various bitwise operations (e.g. rotations), modular additions, and compression functions are used in iterative mode to ensure high complexity and pseudo-randomness of the output. In this way, the security is very hard to prove and the proof is usually not done. Only a few years ago, one of the most popular hash functions, SHA-1, was shown to be less secure than its length suggested: collisions could be found in only 251 tests, rather than the brute-force number of 280.
In other words, most of the hash functions in use nowadays are not provably collision-resistant. These hashes are not based on purely mathematical functions. This approach results generally in more effective hashing functions, but with the risk that a weakness of such a function will be eventually used to find collisions. One famous case is MD5.
== Provably secure hash functions ==
In this approach, the security of a hash function is based on some hard mathematical problem, and it is proved that finding collisions of the hash function is as hard as breaking the underlying problem. This gives a somewhat stronger notion of security than just relying on complex mixing of bits as in the classical approach.
A cryptographic hash function has provable security against collision attacks if finding collisions is provably polynomial-time reducible from a problem P which is supposed to be unsolvable in polynomial time. The function is then called provably secure, or just provable.
It means that if finding collisions would be feasible in polynomial time by algorithm A, then one could find and use polynomial time algorithm R (reduction algorithm) that would use algorithm A to solve problem P, which is widely supposed to be unsolvable in polynomial time. That is a contradiction. This means that finding collisions cannot be easier than solving P.
However, this only indicates that finding collisions is difficult in some cases, as not all instances of a computationally hard problem are typically hard. Indeed, very large instances of NP-hard problems are routinely solved, while only the hardest are practically impossible to solve.
=== Hard problems ===
Examples of problems that are assumed to be not solvable in polynomial time include
Discrete logarithm
Modular square roots
Integer factorization
Subset sum
=== Downsides of the provable approach ===
Current collision-resistant hash algorithms that have provable security reductions are too inefficient to be used in practice. In comparison to classical hash functions, they tend to be relatively slow and do not always meet all of criteria traditionally expected of cryptographic hashes. Very smooth hash is an example.
Constructing a hash function with provable security is much more difficult than using a classical approach where one just hopes that the complex mixing of bits in the hashing algorithm is strong enough to prevent adversary from finding collisions.
The proof is often a reduction to a problem with asymptotically hard worst-case or average-case complexity. Worst-case complexity measures the difficulty of solving pathological cases rather than typical cases of the underlying problem. Even a reduction to a problem with hard average-case complexity offers only limited security, as there still can be an algorithm that easily solves the problem for a subset of the problem space. For example, early versions of Fast Syndrome Based Hash turned out to be insecure. This problem was solved in the latest version.
SWIFFT is an example of a hash function that circumvents these security problems. It can be shown that, for any algorithm that can break SWIFFT with probability p within an estimated time t, one can find an algorithm that solves the worst-case scenario of a certain difficult mathematical problem within time t′ depending on t and p.
=== Example of (impractical) provably secure hash function ===
Let hash(m) = xm mod n, where n is a hard-to-factor composite number, and x is some prespecified base value. A collision xm1 ≡ xm2 (mod n) reveals a multiple m1 − m2 of the multiplicative order of x modulo n. This information can be used to factor n in polynomial time, assuming certain properties of x.
But the algorithm is quite inefficient because it requires on average 1.5 multiplications modulo n per message-bit.
=== More practical provably secure hash functions ===
VSH—Very Smooth Hash—a provably secure collision-resistant hash function assuming the hardness of finding nontrivial modular square roots modulo composite number n (this is proven to be as hard as factoring n).
MuHASH
ECOH—Elliptic Curve Only hash function—based on the concept of elliptic curves, the subset sum problem, and summation of polynomials. The security proof of the collision resistance was based on weakened assumptionsm, and eventually a second pre-image attack was found.
FSB—Fast Syndrome-Based hash function—it can be proven that breaking FSB is at least as difficult as solving regular syndrome decoding, which is known to be NP-complete.
SWIFFT—SWIFFT is based on the fast Fourier transform and is provably collision resistant, under a relatively mild assumption about the worst-case difficulty of finding short vectors in cyclic/ideal lattices.
Chaum, van Heijst, Pfitzmann hash function—a compression function where finding collisions is as hard as solving the discrete logarithm problem in a finite group F2p+1.
Knapsack-based hash functions—a family of hash functions based on the knapsack problem.
The Zémor-Tillich hash function—a family of hash functions that relies on the arithmetic of the group of matrices SL2. Finding collisions is at least as difficult as finding factorization of certain elements in this group. This is supposed to be hard, at least PSPACE-complete. For this hash, an attack was eventually discovered with a time complexity close to 2n/2. This beat by far the birthday bound and ideal pre-image complexities, which are 23n/2 and 23n for the Zémor-Tillich hash function. As the attacks include a birthday search in a reduced set of size 2n, they indeed do not destroy the idea of provable security or invalidate the scheme but rather suggest that the initial parameters were too small.
Hash functions from Sigma Protocols—there exists a general way of constructing a provably secure hash, specifically from any (suitable) sigma protocol. A faster version of VSH (called VSH*) could be obtained in this way.
== References == | Wikipedia/Security_of_cryptographic_hash_functions |
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were invented repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries.
The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. But often these two terms are used when the random variables are indexed by the integers or an interval of the real line. If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects.
Based on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and branching processes. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications.
== Introduction ==
A stochastic or random process can be defined as a collection of random variables that is indexed by some mathematical set, meaning that each random variable of the stochastic process is uniquely associated with an element in the set. The set used to index the random variables is called the index set. Historically, the index set was some subset of the real line, such as the natural numbers, giving the index set the interpretation of time. Each random variable in the collection takes values from the same mathematical space known as the state space. This state space can be, for example, the integers, the real line or
n
{\displaystyle n}
-dimensional Euclidean space. An increment is the amount that a stochastic process changes between two index values, often interpreted as two points in time. A stochastic process can have many outcomes, due to its randomness, and a single outcome of a stochastic process is called, among other names, a sample function or realization.
=== Classifications ===
A stochastic process can be classified in different ways, for example, by its state space, its index set, or the dependence among the random variables. One common way of classification is by the cardinality of the index set and the state space.
When interpreted as time, if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers, the set of integers, or the natural numbers, then the stochastic process is said to be in discrete time. If the index set is some interval of the real line, then time is said to be continuous. The two types of stochastic processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are considered easier to study because continuous-time processes require more advanced mathematical techniques and knowledge, particularly due to the index set being uncountable. If the index set is the integers, or some subset of them, then the stochastic process can also be called a random sequence.
If the state space is the integers or natural numbers, then the stochastic process is called a discrete or integer-valued stochastic process. If the state space is the real line, then the stochastic process is referred to as a real-valued stochastic process or a process with continuous state space. If the state space is
n
{\displaystyle n}
-dimensional Euclidean space, then the stochastic process is called a
n
{\displaystyle n}
-dimensional vector process or
n
{\displaystyle n}
-vector process.
=== Etymology ===
The word stochastic in English was originally used as an adjective with the definition "pertaining to conjecturing", and stemming from a Greek word meaning "to aim at a mark, guess", and the Oxford English Dictionary gives the year 1662 as its earliest occurrence. In his work on probability Ars Conjectandi, originally published in Latin in 1713, Jakob Bernoulli used the phrase "Ars Conjectandi sive Stochastice", which has been translated to "the art of conjecturing or stochastics". This phrase was used, with reference to Bernoulli, by Ladislaus Bortkiewicz who in 1917 wrote in German the word stochastik with a sense meaning random. The term stochastic process first appeared in English in a 1934 paper by Joseph Doob. For the term and a specific mathematical definition, Doob cited another 1934 paper, where the term stochastischer Prozeß was used in German by Aleksandr Khinchin, though the German term had been used earlier, for example, by Andrei Kolmogorov in 1931.
According to the Oxford English Dictionary, early occurrences of the word random in English with its current meaning, which relates to chance or luck, date back to the 16th century, while earlier recorded usages started in the 14th century as a noun meaning "impetuosity, great speed, force, or violence (in riding, running, striking, etc.)". The word itself comes from a Middle French word meaning "speed, haste", and it is probably derived from a French verb meaning "to run" or "to gallop". The first written appearance of the term random process pre-dates stochastic process, which the Oxford English Dictionary also gives as a synonym, and was used in an article by Francis Edgeworth published in 1888.
=== Terminology ===
The definition of a stochastic process varies, but a stochastic process is traditionally defined as a collection of random variables indexed by some set. The terms random process and stochastic process are considered synonyms and are used interchangeably, without the index set being precisely specified. Both "collection", or "family" are used while instead of "index set", sometimes the terms "parameter set" or "parameter space" are used.
The term random function is also used to refer to a stochastic or random process, though sometimes it is only used when the stochastic process takes real values. This term is also used when the index sets are mathematical spaces other than the real line, while the terms stochastic process and random process are usually used when the index set is interpreted as time, and other terms are used such as random field when the index set is
n
{\displaystyle n}
-dimensional Euclidean space
R
n
{\displaystyle \mathbb {R} ^{n}}
or a manifold.
=== Notation ===
A stochastic process can be denoted, among other ways, by
{
X
(
t
)
}
t
∈
T
{\displaystyle \{X(t)\}_{t\in T}}
,
{
X
t
}
t
∈
T
{\displaystyle \{X_{t}\}_{t\in T}}
,
{
X
t
}
{\displaystyle \{X_{t}\}}
{
X
(
t
)
}
{\displaystyle \{X(t)\}}
or simply as
X
{\displaystyle X}
. Some authors mistakenly write
X
(
t
)
{\displaystyle X(t)}
even though it is an abuse of function notation. For example,
X
(
t
)
{\displaystyle X(t)}
or
X
t
{\displaystyle X_{t}}
are used to refer to the random variable with the index
t
{\displaystyle t}
, and not the entire stochastic process. If the index set is
T
=
[
0
,
∞
)
{\displaystyle T=[0,\infty )}
, then one can write, for example,
(
X
t
,
t
≥
0
)
{\displaystyle (X_{t},t\geq 0)}
to denote the stochastic process.
== Examples ==
=== Bernoulli process ===
One of the simplest stochastic processes is the Bernoulli process, which is a sequence of independent and identically distributed (iid) random variables, where each random variable takes either the value one or zero, say one with probability
p
{\displaystyle p}
and zero with probability
1
−
p
{\displaystyle 1-p}
. This process can be linked to an idealisation of repeatedly flipping a coin, where the probability of obtaining a head is taken to be
p
{\displaystyle p}
and its value is one, while the value of a tail is zero. In other words, a Bernoulli process is a sequence of iid Bernoulli random variables, where each idealised coin flip is an example of a Bernoulli trial.
=== Random walk ===
Random walks are stochastic processes that are usually defined as sums of iid random variables or random vectors in Euclidean space, so they are processes that change in discrete time. But some also use the term to refer to processes that change in continuous time, particularly the Wiener process used in financial models, which has led to some confusion, resulting in its criticism. There are various other types of random walks, defined so their state spaces can be other mathematical objects, such as lattices and groups, and in general they are highly studied and have many applications in different disciplines.
A classic example of a random walk is known as the simple random walk, which is a stochastic process in discrete time with the integers as the state space, and is based on a Bernoulli process, where each Bernoulli variable takes either the value positive one or negative one. In other words, the simple random walk takes place on the integers, and its value increases by one with probability, say,
p
{\displaystyle p}
, or decreases by one with probability
1
−
p
{\displaystyle 1-p}
, so the index set of this random walk is the natural numbers, while its state space is the integers. If
p
=
0.5
{\displaystyle p=0.5}
, this random walk is called a symmetric random walk.
=== Wiener process ===
The Wiener process is a stochastic process with stationary and independent increments that are normally distributed based on the size of the increments. The Wiener process is named after Norbert Wiener, who proved its mathematical existence, but the process is also called the Brownian motion process or just Brownian motion due to its historical connection as a model for Brownian movement in liquids.
Playing a central role in the theory of probability, the Wiener process is often considered the most important and studied stochastic process, with connections to other stochastic processes. Its index set and state space are the non-negative numbers and real numbers, respectively, so it has both continuous index set and states space. But the process can be defined more generally so its state space can be
n
{\displaystyle n}
-dimensional Euclidean space. If the mean of any increment is zero, then the resulting Wiener or Brownian motion process is said to have zero drift. If the mean of the increment for any two points in time is equal to the time difference multiplied by some constant
μ
{\displaystyle \mu }
, which is a real number, then the resulting stochastic process is said to have drift
μ
{\displaystyle \mu }
.
Almost surely, a sample path of a Wiener process is continuous everywhere but nowhere differentiable. It can be considered as a continuous version of the simple random walk. The process arises as the mathematical limit of other stochastic processes such as certain random walks rescaled, which is the subject of Donsker's theorem or invariance principle, also known as the functional central limit theorem.
The Wiener process is a member of some important families of stochastic processes, including Markov processes, Lévy processes and Gaussian processes. The process also has many applications and is the main stochastic process used in stochastic calculus. It plays a central role in quantitative finance, where it is used, for example, in the Black–Scholes–Merton model. The process is also used in different fields, including the majority of natural sciences as well as some branches of social sciences, as a mathematical model for various random phenomena.
=== Poisson process ===
The Poisson process is a stochastic process that has different forms and definitions. It can be defined as a counting process, which is a stochastic process that represents the random number of points or events up to some time. The number of points of the process that are located in the interval from zero to some given time is a Poisson random variable that depends on that time and some parameter. This process has the natural numbers as its state space and the non-negative numbers as its index set. This process is also called the Poisson counting process, since it can be interpreted as an example of a counting process.
If a Poisson process is defined with a single positive constant, then the process is called a homogeneous Poisson process. The homogeneous Poisson process is a member of important classes of stochastic processes such as Markov processes and Lévy processes.
The homogeneous Poisson process can be defined and generalized in different ways. It can be defined such that its index set is the real line, and this stochastic process is also called the stationary Poisson process. If the parameter constant of the Poisson process is replaced with some non-negative integrable function of
t
{\displaystyle t}
, the resulting process is called an inhomogeneous or nonhomogeneous Poisson process, where the average density of points of the process is no longer constant. Serving as a fundamental process in queueing theory, the Poisson process is an important process for mathematical models, where it finds applications for models of events randomly occurring in certain time windows.
Defined on the real line, the Poisson process can be interpreted as a stochastic process, among other random objects. But then it can be defined on the
n
{\displaystyle n}
-dimensional Euclidean space or other mathematical spaces, where it is often interpreted as a random set or a random counting measure, instead of a stochastic process. In this setting, the Poisson process, also called the Poisson point process, is one of the most important objects in probability theory, both for applications and theoretical reasons. But it has been remarked that the Poisson process does not receive as much attention as it should, partly due to it often being considered just on the real line, and not on other mathematical spaces.
== Definitions ==
=== Stochastic process ===
A stochastic process is defined as a collection of random variables defined on a common probability space
(
Ω
,
F
,
P
)
{\displaystyle (\Omega ,{\mathcal {F}},P)}
, where
Ω
{\displaystyle \Omega }
is a sample space,
F
{\displaystyle {\mathcal {F}}}
is a
σ
{\displaystyle \sigma }
-algebra, and
P
{\displaystyle P}
is a probability measure; and the random variables, indexed by some set
T
{\displaystyle T}
, all take values in the same mathematical space
S
{\displaystyle S}
, which must be measurable with respect to some
σ
{\displaystyle \sigma }
-algebra
Σ
{\displaystyle \Sigma }
.
In other words, for a given probability space
(
Ω
,
F
,
P
)
{\displaystyle (\Omega ,{\mathcal {F}},P)}
and a measurable space
(
S
,
Σ
)
{\displaystyle (S,\Sigma )}
, a stochastic process is a collection of
S
{\displaystyle S}
-valued random variables, which can be written as:
Historically, in many problems from the natural sciences a point
t
∈
T
{\displaystyle t\in T}
had the meaning of time, so
X
(
t
)
{\displaystyle X(t)}
is a random variable representing a value observed at time
t
{\displaystyle t}
. A stochastic process can also be written as
{
X
(
t
,
ω
)
:
t
∈
T
}
{\displaystyle \{X(t,\omega ):t\in T\}}
to reflect that it is actually a function of two variables,
t
∈
T
{\displaystyle t\in T}
and
ω
∈
Ω
{\displaystyle \omega \in \Omega }
.
There are other ways to consider a stochastic process, with the above definition being considered the traditional one. For example, a stochastic process can be interpreted or defined as a
S
T
{\displaystyle S^{T}}
-valued random variable, where
S
T
{\displaystyle S^{T}}
is the space of all the possible functions from the set
T
{\displaystyle T}
into the space
S
{\displaystyle S}
. However this alternative definition as a "function-valued random variable" in general requires additional regularity assumptions to be well-defined.
=== Index set ===
The set
T
{\displaystyle T}
is called the index set or parameter set of the stochastic process. Often this set is some subset of the real line, such as the natural numbers or an interval, giving the set
T
{\displaystyle T}
the interpretation of time. In addition to these sets, the index set
T
{\displaystyle T}
can be another set with a total order or a more general set, such as the Cartesian plane
R
2
{\displaystyle \mathbb {R} ^{2}}
or
n
{\displaystyle n}
-dimensional Euclidean space, where an element
t
∈
T
{\displaystyle t\in T}
can represent a point in space. That said, many results and theorems are only possible for stochastic processes with a totally ordered index set.
=== State space ===
The mathematical space
S
{\displaystyle S}
of a stochastic process is called its state space. This mathematical space can be defined using integers, real lines,
n
{\displaystyle n}
-dimensional Euclidean spaces, complex planes, or more abstract mathematical spaces. The state space is defined using elements that reflect the different values that the stochastic process can take.
=== Sample function ===
A sample function is a single outcome of a stochastic process, so it is formed by taking a single possible value of each random variable of the stochastic process. More precisely, if
{
X
(
t
,
ω
)
:
t
∈
T
}
{\displaystyle \{X(t,\omega ):t\in T\}}
is a stochastic process, then for any point
ω
∈
Ω
{\displaystyle \omega \in \Omega }
, the mapping
is called a sample function, a realization, or, particularly when
T
{\displaystyle T}
is interpreted as time, a sample path of the stochastic process
{
X
(
t
,
ω
)
:
t
∈
T
}
{\displaystyle \{X(t,\omega ):t\in T\}}
. This means that for a fixed
ω
∈
Ω
{\displaystyle \omega \in \Omega }
, there exists a sample function that maps the index set
T
{\displaystyle T}
to the state space
S
{\displaystyle S}
. Other names for a sample function of a stochastic process include trajectory, path function or path.
=== Increment ===
An increment of a stochastic process is the difference between two random variables of the same stochastic process. For a stochastic process with an index set that can be interpreted as time, an increment is how much the stochastic process changes over a certain time period. For example, if
{
X
(
t
)
:
t
∈
T
}
{\displaystyle \{X(t):t\in T\}}
is a stochastic process with state space
S
{\displaystyle S}
and index set
T
=
[
0
,
∞
)
{\displaystyle T=[0,\infty )}
, then for any two non-negative numbers
t
1
∈
[
0
,
∞
)
{\displaystyle t_{1}\in [0,\infty )}
and
t
2
∈
[
0
,
∞
)
{\displaystyle t_{2}\in [0,\infty )}
such that
t
1
≤
t
2
{\displaystyle t_{1}\leq t_{2}}
, the difference
X
t
2
−
X
t
1
{\displaystyle X_{t_{2}}-X_{t_{1}}}
is a
S
{\displaystyle S}
-valued random variable known as an increment. When interested in the increments, often the state space
S
{\displaystyle S}
is the real line or the natural numbers, but it can be
n
{\displaystyle n}
-dimensional Euclidean space or more abstract spaces such as Banach spaces.
=== Further definitions ===
==== Law ====
For a stochastic process
X
:
Ω
→
S
T
{\displaystyle X\colon \Omega \rightarrow S^{T}}
defined on the probability space
(
Ω
,
F
,
P
)
{\displaystyle (\Omega ,{\mathcal {F}},P)}
, the law of stochastic process
X
{\displaystyle X}
is defined as the pushforward measure:
where
P
{\displaystyle P}
is a probability measure, the symbol
∘
{\displaystyle \circ }
denotes function composition and
X
−
1
{\displaystyle X^{-1}}
is the pre-image of the measurable function or, equivalently, the
S
T
{\displaystyle S^{T}}
-valued random variable
X
{\displaystyle X}
, where
S
T
{\displaystyle S^{T}}
is the space of all the possible
S
{\displaystyle S}
-valued functions of
t
∈
T
{\displaystyle t\in T}
, so the law of a stochastic process is a probability measure.
For a measurable subset
B
{\displaystyle B}
of
S
T
{\displaystyle S^{T}}
, the pre-image of
X
{\displaystyle X}
gives
so the law of a
X
{\displaystyle X}
can be written as:
The law of a stochastic process or a random variable is also called the probability law, probability distribution, or the distribution.
==== Finite-dimensional probability distributions ====
For a stochastic process
X
{\displaystyle X}
with law
μ
{\displaystyle \mu }
, its finite-dimensional distribution for
t
1
,
…
,
t
n
∈
T
{\displaystyle t_{1},\dots ,t_{n}\in T}
is defined as:
This measure
μ
t
1
,
.
.
,
t
n
{\displaystyle \mu _{t_{1},..,t_{n}}}
is the joint distribution of the random vector
(
X
(
t
1
)
,
…
,
X
(
t
n
)
)
{\displaystyle (X({t_{1}}),\dots ,X({t_{n}}))}
; it can be viewed as a "projection" of the law
μ
{\displaystyle \mu }
onto a finite subset of
T
{\displaystyle T}
.
For any measurable subset
C
{\displaystyle C}
of the
n
{\displaystyle n}
-fold Cartesian power
S
n
=
S
×
⋯
×
S
{\displaystyle S^{n}=S\times \dots \times S}
, the finite-dimensional distributions of a stochastic process
X
{\displaystyle X}
can be written as:
The finite-dimensional distributions of a stochastic process satisfy two mathematical conditions known as consistency conditions.
==== Stationarity ====
Stationarity is a mathematical property that a stochastic process has when all the random variables of that stochastic process are identically distributed. In other words, if
X
{\displaystyle X}
is a stationary stochastic process, then for any
t
∈
T
{\displaystyle t\in T}
the random variable
X
t
{\displaystyle X_{t}}
has the same distribution, which means that for any set of
n
{\displaystyle n}
index set values
t
1
,
…
,
t
n
{\displaystyle t_{1},\dots ,t_{n}}
, the corresponding
n
{\displaystyle n}
random variables
all have the same probability distribution. The index set of a stationary stochastic process is usually interpreted as time, so it can be the integers or the real line. But the concept of stationarity also exists for point processes and random fields, where the index set is not interpreted as time.
When the index set
T
{\displaystyle T}
can be interpreted as time, a stochastic process is said to be stationary if its finite-dimensional distributions are invariant under translations of time. This type of stochastic process can be used to describe a physical system that is in steady state, but still experiences random fluctuations. The intuition behind stationarity is that as time passes the distribution of the stationary stochastic process remains the same. A sequence of random variables forms a stationary stochastic process only if the random variables are identically distributed.
A stochastic process with the above definition of stationarity is sometimes said to be strictly stationary, but there are other forms of stationarity. One example is when a discrete-time or continuous-time stochastic process
X
{\displaystyle X}
is said to be stationary in the wide sense, then the process
X
{\displaystyle X}
has a finite second moment for all
t
∈
T
{\displaystyle t\in T}
and the covariance of the two random variables
X
t
{\displaystyle X_{t}}
and
X
t
+
h
{\displaystyle X_{t+h}}
depends only on the number
h
{\displaystyle h}
for all
t
∈
T
{\displaystyle t\in T}
. Khinchin introduced the related concept of stationarity in the wide sense, which has other names including covariance stationarity or stationarity in the broad sense.
==== Filtration ====
A filtration is an increasing sequence of sigma-algebras defined in relation to some probability space and an index set that has some total order relation, such as in the case of the index set being some subset of the real numbers. More formally, if a stochastic process has an index set with a total order, then a filtration
{
F
t
}
t
∈
T
{\displaystyle \{{\mathcal {F}}_{t}\}_{t\in T}}
, on a probability space
(
Ω
,
F
,
P
)
{\displaystyle (\Omega ,{\mathcal {F}},P)}
is a family of sigma-algebras such that
F
s
⊆
F
t
⊆
F
{\displaystyle {\mathcal {F}}_{s}\subseteq {\mathcal {F}}_{t}\subseteq {\mathcal {F}}}
for all
s
≤
t
{\displaystyle s\leq t}
, where
t
,
s
∈
T
{\displaystyle t,s\in T}
and
≤
{\displaystyle \leq }
denotes the total order of the index set
T
{\displaystyle T}
. With the concept of a filtration, it is possible to study the amount of information contained in a stochastic process
X
t
{\displaystyle X_{t}}
at
t
∈
T
{\displaystyle t\in T}
, which can be interpreted as time
t
{\displaystyle t}
. The intuition behind a filtration
F
t
{\displaystyle {\mathcal {F}}_{t}}
is that as time
t
{\displaystyle t}
passes, more and more information on
X
t
{\displaystyle X_{t}}
is known or available, which is captured in
F
t
{\displaystyle {\mathcal {F}}_{t}}
, resulting in finer and finer partitions of
Ω
{\displaystyle \Omega }
.
==== Modification ====
A modification of a stochastic process is another stochastic process, which is closely related to the original stochastic process. More precisely, a stochastic process
X
{\displaystyle X}
that has the same index set
T
{\displaystyle T}
, state space
S
{\displaystyle S}
, and probability space
(
Ω
,
F
,
P
)
{\displaystyle (\Omega ,{\cal {F}},P)}
as another stochastic process
Y
{\displaystyle Y}
is said to be a modification of
X
{\displaystyle X}
if for all
t
∈
T
{\displaystyle t\in T}
the following
holds. Two stochastic processes that are modifications of each other have the same finite-dimensional law and they are said to be stochastically equivalent or equivalent.
Instead of modification, the term version is also used, however some authors use the term version when two stochastic processes have the same finite-dimensional distributions, but they may be defined on different probability spaces, so two processes that are modifications of each other, are also versions of each other, in the latter sense, but not the converse.
If a continuous-time real-valued stochastic process meets certain moment conditions on its increments, then the Kolmogorov continuity theorem says that there exists a modification of this process that has continuous sample paths with probability one, so the stochastic process has a continuous modification or version. The theorem can also be generalized to random fields so the index set is
n
{\displaystyle n}
-dimensional Euclidean space as well as to stochastic processes with metric spaces as their state spaces.
==== Indistinguishable ====
Two stochastic processes
X
{\displaystyle X}
and
Y
{\displaystyle Y}
defined on the same probability space
(
Ω
,
F
,
P
)
{\displaystyle (\Omega ,{\mathcal {F}},P)}
with the same index set
T
{\displaystyle T}
and set space
S
{\displaystyle S}
are said be indistinguishable if the following
holds. If two
X
{\displaystyle X}
and
Y
{\displaystyle Y}
are modifications of each other and are almost surely continuous, then
X
{\displaystyle X}
and
Y
{\displaystyle Y}
are indistinguishable.
==== Separability ====
Separability is a property of a stochastic process based on its index set in relation to the probability measure. The property is assumed so that functionals of stochastic processes or random fields with uncountable index sets can form random variables. For a stochastic process to be separable, in addition to other conditions, its index set must be a separable space, which means that the index set has a dense countable subset.
More precisely, a real-valued continuous-time stochastic process
X
{\displaystyle X}
with a probability space
(
Ω
,
F
,
P
)
{\displaystyle (\Omega ,{\cal {F}},P)}
is separable if its index set
T
{\displaystyle T}
has a dense countable subset
U
⊂
T
{\displaystyle U\subset T}
and there is a set
Ω
0
⊂
Ω
{\displaystyle \Omega _{0}\subset \Omega }
of probability zero, so
P
(
Ω
0
)
=
0
{\displaystyle P(\Omega _{0})=0}
, such that for every open set
G
⊂
T
{\displaystyle G\subset T}
and every closed set
F
⊂
R
=
(
−
∞
,
∞
)
{\displaystyle F\subset \textstyle R=(-\infty ,\infty )}
, the two events
{
X
t
∈
F
for all
t
∈
G
∩
U
}
{\displaystyle \{X_{t}\in F{\text{ for all }}t\in G\cap U\}}
and
{
X
t
∈
F
for all
t
∈
G
}
{\displaystyle \{X_{t}\in F{\text{ for all }}t\in G\}}
differ from each other at most on a subset of
Ω
0
{\displaystyle \Omega _{0}}
.
The definition of separability can also be stated for other index sets and state spaces, such as in the case of random fields, where the index set as well as the state space can be
n
{\displaystyle n}
-dimensional Euclidean space.
The concept of separability of a stochastic process was introduced by Joseph Doob,. The underlying idea of separability is to make a countable set of points of the index set determine the properties of the stochastic process. Any stochastic process with a countable index set already meets the separability conditions, so discrete-time stochastic processes are always separable. A theorem by Doob, sometimes known as Doob's separability theorem, says that any real-valued continuous-time stochastic process has a separable modification. Versions of this theorem also exist for more general stochastic processes with index sets and state spaces other than the real line.
==== Independence ====
Two stochastic processes
X
{\displaystyle X}
and
Y
{\displaystyle Y}
defined on the same probability space
(
Ω
,
F
,
P
)
{\displaystyle (\Omega ,{\mathcal {F}},P)}
with the same index set
T
{\displaystyle T}
are said be independent if for all
n
∈
N
{\displaystyle n\in \mathbb {N} }
and for every choice of epochs
t
1
,
…
,
t
n
∈
T
{\displaystyle t_{1},\ldots ,t_{n}\in T}
, the random vectors
(
X
(
t
1
)
,
…
,
X
(
t
n
)
)
{\displaystyle \left(X(t_{1}),\ldots ,X(t_{n})\right)}
and
(
Y
(
t
1
)
,
…
,
Y
(
t
n
)
)
{\displaystyle \left(Y(t_{1}),\ldots ,Y(t_{n})\right)}
are independent.: p. 515
==== Uncorrelatedness ====
Two stochastic processes
{
X
t
}
{\displaystyle \left\{X_{t}\right\}}
and
{
Y
t
}
{\displaystyle \left\{Y_{t}\right\}}
are called uncorrelated if their cross-covariance
K
X
Y
(
t
1
,
t
2
)
=
E
[
(
X
(
t
1
)
−
μ
X
(
t
1
)
)
(
Y
(
t
2
)
−
μ
Y
(
t
2
)
)
]
{\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {Y} }(t_{1},t_{2})=\operatorname {E} \left[\left(X(t_{1})-\mu _{X}(t_{1})\right)\left(Y(t_{2})-\mu _{Y}(t_{2})\right)\right]}
is zero for all times.: p. 142 Formally:
{
X
t
}
,
{
Y
t
}
uncorrelated
⟺
K
X
Y
(
t
1
,
t
2
)
=
0
∀
t
1
,
t
2
{\displaystyle \left\{X_{t}\right\},\left\{Y_{t}\right\}{\text{ uncorrelated}}\quad \iff \quad \operatorname {K} _{\mathbf {X} \mathbf {Y} }(t_{1},t_{2})=0\quad \forall t_{1},t_{2}}
.
==== Independence implies uncorrelatedness ====
If two stochastic processes
X
{\displaystyle X}
and
Y
{\displaystyle Y}
are independent, then they are also uncorrelated.: p. 151
==== Orthogonality ====
Two stochastic processes
{
X
t
}
{\displaystyle \left\{X_{t}\right\}}
and
{
Y
t
}
{\displaystyle \left\{Y_{t}\right\}}
are called orthogonal if their cross-correlation
R
X
Y
(
t
1
,
t
2
)
=
E
[
X
(
t
1
)
Y
(
t
2
)
¯
]
{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {Y} }(t_{1},t_{2})=\operatorname {E} [X(t_{1}){\overline {Y(t_{2})}}]}
is zero for all times.: p. 142 Formally:
{
X
t
}
,
{
Y
t
}
orthogonal
⟺
R
X
Y
(
t
1
,
t
2
)
=
0
∀
t
1
,
t
2
{\displaystyle \left\{X_{t}\right\},\left\{Y_{t}\right\}{\text{ orthogonal}}\quad \iff \quad \operatorname {R} _{\mathbf {X} \mathbf {Y} }(t_{1},t_{2})=0\quad \forall t_{1},t_{2}}
.
==== Skorokhod space ====
A Skorokhod space, also written as Skorohod space, is a mathematical space of all the functions that are right-continuous with left limits, defined on some interval of the real line such as
[
0
,
1
]
{\displaystyle [0,1]}
or
[
0
,
∞
)
{\displaystyle [0,\infty )}
, and take values on the real line or on some metric space. Such functions are known as càdlàg or cadlag functions, based on the acronym of the French phrase continue à droite, limite à gauche. A Skorokhod function space, introduced by Anatoliy Skorokhod, is often denoted with the letter
D
{\displaystyle D}
, so the function space is also referred to as space
D
{\displaystyle D}
. The notation of this function space can also include the interval on which all the càdlàg functions are defined, so, for example,
D
[
0
,
1
]
{\displaystyle D[0,1]}
denotes the space of càdlàg functions defined on the unit interval
[
0
,
1
]
{\displaystyle [0,1]}
.
Skorokhod function spaces are frequently used in the theory of stochastic processes because it often assumed that the sample functions of continuous-time stochastic processes belong to a Skorokhod space. Such spaces contain continuous functions, which correspond to sample functions of the Wiener process. But the space also has functions with discontinuities, which means that the sample functions of stochastic processes with jumps, such as the Poisson process (on the real line), are also members of this space.
==== Regularity ====
In the context of mathematical construction of stochastic processes, the term regularity is used when discussing and assuming certain conditions for a stochastic process to resolve possible construction issues. For example, to study stochastic processes with uncountable index sets, it is assumed that the stochastic process adheres to some type of regularity condition such as the sample functions being continuous.
== Further examples ==
=== Markov processes and chains ===
Markov processes are stochastic processes, traditionally in discrete or continuous time, that have the Markov property, which means the next value of the Markov process depends on the current value, but it is conditionally independent of the previous values of the stochastic process. In other words, the behavior of the process in the future is stochastically independent of its behavior in the past, given the current state of the process.
The Brownian motion process and the Poisson process (in one dimension) are both examples of Markov processes in continuous time, while random walks on the integers and the gambler's ruin problem are examples of Markov processes in discrete time.
A Markov chain is a type of Markov process that has either discrete state space or discrete index set (often representing time), but the precise definition of a Markov chain varies. For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless of the nature of time), but it has been also common to define a Markov chain as having discrete time in either countable or continuous state space (thus regardless of the state space). It has been argued that the first definition of a Markov chain, where it has discrete time, now tends to be used, despite the second definition having been used by researchers like Joseph Doob and Kai Lai Chung.
Markov processes form an important class of stochastic processes and have applications in many areas. For example, they are the basis for a general stochastic simulation method known as Markov chain Monte Carlo, which is used for simulating random objects with specific probability distributions, and has found application in Bayesian statistics.
The concept of the Markov property was originally for stochastic processes in continuous and discrete time, but the property has been adapted for other index sets such as
n
{\displaystyle n}
-dimensional Euclidean space, which results in collections of random variables known as Markov random fields.
=== Martingale ===
A martingale is a discrete-time or continuous-time stochastic process with the property that, at every instant, given the current value and all the past values of the process, the conditional expectation of every future value is equal to the current value. In discrete time, if this property holds for the next value, then it holds for all future values. The exact mathematical definition of a martingale requires two other conditions coupled with the mathematical concept of a filtration, which is related to the intuition of increasing available information as time passes. Martingales are usually defined to be real-valued, but they can also be complex-valued or even more general.
A symmetric random walk and a Wiener process (with zero drift) are both examples of martingales, respectively, in discrete and continuous time. For a sequence of independent and identically distributed random variables
X
1
,
X
2
,
X
3
,
…
{\displaystyle X_{1},X_{2},X_{3},\dots }
with zero mean, the stochastic process formed from the successive partial sums
X
1
,
X
1
+
X
2
,
X
1
+
X
2
+
X
3
,
…
{\displaystyle X_{1},X_{1}+X_{2},X_{1}+X_{2}+X_{3},\dots }
is a discrete-time martingale. In this aspect, discrete-time martingales generalize the idea of partial sums of independent random variables.
Martingales can also be created from stochastic processes by applying some suitable transformations, which is the case for the homogeneous Poisson process (on the real line) resulting in a martingale called the compensated Poisson process. Martingales can also be built from other martingales. For example, there are martingales based on the martingale the Wiener process, forming continuous-time martingales.
Martingales mathematically formalize the idea of a 'fair game' where it is possible form reasonable expectations for payoffs, and they were originally developed to show that it is not possible to gain an 'unfair' advantage in such a game. But now they are used in many areas of probability, which is one of the main reasons for studying them. Many problems in probability have been solved by finding a martingale in the problem and studying it. Martingales will converge, given some conditions on their moments, so they are often used to derive convergence results, due largely to martingale convergence theorems.
Martingales have many applications in statistics, but it has been remarked that its use and application are not as widespread as it could be in the field of statistics, particularly statistical inference. They have found applications in areas in probability theory such as queueing theory and Palm calculus and other fields such as economics and finance.
=== Lévy process ===
Lévy processes are types of stochastic processes that can be considered as generalizations of random walks in continuous time. These processes have many applications in fields such as finance, fluid mechanics, physics and biology. The main defining characteristics of these processes are their stationarity and independence properties, so they were known as processes with stationary and independent increments. In other words, a stochastic process
X
{\displaystyle X}
is a Lévy process if for
n
{\displaystyle n}
non-negatives numbers,
0
≤
t
1
≤
⋯
≤
t
n
{\displaystyle 0\leq t_{1}\leq \dots \leq t_{n}}
, the corresponding
n
−
1
{\displaystyle n-1}
increments
are all independent of each other, and the distribution of each increment only depends on the difference in time.
A Lévy process can be defined such that its state space is some abstract mathematical space, such as a Banach space, but the processes are often defined so that they take values in Euclidean space. The index set is the non-negative numbers, so
I
=
[
0
,
∞
)
{\displaystyle I=[0,\infty )}
, which gives the interpretation of time. Important stochastic processes such as the Wiener process, the homogeneous Poisson process (in one dimension), and subordinators are all Lévy processes.
=== Random field ===
A random field is a collection of random variables indexed by a
n
{\displaystyle n}
-dimensional Euclidean space or some manifold. In general, a random field can be considered an example of a stochastic or random process, where the index set is not necessarily a subset of the real line. But there is a convention that an indexed collection of random variables is called a random field when the index has two or more dimensions. If the specific definition of a stochastic process requires the index set to be a subset of the real line, then the random field can be considered as a generalization of stochastic process.
=== Point process ===
A point process is a collection of points randomly located on some mathematical space such as the real line,
n
{\displaystyle n}
-dimensional Euclidean space, or more abstract spaces. Sometimes the term point process is not preferred, as historically the word process denoted an evolution of some system in time, so a point process is also called a random point field. There are different interpretations of a point process, such a random counting measure or a random set. Some authors regard a point process and stochastic process as two different objects such that a point process is a random object that arises from or is associated with a stochastic process, though it has been remarked that the difference between point processes and stochastic processes is not clear.
Other authors consider a point process as a stochastic process, where the process is indexed by sets of the underlying space on which it is defined, such as the real line or
n
{\displaystyle n}
-dimensional Euclidean space. Other stochastic processes such as renewal and counting processes are studied in the theory of point processes.
== History ==
=== Early probability theory ===
Probability theory has its origins in games of chance, which have a long history, with some games being played thousands of years ago, but very little analysis on them was done in terms of probability. The year 1654 is often considered the birth of probability theory when French mathematicians Pierre Fermat and Blaise Pascal had a written correspondence on probability, motivated by a gambling problem. But there was earlier mathematical work done on the probability of gambling games such as Liber de Ludo Aleae by Gerolamo Cardano, written in the 16th century but posthumously published later in 1663.
After Cardano, Jakob Bernoulli wrote Ars Conjectandi, which is considered a significant event in the history of probability theory. Bernoulli's book was published, also posthumously, in 1713 and inspired many mathematicians to study probability. But despite some renowned mathematicians contributing to probability theory, such as Pierre-Simon Laplace, Abraham de Moivre, Carl Gauss, Siméon Poisson and Pafnuty Chebyshev, most of the mathematical community did not consider probability theory to be part of mathematics until the 20th century.
=== Statistical mechanics ===
In the physical sciences, scientists developed in the 19th century the discipline of statistical mechanics, where physical systems, such as containers filled with gases, are regarded or treated mathematically as collections of many moving particles. Although there were attempts to incorporate randomness into statistical physics by some scientists, such as Rudolf Clausius, most of the work had little or no randomness.
This changed in 1859 when James Clerk Maxwell contributed significantly to the field, more specifically, to the kinetic theory of gases, by presenting work where he modelled the gas particles as moving in random directions at random velocities. The kinetic theory of gases and statistical physics continued to be developed in the second half of the 19th century, with work done chiefly by Clausius, Ludwig Boltzmann and Josiah Gibbs, which would later have an influence on Albert Einstein's mathematical model for Brownian movement.
=== Measure theory and probability theory ===
At the International Congress of Mathematicians in Paris in 1900, David Hilbert presented a list of mathematical problems, where his sixth problem asked for a mathematical treatment of physics and probability involving axioms. Around the start of the 20th century, mathematicians developed measure theory, a branch of mathematics for studying integrals of mathematical functions, where two of the founders were French mathematicians, Henri Lebesgue and Émile Borel. In 1925, another French mathematician Paul Lévy published the first probability book that used ideas from measure theory.
In the 1920s, fundamental contributions to probability theory were made in the Soviet Union by mathematicians such as Sergei Bernstein, Aleksandr Khinchin, and Andrei Kolmogorov. Kolmogorov published in 1929 his first attempt at presenting a mathematical foundation, based on measure theory, for probability theory. In the early 1930s, Khinchin and Kolmogorov set up probability seminars, which were attended by researchers such as Eugene Slutsky and Nikolai Smirnov, and Khinchin gave the first mathematical definition of a stochastic process as a set of random variables indexed by the real line.
=== Birth of modern probability theory ===
In 1933, Andrei Kolmogorov published in German, his book on the foundations of probability theory titled Grundbegriffe der Wahrscheinlichkeitsrechnung, where Kolmogorov used measure theory to develop an axiomatic framework for probability theory. The publication of this book is now widely considered to be the birth of modern probability theory, when the theories of probability and stochastic processes became parts of mathematics.
After the publication of Kolmogorov's book, further fundamental work on probability theory and stochastic processes was done by Khinchin and Kolmogorov as well as other mathematicians such as Joseph Doob, William Feller, Maurice Fréchet, Paul Lévy, Wolfgang Doeblin, and Harald Cramér.
Decades later, Cramér referred to the 1930s as the "heroic period of mathematical probability theory". World War II greatly interrupted the development of probability theory, causing, for example, the migration of Feller from Sweden to the United States of America and the death of Doeblin, considered now a pioneer in stochastic processes.
=== Stochastic processes after World War II ===
After World War II, the study of probability theory and stochastic processes gained more attention from mathematicians, with significant contributions made in many areas of probability and mathematics as well as the creation of new areas. Starting in the 1940s, Kiyosi Itô published papers developing the field of stochastic calculus, which involves stochastic integrals and stochastic differential equations based on the Wiener or Brownian motion process.
Also starting in the 1940s, connections were made between stochastic processes, particularly martingales, and the mathematical field of potential theory, with early ideas by Shizuo Kakutani and then later work by Joseph Doob. Further work, considered pioneering, was done by Gilbert Hunt in the 1950s, connecting Markov processes and potential theory, which had a significant effect on the theory of Lévy processes and led to more interest in studying Markov processes with methods developed by Itô.
In 1953, Doob published his book Stochastic processes, which had a strong influence on the theory of stochastic processes and stressed the importance of measure theory in probability.
Doob also chiefly developed the theory of martingales, with later substantial contributions by Paul-André Meyer. Earlier work had been carried out by Sergei Bernstein, Paul Lévy and Jean Ville, the latter adopting the term martingale for the stochastic process. Methods from the theory of martingales became popular for solving various probability problems. Techniques and theory were developed to study Markov processes and then applied to martingales. Conversely, methods from the theory of martingales were established to treat Markov processes.
Other fields of probability were developed and used to study stochastic processes, with one main approach being the theory of large deviations. The theory has many applications in statistical physics, among other fields, and has core ideas going back to at least the 1930s. Later in the 1960s and 1970s, fundamental work was done by Alexander Wentzell in the Soviet Union and Monroe D. Donsker and Srinivasa Varadhan in the United States of America, which would later result in Varadhan winning the 2007 Abel Prize. In the 1990s and 2000s the theories of Schramm–Loewner evolution and rough paths were introduced and developed to study stochastic processes and other mathematical objects in probability theory, which respectively resulted in Fields Medals being awarded to Wendelin Werner in 2008 and to Martin Hairer in 2014.
The theory of stochastic processes still continues to be a focus of research, with yearly international conferences on the topic of stochastic processes.
=== Discoveries of specific stochastic processes ===
Although Khinchin gave mathematical definitions of stochastic processes in the 1930s, specific stochastic processes had already been discovered in different settings, such as the Brownian motion process and the Poisson process. Some families of stochastic processes such as point processes or renewal processes have long and complex histories, stretching back centuries.
==== Bernoulli process ====
The Bernoulli process, which can serve as a mathematical model for flipping a biased coin, is possibly the first stochastic process to have been studied. The process is a sequence of independent Bernoulli trials, which are named after Jacob Bernoulli who used them to study games of chance, including probability problems proposed and studied earlier by Christiaan Huygens. Bernoulli's work, including the Bernoulli process, were published in his book Ars Conjectandi in 1713.
==== Random walks ====
In 1905, Karl Pearson coined the term random walk while posing a problem describing a random walk on the plane, which was motivated by an application in biology, but such problems involving random walks had already been studied in other fields. Certain gambling problems that were studied centuries earlier can be considered as problems involving random walks. For example, the problem known as the Gambler's ruin is based on a simple random walk, and is an example of a random walk with absorbing barriers. Pascal, Fermat and Huyens all gave numerical solutions to this problem without detailing their methods, and then more detailed solutions were presented by Jakob Bernoulli and Abraham de Moivre.
For random walks in
n
{\displaystyle n}
-dimensional integer lattices, George Pólya published, in 1919 and 1921, work where he studied the probability of a symmetric random walk returning to a previous position in the lattice. Pólya showed that a symmetric random walk, which has an equal probability to advance in any direction in the lattice, will return to a previous position in the lattice an infinite number of times with probability one in one and two dimensions, but with probability zero in three or higher dimensions.
==== Wiener process ====
The Wiener process or Brownian motion process has its origins in different fields including statistics, finance and physics. In 1880, Danish astronomer Thorvald Thiele wrote a paper on the method of least squares, where he used the process to study the errors of a model in time-series analysis. The work is now considered as an early discovery of the statistical method known as Kalman filtering, but the work was largely overlooked. It is thought that the ideas in Thiele's paper were too advanced to have been understood by the broader mathematical and statistical community at the time.
The French mathematician Louis Bachelier used a Wiener process in his 1900 thesis in order to model price changes on the Paris Bourse, a stock exchange, without knowing the work of Thiele. It has been speculated that Bachelier drew ideas from the random walk model of Jules Regnault, but Bachelier did not cite him, and Bachelier's thesis is now considered pioneering in the field of financial mathematics.
It is commonly thought that Bachelier's work gained little attention and was forgotten for decades until it was rediscovered in the 1950s by the Leonard Savage, and then become more popular after Bachelier's thesis was translated into English in 1964. But the work was never forgotten in the mathematical community, as Bachelier published a book in 1912 detailing his ideas, which was cited by mathematicians including Doob, Feller and Kolmogorov. The book continued to be cited, but then starting in the 1960s, the original thesis by Bachelier began to be cited more than his book when economists started citing Bachelier's work.
In 1905, Albert Einstein published a paper where he studied the physical observation of Brownian motion or movement to explain the seemingly random movements of particles in liquids by using ideas from the kinetic theory of gases. Einstein derived a differential equation, known as a diffusion equation, for describing the probability of finding a particle in a certain region of space. Shortly after Einstein's first paper on Brownian movement, Marian Smoluchowski published work where he cited Einstein, but wrote that he had independently derived the equivalent results by using a different method.
Einstein's work, as well as experimental results obtained by Jean Perrin, later inspired Norbert Wiener in the 1920s to use a type of measure theory, developed by Percy Daniell, and Fourier analysis to prove the existence of the Wiener process as a mathematical object.
==== Poisson process ====
The Poisson process is named after Siméon Poisson, due to its definition involving the Poisson distribution, but Poisson never studied the process. There are a number of claims for early uses or discoveries of the Poisson
process.
At the beginning of the 20th century, the Poisson process would arise independently in different situations.
In Sweden 1903, Filip Lundberg published a thesis containing work, now considered fundamental and pioneering, where he proposed to model insurance claims with a homogeneous Poisson process.
Another discovery occurred in Denmark in 1909 when A.K. Erlang derived the Poisson distribution when developing a mathematical model for the number of incoming phone calls in a finite time interval. Erlang was not at the time aware of Poisson's earlier work and assumed that the number phone calls arriving in each interval of time were independent to each other. He then found the limiting case, which is effectively recasting the Poisson distribution as a limit of the binomial distribution.
In 1910, Ernest Rutherford and Hans Geiger published experimental results on counting alpha particles. Motivated by their work, Harry Bateman studied the counting problem and derived Poisson probabilities as a solution to a family of differential equations, resulting in the independent discovery of the Poisson process. After this time there were many studies and applications of the Poisson process, but its early history is complicated, which has been explained by the various applications of the process in numerous fields by biologists, ecologists, engineers and various physical scientists.
==== Markov processes ====
Markov processes and Markov chains are named after Andrey Markov who studied Markov chains in the early 20th century. Markov was interested in studying an extension of independent random sequences. In his first paper on Markov chains, published in 1906, Markov showed that under certain conditions the average outcomes of the Markov chain would converge to a fixed vector of values, so proving a weak law of large numbers without the independence assumption, which had been commonly regarded as a requirement for such mathematical laws to hold. Markov later used Markov chains to study the distribution of vowels in Eugene Onegin, written by Alexander Pushkin, and proved a central limit theorem for such chains.
In 1912, Poincaré studied Markov chains on finite groups with an aim to study card shuffling. Other early uses of Markov chains include a diffusion model, introduced by Paul and Tatyana Ehrenfest in 1907, and a branching process, introduced by Francis Galton and Henry William Watson in 1873, preceding the work of Markov. After the work of Galton and Watson, it was later revealed that their branching process had been independently discovered and studied around three decades earlier by Irénée-Jules Bienaymé. Starting in 1928, Maurice Fréchet became interested in Markov chains, eventually resulting in him publishing in 1938 a detailed study on Markov chains.
Andrei Kolmogorov developed in a 1931 paper a large part of the early theory of continuous-time Markov processes. Kolmogorov was partly inspired by Louis Bachelier's 1900 work on fluctuations in the stock market as well as Norbert Wiener's work on Einstein's model of Brownian movement. He introduced and studied a particular set of Markov processes known as diffusion processes, where he derived a set of differential equations describing the processes. Independent of Kolmogorov's work, Sydney Chapman derived in a 1928 paper an equation, now called the Chapman–Kolmogorov equation, in a less mathematically rigorous way than Kolmogorov, while studying Brownian movement. The differential equations are now called the Kolmogorov equations or the Kolmogorov–Chapman equations. Other mathematicians who contributed significantly to the foundations of Markov processes include William Feller, starting in the 1930s, and then later Eugene Dynkin, starting in the 1950s.
==== Lévy processes ====
Lévy processes such as the Wiener process and the Poisson process (on the real line) are named after Paul Lévy who started studying them in the 1930s, but they have connections to infinitely divisible distributions going back to the 1920s. In a 1932 paper, Kolmogorov derived a characteristic function for random variables associated with Lévy processes. This result was later derived under more general conditions by Lévy in 1934, and then Khinchin independently gave an alternative form for this characteristic function in 1937. In addition to Lévy, Khinchin and Kolomogrov, early fundamental contributions to the theory of Lévy processes were made by Bruno de Finetti and Kiyosi Itô.
== Mathematical construction ==
In mathematics, constructions of mathematical objects are needed, which is also the case for stochastic processes, to prove that they exist mathematically. There are two main approaches for constructing a stochastic process. One approach involves considering a measurable space of functions, defining a suitable measurable mapping from a probability space to this measurable space of functions, and then deriving the corresponding finite-dimensional distributions.
Another approach involves defining a collection of random variables to have specific finite-dimensional distributions, and then using Kolmogorov's existence theorem to prove a corresponding stochastic process exists. This theorem, which is an existence theorem for measures on infinite product spaces, says that if any finite-dimensional distributions satisfy two conditions, known as consistency conditions, then there exists a stochastic process with those finite-dimensional distributions.
=== Construction issues ===
When constructing continuous-time stochastic processes certain mathematical difficulties arise, due to the uncountable index sets, which do not occur with discrete-time processes. One problem is that it is possible to have more than one stochastic process with the same finite-dimensional distributions. For example, both the left-continuous modification and the right-continuous modification of a Poisson process have the same finite-dimensional distributions. This means that the distribution of the stochastic process does not, necessarily, specify uniquely the properties of the sample functions of the stochastic process.
Another problem is that functionals of continuous-time process that rely upon an uncountable number of points of the index set may not be measurable, so the probabilities of certain events may not be well-defined. For example, the supremum of a stochastic process or random field is not necessarily a well-defined random variable. For a continuous-time stochastic process
X
{\displaystyle X}
, other characteristics that depend on an uncountable number of points of the index set
T
{\displaystyle T}
include:
a sample function of a stochastic process
X
{\displaystyle X}
is a continuous function of
t
∈
T
{\displaystyle t\in T}
;
a sample function of a stochastic process
X
{\displaystyle X}
is a bounded function of
t
∈
T
{\displaystyle t\in T}
; and
a sample function of a stochastic process
X
{\displaystyle X}
is an increasing function of
t
∈
T
{\displaystyle t\in T}
.
where the symbol ∈ can be read "a member of the set", as in
t
{\displaystyle t}
a member of the set
T
{\displaystyle T}
.
To overcome the two difficulties described above, i.e., "more than one..." and "functionals of...", different assumptions and approaches are possible.
=== Resolving construction issues ===
One approach for avoiding mathematical construction issues of stochastic processes, proposed by Joseph Doob, is to assume that the stochastic process is separable. Separability ensures that infinite-dimensional distributions determine the properties of sample functions by requiring that sample functions are essentially determined by their values on a dense countable set of points in the index set. Furthermore, if a stochastic process is separable, then functionals of an uncountable number of points of the index set are measurable and their probabilities can be studied.
Another approach is possible, originally developed by Anatoliy Skorokhod and Andrei Kolmogorov, for a continuous-time stochastic process with any metric space as its state space. For the construction of such a stochastic process, it is assumed that the sample functions of the stochastic process belong to some suitable function space, which is usually the Skorokhod space consisting of all right-continuous functions with left limits. This approach is now more used than the separability assumption, but such a stochastic process based on this approach will be automatically separable.
Although less used, the separability assumption is considered more general because every stochastic process has a separable version. It is also used when it is not possible to construct a stochastic process in a Skorokhod space. For example, separability is assumed when constructing and studying random fields, where the collection of random variables is now indexed by sets other than the real line such as
n
{\displaystyle n}
-dimensional Euclidean space.
== Application ==
=== Applications in Finance ===
==== Black-Scholes Model ====
One of the most famous applications of stochastic processes in finance is the Black-Scholes model for option pricing. Developed by Fischer Black, Myron Scholes, and Robert Solow, this model uses Geometric Brownian motion, a specific type of stochastic process, to describe the dynamics of asset prices. The model assumes that the price of a stock follows a continuous-time stochastic process and provides a closed-form solution for pricing European-style options. The Black-Scholes formula has had a profound impact on financial markets, forming the basis for much of modern options trading.
The key assumption of the Black-Scholes model is that the price of a financial asset, such as a stock, follows a log-normal distribution, with its continuous returns following a normal distribution. Although the model has limitations, such as the assumption of constant volatility, it remains widely used due to its simplicity and practical relevance.
==== Stochastic Volatility Models ====
Another significant application of stochastic processes in finance is in stochastic volatility models, which aim to capture the time-varying nature of market volatility. The Heston model is a popular example, allowing for the volatility of asset prices to follow its own stochastic process. Unlike the Black-Scholes model, which assumes constant volatility, stochastic volatility models provide a more flexible framework for modeling market dynamics, particularly during periods of high uncertainty or market stress.
=== Applications in Biology ===
==== Population Dynamics ====
One of the primary applications of stochastic processes in biology is in population dynamics. In contrast to deterministic models, which assume that populations change in predictable ways, stochastic models account for the inherent randomness in births, deaths, and migration. The birth-death process, a simple stochastic model, describes how populations fluctuate over time due to random births and deaths. These models are particularly important when dealing with small populations, where random events can have large impacts, such as in the case of endangered species or small microbial populations.
Another example is the branching process, which models the growth of a population where each individual reproduces independently. The branching process is often used to describe population extinction or explosion, particularly in epidemiology, where it can model the spread of infectious diseases within a population.
=== Applications in Computer Science ===
==== Randomized Algorithms ====
Stochastic processes play a critical role in computer science, particularly in the analysis and development of randomized algorithms. These algorithms utilize random inputs to simplify problem-solving or enhance performance in complex computational tasks. For instance, Markov chains are widely used in probabilistic algorithms for optimization and sampling tasks, such as those employed in search engines like Google's PageRank. These methods balance computational efficiency with accuracy, making them invaluable for handling large datasets. Randomized algorithms are also extensively applied in areas such as cryptography, large-scale simulations, and artificial intelligence, where uncertainty must be managed effectively.
==== Queuing Theory ====
Another significant application of stochastic processes in computer science is in queuing theory, which models the random arrival and service of tasks in a system. This is particularly relevant in network traffic analysis and server management. For instance, queuing models help predict delays, manage resource allocation, and optimize throughput in web servers and communication networks. The flexibility of stochastic models allows researchers to simulate and improve the performance of high-traffic environments. For example, queueing theory is crucial for designing efficient data centers and cloud computing infrastructures.
== See also ==
== Notes ==
== References ==
== Further reading ==
=== Articles ===
Applebaum, David (2004). "Lévy processes: From probability to finance and quantum groups". Notices of the AMS. 51 (11): 1336–1347.
Cramer, Harald (1976). "Half a Century with Probability Theory: Some Personal Recollections". The Annals of Probability. 4 (4): 509–546. doi:10.1214/aop/1176996025. ISSN 0091-1798.
Guttorp, Peter; Thorarinsdottir, Thordis L. (2012). "What Happened to Discrete Chaos, the Quenouille Process, and the Sharp Markov Property? Some History of Stochastic Point Processes". International Statistical Review. 80 (2): 253–268. doi:10.1111/j.1751-5823.2012.00181.x. ISSN 0306-7734. S2CID 80836.
Jarrow, Robert; Protter, Philip (2004). "A short history of stochastic integration and mathematical finance: the early years, 1880–1970". A Festschrift for Herman Rubin. Institute of Mathematical Statistics Lecture Notes - Monograph Series. pp. 75–91. doi:10.1214/lnms/1196285381. ISBN 978-0-940600-61-4. ISSN 0749-2170.
Meyer, Paul-André (2009). "Stochastic Processes from 1950 to the Present". Electronic Journal for History of Probability and Statistics. 5 (1): 1–42.
=== Books ===
Robert J. Adler (2010). The Geometry of Random Fields. SIAM. ISBN 978-0-89871-693-1.
Robert J. Adler; Jonathan E. Taylor (2009). Random Fields and Geometry. Springer Science & Business Media. ISBN 978-0-387-48116-6.
Pierre Brémaud (2013). Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer Science & Business Media. ISBN 978-1-4757-3124-8.
Joseph L. Doob (1990). Stochastic processes. Wiley.
Anders Hald (2005). A History of Probability and Statistics and Their Applications before 1750. John Wiley & Sons. ISBN 978-0-471-72517-6.
Crispin Gardiner (2010). Stochastic Methods. Springer. ISBN 978-3-540-70712-7.
Iosif I. Gikhman; Anatoly Vladimirovich Skorokhod (1996). Introduction to the Theory of Random Processes. Courier Corporation. ISBN 978-0-486-69387-3.
Emanuel Parzen (2015). Stochastic Processes. Courier Dover Publications. ISBN 978-0-486-79688-8.
Murray Rosenblatt (1962). Random Processes. Oxford University Press.
== External links ==
Media related to Stochastic processes at Wikimedia Commons | Wikipedia/Random_function |
A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles. GPUs were later found to be useful for non-graphic calculations involving embarrassingly parallel problems due to their parallel structure. The ability of GPUs to rapidly perform vast numbers of calculations has led to their adoption in diverse fields including artificial intelligence (AI) where they excel at handling data-intensive and computationally demanding tasks. Other non-graphical uses include the training of neural networks and cryptocurrency mining.
== History ==
=== 1970s ===
Arcade system boards have used specialized graphics circuits since the 1970s. In early video game hardware, RAM for frame buffers was expensive, so video chips composited data together as the display was being scanned out on the monitor.
A specialized barrel shifter circuit helped the CPU animate the framebuffer graphics for various 1970s arcade video games from Midway and Taito, such as Gun Fight (1975), Sea Wolf (1976), and Space Invaders (1978). The Namco Galaxian arcade system in 1979 used specialized graphics hardware that supported RGB color, multi-colored sprites, and tilemap backgrounds. The Galaxian hardware was widely used during the golden age of arcade video games, by game companies such as Namco, Centuri, Gremlin, Irem, Konami, Midway, Nichibutsu, Sega, and Taito.
The Atari 2600 in 1977 used a video shifter called the Television Interface Adaptor. Atari 8-bit computers (1979) had ANTIC, a video processor which interpreted instructions describing a "display list"—the way the scan lines map to specific bitmapped or character modes and where the memory is stored (so there did not need to be a contiguous frame buffer). 6502 machine code subroutines could be triggered on scan lines by setting a bit on a display list instruction. ANTIC also supported smooth vertical and horizontal scrolling independent of the CPU.
=== 1980s ===
The NEC μPD7220 was the first implementation of a personal computer graphics display processor as a single large-scale integration (LSI) integrated circuit chip. This enabled the design of low-cost, high-performance video graphics cards such as those from Number Nine Visual Technology. It became the best-known GPU until the mid-1980s. It was the first fully integrated VLSI (very large-scale integration) metal–oxide–semiconductor (NMOS) graphics display processor for PCs, supported up to 1024×1024 resolution, and laid the foundations for the PC graphics market. It was used in a number of graphics cards and was licensed for clones such as the Intel 82720, the first of Intel's graphics processing units. The Williams Electronics arcade games Robotron 2084, Joust, Sinistar, and Bubbles, all released in 1982, contain custom blitter chips for operating on 16-color bitmaps.
In 1984, Hitachi released the ARTC HD63484, the first major CMOS graphics processor for personal computers. The ARTC could display up to 4K resolution when in monochrome mode. It was used in a number of graphics cards and terminals during the late 1980s. In 1985, the Amiga was released with a custom graphics chip including a blitter for bitmap manipulation, line drawing, and area fill. It also included a coprocessor with its own simple instruction set, that was capable of manipulating graphics hardware registers in sync with the video beam (e.g. for per-scanline palette switches, sprite multiplexing, and hardware windowing), or driving the blitter. In 1986, Texas Instruments released the TMS34010, the first fully programmable graphics processor. It could run general-purpose code but also had a graphics-oriented instruction set. During 1990–1992, this chip became the basis of the Texas Instruments Graphics Architecture ("TIGA") Windows accelerator cards.
In 1987, the IBM 8514 graphics system was released. It was one of the first video cards for IBM PC compatibles that implemented fixed-function 2D primitives in electronic hardware. Sharp's X68000, released in 1987, used a custom graphics chipset with a 65,536 color palette and hardware support for sprites, scrolling, and multiple playfields. It served as a development machine for Capcom's CP System arcade board. Fujitsu's FM Towns computer, released in 1989, had support for a 16,777,216 color palette. In 1988, the first dedicated polygonal 3D graphics boards were introduced in arcades with the Namco System 21 and Taito Air System.
IBM introduced its proprietary Video Graphics Array (VGA) display standard in 1987, with a maximum resolution of 640×480 pixels. In November 1988, NEC Home Electronics announced its creation of the Video Electronics Standards Association (VESA) to develop and promote a Super VGA (SVGA) computer display standard as a successor to VGA. Super VGA enabled graphics display resolutions up to 800×600 pixels, a 56% increase.
=== 1990s ===
In 1991, S3 Graphics introduced the S3 86C911, which its designers named after the Porsche 911 as an indication of the performance increase it promised. The 86C911 spawned a variety of imitators: by 1995, all major PC graphics chip makers had added 2D acceleration support to their chips. Fixed-function Windows accelerators surpassed expensive general-purpose graphics coprocessors in Windows performance, and such coprocessors faded from the PC market.
Throughout the 1990s, 2D GUI acceleration evolved. As manufacturing capabilities improved, so did the level of integration of graphics chips. Additional application programming interfaces (APIs) arrived for a variety of tasks, such as Microsoft's WinG graphics library for Windows 3.x, and their later DirectDraw interface for hardware acceleration of 2D games in Windows 95 and later.
In the early- and mid-1990s, real-time 3D graphics became increasingly common in arcade, computer, and console games, which led to increasing public demand for hardware-accelerated 3D graphics. Early examples of mass-market 3D graphics hardware can be found in arcade system boards such as the Sega Model 1, Namco System 22, and Sega Model 2, and the fifth-generation video game consoles such as the Saturn, PlayStation, and Nintendo 64. Arcade systems such as the Sega Model 2 and SGI Onyx-based Namco Magic Edge Hornet Simulator in 1993 were capable of hardware T&L (transform, clipping, and lighting) years before appearing in consumer graphics cards. Another early example is the Super FX chip, a RISC-based on-cartridge graphics chip used in some SNES games, notably Doom and Star Fox. Some systems used DSPs to accelerate transformations. Fujitsu, which worked on the Sega Model 2 arcade system, began working on integrating T&L into a single LSI solution for use in home computers in 1995; the Fujitsu Pinolite, the first 3D geometry processor for personal computers, released in 1997. The first hardware T&L GPU on home video game consoles was the Nintendo 64's Reality Coprocessor, released in 1996. In 1997, Mitsubishi released the 3Dpro/2MP, a GPU capable of transformation and lighting, for workstations and Windows NT desktops; ATi used it for its FireGL 4000 graphics card, released in 1997.
The term "GPU" was coined by Sony in reference to the 32-bit Sony GPU (designed by Toshiba) in the PlayStation video game console, released in 1994.
In the PC world, notable failed attempts for low-cost 3D graphics chips included the S3 ViRGE, ATI Rage, and Matrox Mystique. These chips were essentially previous-generation 2D accelerators with 3D features bolted on. Many were pin-compatible with the earlier-generation chips for ease of implementation and minimal cost. Initially, 3D graphics were possible only with discrete boards dedicated to accelerating 3D functions (and lacking 2D graphical user interface (GUI) acceleration entirely) such as the PowerVR and the 3dfx Voodoo. However, as manufacturing technology continued to progress, video, 2D GUI acceleration, and 3D functionality were all integrated into one chip. Rendition's Verite chipsets were among the first to do this well. In 1997, Rendition collaborated with Hercules and Fujitsu on a "Thriller Conspiracy" project which combined a Fujitsu FXG-1 Pinolite geometry processor with a Vérité V2200 core to create a graphics card with a full T&L engine years before Nvidia's GeForce 256; This card, designed to reduce the load placed upon the system's CPU, never made it to market. NVIDIA RIVA 128 was one of the first consumer-facing GPU integrated 3D processing unit and 2D processing unit on a chip.
OpenGL was introduced in the early 1990s by Silicon Graphics as a professional graphics API, with proprietary hardware support for 3D rasterization. In 1994, Microsoft acquired Softimage, the dominant CGI movie production tool used for early CGI movie hits like Jurassic Park, Terminator 2 and Titanic. With that deal came a strategic relationship with SGI and a commercial license of their OpenGL libraries, enabling Microsoft to port the API to the Windows NT OS but not to the upcoming release of Windows 95. Although it was little known at the time, SGI had contracted with Microsoft to transition from Unix to the forthcoming Windows NT OS; the deal which was signed in 1995 was not announced publicly until 1998. In the intervening period, Microsoft worked closely with SGI to port OpenGL to Windows NT. In that era, OpenGL had no standard driver model for competing hardware accelerators to compete on the basis of support for higher level 3D texturing and lighting functionality. In 1994 Microsoft announced DirectX 1.0 and support for gaming in the forthcoming Windows 95 consumer OS. In 1995 Microsoft announced the acquisition of UK based Rendermorphics Ltd and the Direct3D driver model for the acceleration of consumer 3D graphics. The Direct3D driver model shipped with DirectX 2.0 in 1996. It included standards and specifications for 3D chip makers to compete to support 3D texture, lighting and Z-buffering. ATI, which was later to be acquired by AMD, began development on the first Direct3D GPUs. Nvidia quickly pivoted from a failed deal with Sega in 1996 to aggressively embracing support for Direct3D. In this era Microsoft merged their internal Direct3D and OpenGL teams and worked closely with SGI to unify driver standards for both industrial and consumer 3D graphics hardware accelerators. Microsoft ran annual events for 3D chip makers called "Meltdowns" to test their 3D hardware and drivers to work both with Direct3D and OpenGL. It was during this period of strong Microsoft influence over 3D standards that 3D accelerator cards moved beyond being simple rasterizers to become more powerful general purpose processors as support for hardware accelerated texture mapping, lighting, Z-buffering and compute created the modern GPU. During this period the same Microsoft team responsible for Direct3D and OpenGL driver standardization introduced their own Microsoft 3D chip design called Talisman. Details of this era are documented extensively in the books "Game of X" v.1 and v.2 by Russel Demaria, "Renegades of the Empire" by Mike Drummond, "Opening the Xbox" by Dean Takahashi and "Masters of Doom" by David Kushner. The Nvidia GeForce 256 (also known as NV10) was the first consumer-level card with hardware-accelerated T&L. While the OpenGL API provided software support for texture mapping and lighting, the first 3D hardware acceleration for these features arrived with the first Direct3D accelerated consumer GPU's.
=== 2000s ===
NVIDIA released the GeForce 256, marketed as the world's first GPU, integrating transform and lighting engines for advanced 3D graphics rendering. Nvidia was first to produce a chip capable of programmable shading: the GeForce 3. Each pixel could now be processed by a short program that could include additional image textures as inputs, and each geometric vertex could likewise be processed by a short program before it was projected onto the screen. Used in the Xbox console, this chip competed with the one in the PlayStation 2, which used a custom vector unit for hardware-accelerated vertex processing (commonly referred to as VU0/VU1). The earliest incarnations of shader execution engines used in Xbox were not general-purpose and could not execute arbitrary pixel code. Vertices and pixels were processed by different units, which had their resources, with pixel shaders having tighter constraints (because they execute at higher frequencies than vertices). Pixel shading engines were more akin to a highly customizable function block and did not "run" a program. Many of these disparities between vertex and pixel shading were not addressed until the Unified Shader Model.
In October 2002, with the introduction of the ATI Radeon 9700 (also known as R300), the world's first Direct3D 9.0 accelerator, pixel and vertex shaders could implement looping and lengthy floating point math, and were quickly becoming as flexible as CPUs, yet orders of magnitude faster for image-array operations. Pixel shading is often used for bump mapping, which adds texture to make an object look shiny, dull, rough, or even round or extruded.
With the introduction of the Nvidia GeForce 8 series and new generic stream processing units, GPUs became more generalized computing devices. Parallel GPUs are making computational inroads against the CPU, and a subfield of research, dubbed GPU computing or GPGPU for general purpose computing on GPU, has found applications in fields as diverse as machine learning, oil exploration, scientific image processing, linear algebra, statistics, 3D reconstruction, and stock options pricing. GPGPU was the precursor to what is now called a compute shader (e.g. CUDA, OpenCL, DirectCompute) and actually abused the hardware to a degree by treating the data passed to algorithms as texture maps and executing algorithms by drawing a triangle or quad with an appropriate pixel shader. This entails some overheads since units like the scan converter are involved where they are not needed (nor are triangle manipulations even a concern—except to invoke the pixel shader).
Nvidia's CUDA platform, first introduced in 2007, was the earliest widely adopted programming model for GPU computing. OpenCL is an open standard defined by the Khronos Group that allows for the development of code for both GPUs and CPUs with an emphasis on portability. OpenCL solutions are supported by Intel, AMD, Nvidia, and ARM, and according to a report in 2011 by Evans Data, OpenCL had become the second most popular HPC tool.
=== 2010s ===
In 2010, Nvidia partnered with Audi to power their cars' dashboards, using the Tegra GPU to provide increased functionality to cars' navigation and entertainment systems. Advances in GPU technology in cars helped advance self-driving technology. AMD's Radeon HD 6000 series cards were released in 2010, and in 2011 AMD released its 6000M Series discrete GPUs for mobile devices. The Kepler line of graphics cards by Nvidia were released in 2012 and were used in the Nvidia's 600 and 700 series cards. A feature in this GPU microarchitecture included GPU boost, a technology that adjusts the clock-speed of a video card to increase or decrease it according to its power draw. The Kepler microarchitecture was manufactured.
The PS4 and Xbox One were released in 2013; they both use GPUs based on AMD's Radeon HD 7850 and 7790. Nvidia's Kepler line of GPUs was followed by the Maxwell line, manufactured on the same process. Nvidia's 28 nm chips were manufactured by TSMC in Taiwan using the 28 nm process. Compared to the 40 nm technology from the past, this manufacturing process allowed a 20 percent boost in performance while drawing less power. Virtual reality headsets have high system requirements; manufacturers recommended the GTX 970 and the R9 290X or better at the time of their release. Cards based on the Pascal microarchitecture were released in 2016. The GeForce 10 series of cards are of this generation of graphics cards. They are made using the 16 nm manufacturing process which improves upon previous microarchitectures. Nvidia released one non-consumer card under the new Volta architecture, the Titan V. Changes from the Titan XP, Pascal's high-end card, include an increase in the number of CUDA cores, the addition of tensor cores, and HBM2. Tensor cores are designed for deep learning, while high-bandwidth memory is on-die, stacked, lower-clocked memory that offers an extremely wide memory bus. To emphasize that the Titan V is not a gaming card, Nvidia removed the "GeForce GTX" suffix it adds to consumer gaming cards.
In 2018, Nvidia launched the RTX 20 series GPUs that added ray-tracing cores to GPUs, improving their performance on lighting effects. Polaris 11 and Polaris 10 GPUs from AMD are fabricated by a 14 nm process. Their release resulted in a substantial increase in the performance per watt of AMD video cards. AMD also released the Vega GPU series for the high end market as a competitor to Nvidia's high end Pascal cards, also featuring HBM2 like the Titan V.
In 2019, AMD released the successor to their Graphics Core Next (GCN) microarchitecture/instruction set. Dubbed RDNA, the first product featuring it was the Radeon RX 5000 series of video cards. The company announced that the successor to the RDNA microarchitecture would be incremental (a "refresh"). AMD unveiled the Radeon RX 6000 series, its RDNA 2 graphics cards with support for hardware-accelerated ray tracing. The product series, launched in late 2020, consisted of the RX 6800, RX 6800 XT, and RX 6900 XT. The RX 6700 XT, which is based on Navi 22, was launched in early 2021.
The PlayStation 5 and Xbox Series X and Series S were released in 2020; they both use GPUs based on the RDNA 2 microarchitecture with incremental improvements and different GPU configurations in each system's implementation.
Intel first entered the GPU market in the late 1990s, but produced lackluster 3D accelerators compared to the competition at the time. Rather than attempting to compete with the high-end manufacturers Nvidia and ATI/AMD, they began integrating Intel Graphics Technology GPUs into motherboard chipsets, beginning with the Intel 810 for the Pentium III, and later into CPUs. They began with the Intel Atom 'Pineview' laptop processor in 2009, continuing in 2010 with desktop processors in the first generation of the Intel Core line and with contemporary Pentiums and Celerons. This resulted in a large nominal market share, as the majority of computers with an Intel CPU also featured this embedded graphics processor. These generally lagged behind discrete processors in performance. Intel re-entered the discrete GPU market in 2022 with its Arc series, which competed with the then-current GeForce 30 series and Radeon 6000 series cards at competitive prices.
=== 2020s ===
In the 2020s, GPUs have been increasingly used for calculations involving embarrassingly parallel problems, such as training of neural networks on enormous datasets that are needed for large language models. Specialized processing cores on some modern workstation's GPUs are dedicated for deep learning since they have significant FLOPS performance increases, using 4×4 matrix multiplication and division, resulting in hardware performance up to 128 TFLOPS in some applications. These tensor cores are expected to appear in consumer cards, as well.
== GPU companies ==
Many companies have produced GPUs under a number of brand names. In 2009, Intel, Nvidia, and AMD/ATI were the market share leaders, with 49.4%, 27.8%, and 20.6% market share respectively. In addition, Matrox produces GPUs. Chinese companies such as Jingjia Micro have also produced GPUs for the domestic market although in terms of worldwide sales, they still lag behind market leaders.
Modern smartphones use mostly Adreno GPUs from Qualcomm, PowerVR GPUs from Imagination Technologies, and Mali GPUs from ARM.
== Computational functions ==
Modern GPUs have traditionally used most of their transistors to do calculations related to 3D computer graphics. In addition to the 3D hardware, today's GPUs include basic 2D acceleration and framebuffer capabilities (usually with a VGA compatibility mode). Newer cards such as AMD/ATI HD5000–HD7000 lack dedicated 2D acceleration; it is emulated by 3D hardware. GPUs were initially used to accelerate the memory-intensive work of texture mapping and rendering polygons. Later, dedicated hardware was added to accelerate geometric calculations such as the rotation and translation of vertices into different coordinate systems. Recent developments in GPUs include support for programmable shaders which can manipulate vertices and textures with many of the same operations that are supported by CPUs, oversampling and interpolation techniques to reduce aliasing, and very high-precision color spaces.
Several factors of GPU construction affect the performance of the card for real-time rendering, such as the size of the connector pathways in the semiconductor device fabrication, the clock signal frequency, and the number and size of various on-chip memory caches. Performance is also affected by the number of streaming multiprocessors (SM) for NVidia GPUs, or compute units (CU) for AMD GPUs, or Xe cores for Intel discrete GPUs, which describe the number of on-silicon processor core units within the GPU chip that perform the core calculations, typically working in parallel with other SM/CUs on the GPU. GPU performance is typically measured in floating point operations per second (FLOPS); GPUs in the 2010s and 2020s typically deliver performance measured in teraflops (TFLOPS). This is an estimated performance measure, as other factors can affect the actual display rate.
=== GPU accelerated video decoding and encoding ===
Most GPUs made since 1995 support the YUV color space and hardware overlays, important for digital video playback, and many GPUs made since 2000 also support MPEG primitives such as motion compensation and iDCT. This hardware-accelerated video decoding, in which portions of the video decoding process and video post-processing are offloaded to the GPU hardware, is commonly referred to as "GPU accelerated video decoding", "GPU assisted video decoding", "GPU hardware accelerated video decoding", or "GPU hardware assisted video decoding".
Recent graphics cards decode high-definition video on the card, offloading the central processing unit. The most common APIs for GPU accelerated video decoding are DxVA for Microsoft Windows operating systems and VDPAU, VAAPI, XvMC, and XvBA for Linux-based and UNIX-like operating systems. All except XvMC are capable of decoding videos encoded with MPEG-1, MPEG-2, MPEG-4 ASP (MPEG-4 Part 2), MPEG-4 AVC (H.264 / DivX 6), VC-1, WMV3/WMV9, Xvid / OpenDivX (DivX 4), and DivX 5 codecs, while XvMC is only capable of decoding MPEG-1 and MPEG-2.
There are several dedicated hardware video decoding and encoding solutions.
==== Video decoding processes that can be accelerated ====
Video decoding processes that can be accelerated by modern GPU hardware are:
Motion compensation (mocomp)
Inverse discrete cosine transform (iDCT)
Inverse telecine 3:2 and 2:2 pull-down correction
Inverse modified discrete cosine transform (iMDCT)
In-loop deblocking filter
Intra-frame prediction
Inverse quantization (IQ)
Variable-length decoding (VLD), more commonly known as slice-level acceleration
Spatial-temporal deinterlacing and automatic interlace/progressive source detection
Bitstream processing (Context-adaptive variable-length coding/Context-adaptive binary arithmetic coding) and perfect pixel positioning
These operations also have applications in video editing, encoding, and transcoding.
=== 2D graphics APIs ===
An earlier GPU may support one or more 2D graphics API for 2D acceleration, such as GDI and DirectDraw.
=== 3D graphics APIs ===
A GPU can support one or more 3D graphics API, such as DirectX, Metal, OpenGL, OpenGL ES, Vulkan.
== GPU forms ==
=== Terminology ===
In the 1970s, the term "GPU" originally stood for graphics processor unit and described a programmable processing unit working independently from the CPU that was responsible for graphics manipulation and output. In 1994, Sony used the term (now standing for graphics processing unit) in reference to the PlayStation console's Toshiba-designed Sony GPU. The term was popularized by Nvidia in 1999, who marketed the GeForce 256 as "the world's first GPU". It was presented as a "single-chip processor with integrated transform, lighting, triangle setup/clipping, and rendering engines". Rival ATI Technologies coined the term "visual processing unit" or VPU with the release of the Radeon 9700 in 2002. The AMD Alveo MA35D features dual VPU’s, each using the 5 nm process in 2023.
In personal computers, there are two main forms of GPUs. Each has many synonyms:
Dedicated graphics also called discrete graphics.
Integrated graphics also called shared graphics solutions, integrated graphics processors (IGP), or unified memory architecture (UMA).
==== Usage-specific GPU ====
Most GPUs are designed for a specific use, real-time 3D graphics, or other mass calculations:
Gaming
GeForce GTX, RTX
Nvidia Titan
Radeon HD, R5, R7, R9, RX, Vega and Navi series
Radeon VII
Intel Arc
Cloud Gaming
Nvidia GRID
Radeon Sky
Workstation
Nvidia Quadro
Nvidia RTX
AMD FirePro
AMD Radeon Pro
Intel Arc Pro
Cloud Workstation
Nvidia Tesla
AMD FireStream
Artificial Intelligence training and Cloud
Nvidia Tesla
AMD Radeon Instinct
Automated/Driverless car
Nvidia Drive PX
=== Dedicated graphics processing unit ===
Dedicated graphics processing units uses RAM that is dedicated to the GPU rather than relying on the computer’s main system memory. This RAM is usually specially selected for the expected serial workload of the graphics card (see GDDR). Sometimes systems with dedicated discrete GPUs were called "DIS" systems as opposed to "UMA" systems (see next section).
Dedicated GPUs are not necessarily removable, nor does it necessarily interface with the motherboard in a standard fashion. The term "dedicated" refers to the fact that graphics cards have RAM that is dedicated to the card's use, not to the fact that most dedicated GPUs are removable. Dedicated GPUs for portable computers are most commonly interfaced through a non-standard and often proprietary slot due to size and weight constraints. Such ports may still be considered PCIe or AGP in terms of their logical host interface, even if they are not physically interchangeable with their counterparts.
Graphics cards with dedicated GPUs typically interface with the motherboard by means of an expansion slot such as PCI Express (PCIe) or Accelerated Graphics Port (AGP). They can usually be replaced or upgraded with relative ease, assuming the motherboard is capable of supporting the upgrade. A few graphics cards still use Peripheral Component Interconnect (PCI) slots, but their bandwidth is so limited that they are generally used only when a PCIe or AGP slot is not available.
Technologies such as Scan-Line Interleave by 3dfx, SLI and NVLink by Nvidia and CrossFire by AMD allow multiple GPUs to draw images simultaneously for a single screen, increasing the processing power available for graphics. These technologies, however, are increasingly uncommon; most games do not fully use multiple GPUs, as most users cannot afford them. Multiple GPUs are still used on supercomputers (like in Summit), on workstations to accelerate video (processing multiple videos at once) and 3D rendering, for VFX, GPGPU workloads and for simulations, and in AI to expedite training, as is the case with Nvidia's lineup of DGX workstations and servers, Tesla GPUs, and Intel's Ponte Vecchio GPUs.
=== Integrated graphics processing unit ===
Integrated graphics processing units (IGPU), integrated graphics, shared graphics solutions, integrated graphics processors (IGP), or unified memory architectures (UMA) use a portion of a computer's system RAM rather than dedicated graphics memory. IGPs can be integrated onto a motherboard as part of its northbridge chipset, or on the same die (integrated circuit) with the CPU (like AMD APU or Intel HD Graphics). On certain motherboards, AMD's IGPs can use dedicated sideport memory: a separate fixed block of high performance memory that is dedicated for use by the GPU. As of early 2007 computers with integrated graphics account for about 90% of all PC shipments. They are less costly to implement than dedicated graphics processing, but tend to be less capable. Historically, integrated processing was considered unfit for 3D games or graphically intensive programs but could run less intensive programs such as Adobe Flash. Examples of such IGPs would be offerings from SiS and VIA circa 2004. However, modern integrated graphics processors such as AMD Accelerated Processing Unit and Intel Graphics Technology (HD, UHD, Iris, Iris Pro, Iris Plus, and Xe-LP) can handle 2D graphics or low-stress 3D graphics.
Since GPU computations are memory-intensive, integrated processing may compete with the CPU for relatively slow system RAM, as it has minimal or no dedicated video memory. IGPs use system memory with bandwidth up to a current maximum of 128 GB/s, whereas a discrete graphics card may have a bandwidth of more than 1000 GB/s between its VRAM and GPU core. This memory bus bandwidth can limit the performance of the GPU, though multi-channel memory can mitigate this deficiency. Older integrated graphics chipsets lacked hardware transform and lighting, but newer ones include it.
On systems with "Unified Memory Architecture" (UMA), including modern AMD processors with integrated graphics, modern Intel processors with integrated graphics, Apple processors, the PS5 and Xbox Series (among others), the CPU cores and the GPU block share the same pool of RAM and memory address space. This allows the system to dynamically allocate memory between the CPU cores and the GPU block based on memory needs (without needing a large static split of the RAM) and thanks to zero copy transfers, removes the need for either copying data over a bus between physically separate RAM pools or copying between separate address spaces on a single physical pool of RAM, allowing more efficient transfer of data.
=== Hybrid graphics processing ===
Hybrid GPUs compete with integrated graphics in the low-end desktop and notebook markets. The most common implementations of this are ATI's HyperMemory and Nvidia's TurboCache.
Hybrid graphics cards are somewhat more expensive than integrated graphics, but much less expensive than dedicated graphics cards. They share memory with the system and have a small dedicated memory cache, to make up for the high latency of the system RAM. Technologies within PCI Express make this possible. While these solutions are sometimes advertised as having as much as 768 MB of RAM, this refers to how much can be shared with the system memory.
=== Stream processing and general purpose GPUs (GPGPU) ===
It is common to use a general purpose graphics processing unit (GPGPU) as a modified form of stream processor (or a vector processor), running compute kernels. This turns the massive computational power of a modern graphics accelerator's shader pipeline into general-purpose computing power. In certain applications requiring massive vector operations, this can yield several orders of magnitude higher performance than a conventional CPU. The two largest discrete (see "Dedicated graphics processing unit" above) GPU designers, AMD and Nvidia, are pursuing this approach with an array of applications. Both Nvidia and AMD teamed with Stanford University to create a GPU-based client for the Folding@home distributed computing project for protein folding calculations. In certain circumstances, the GPU calculates forty times faster than the CPUs traditionally used by such applications.
GPGPUs can be used for many types of embarrassingly parallel tasks including ray tracing. They are generally suited to high-throughput computations that exhibit data-parallelism to exploit the wide vector width SIMD architecture of the GPU.
GPU-based high performance computers play a significant role in large-scale modelling. Three of the ten most powerful supercomputers in the world take advantage of GPU acceleration.
GPUs support API extensions to the C programming language such as OpenCL and OpenMP. Furthermore, each GPU vendor introduced its own API which only works with their cards: AMD APP SDK from AMD, and CUDA from Nvidia. These allow functions called compute kernels to run on the GPU's stream processors. This makes it possible for C programs to take advantage of a GPU's ability to operate on large buffers in parallel, while still using the CPU when appropriate. CUDA was the first API to allow CPU-based applications to directly access the resources of a GPU for more general purpose computing without the limitations of using a graphics API.
Since 2005 there has been interest in using the performance offered by GPUs for evolutionary computation in general, and for accelerating the fitness evaluation in genetic programming in particular. Most approaches compile linear or tree programs on the host PC and transfer the executable to the GPU to be run. Typically a performance advantage is only obtained by running the single active program simultaneously on many example problems in parallel, using the GPU's SIMD architecture. However, substantial acceleration can also be obtained by not compiling the programs, and instead transferring them to the GPU, to be interpreted there. Acceleration can then be obtained by either interpreting multiple programs simultaneously, simultaneously running multiple example problems, or combinations of both. A modern GPU can simultaneously interpret hundreds of thousands of very small programs.
=== External GPU (eGPU) ===
An external GPU is a graphics processor located outside of the housing of the computer, similar to a large external hard drive. External graphics processors are sometimes used with laptop computers. Laptops might have a substantial amount of RAM and a sufficiently powerful central processing unit (CPU), but often lack a powerful graphics processor, and instead have a less powerful but more energy-efficient on-board graphics chip. On-board graphics chips are often not powerful enough for playing video games, or for other graphically intensive tasks, such as editing video or 3D animation/rendering.
Therefore, it is desirable to attach a GPU to some external bus of a notebook. PCI Express is the only bus used for this purpose. The port may be, for example, an ExpressCard or mPCIe port (PCIe ×1, up to 5 or 2.5 Gbit/s respectively), a Thunderbolt 1, 2, or 3 port (PCIe ×4, up to 10, 20, or 40 Gbit/s respectively), a USB4 port with Thunderbolt compatibility, or an OCuLink port. Those ports are only available on certain notebook systems. eGPU enclosures include their own power supply (PSU), because powerful GPUs can consume hundreds of watts.
== Energy efficiency ==
== Sales ==
In 2013, 438.3 million GPUs were shipped globally and the forecast for 2014 was 414.2 million. However, by the third quarter of 2022, shipments of PC GPUs totaled around 75.5 million units, down 19% year-over-year.
== See also ==
=== Hardware ===
List of AMD graphics processing units
List of Nvidia graphics processing units
List of Intel graphics processing units
List of discrete and integrated graphics processing units
Intel GMA
Larrabee
Nvidia PureVideo – the bit-stream technology from Nvidia used in their graphics chips to accelerate video decoding on hardware GPU with DXVA.
SoC
UVD (Unified Video Decoder) – the video decoding bit-stream technology from ATI to support hardware (GPU) decode with DXVA
=== APIs ===
=== Applications ===
GPU cluster
Mathematica – includes built-in support for CUDA and OpenCL GPU execution
Molecular modeling on GPU
Deeplearning4j – open-source, distributed deep learning for Java
== References ==
== Sources ==
Peddie, Jon (1 January 2023). The History of the GPU – New Developments. Springer Nature. ISBN 978-3-03-114047-1. OCLC 1356877844.
== External links == | Wikipedia/Graphics_processor |
A fundamental problem in distributed computing and multi-agent systems is to achieve overall system reliability in the presence of a number of faulty processes. This often requires coordinating processes to reach consensus, or agree on some data value that is needed during computation. Example applications of consensus include agreeing on what transactions to commit to a database in which order, state machine replication, and atomic broadcasts. Real-world applications often requiring consensus include cloud computing, clock synchronization, PageRank, opinion formation, smart power grids, state estimation, control of UAVs (and multiple robots/agents in general), load balancing, blockchain, and others.
== Problem description ==
The consensus problem requires agreement among a number of processes (or agents) on a single data value. Some of the processes (agents) may fail or be unreliable in other ways, so consensus protocols must be fault-tolerant or resilient. The processes must put forth their candidate values, communicate with one another, and agree on a single consensus value.
The consensus problem is a fundamental problem in controlling multi-agent systems. One approach to generating consensus is for all processes (agents) to agree on a majority value. In this context, a majority requires at least one more than half of the available votes (where each process is given a vote). However, one or more faulty processes may skew the resultant outcome such that consensus may not be reached or may be reached incorrectly.
Protocols that solve consensus problems are designed to deal with a limited number of faulty processes. These protocols must satisfy several requirements to be useful. For instance, a trivial protocol could have all processes output binary value 1. This is not useful; thus, the requirement is modified such that the production must depend on the input. That is, the output value of a consensus protocol must be the input value of some process. Another requirement is that a process may decide upon an output value only once, and this decision is irrevocable. A method is correct in an execution if it does not experience a failure. A consensus protocol tolerating halting failures must satisfy the following properties.
Termination
Eventually, every correct process decides some value.
Integrity
If all the correct processes proposed the same value
v
{\displaystyle v}
, then any correct process must decide
v
{\displaystyle v}
.
Agreement
Every correct process must agree on the same value.
Variations on the definition of integrity may be appropriate, according to the application. For example, a weaker type of integrity would be for the decision value to equal a value that some correct process proposed – not necessarily all of them. There is also a condition known as validity in the literature which refers to the property that a message sent by a process must be delivered.
A protocol that can correctly guarantee consensus amongst n processes of which at most t fail is said to be t-resilient.
In evaluating the performance of consensus protocols two factors of interest are running time and message complexity. Running time is given in Big O notation in the number of rounds of message exchange as a function of some input parameters (typically the number of processes and/or the size of the input domain). Message complexity refers to the amount of message traffic that is generated by the protocol. Other factors may include memory usage and the size of messages.
== Models of computation ==
Varying models of computation may define a "consensus problem". Some models may deal with fully connected graphs, while others may deal with rings and trees. In some models message authentication is allowed, whereas in others processes are completely anonymous. Shared memory models in which processes communicate by accessing objects in shared memory are also an important area of research.
=== Communication channels with direct or transferable authentication ===
In most models of communication protocol participants communicate through authenticated channels. This means that messages are not anonymous, and receivers know the source of every message they receive.
Some models assume a stronger, transferable form of authentication, where each message is signed by the sender, so that a receiver knows not just the immediate source of every message, but the participant that initially created the message.
This stronger type of authentication is achieved by digital signatures, and when this stronger form of authentication is available, protocols can tolerate a larger number of faults.
The two different authentication models are often called oral communication and written communication models. In an oral communication model, the immediate source of information is known, whereas in stronger, written communication models, every step along the receiver learns not just the immediate source of the message, but the communication history of the message.
=== Inputs and outputs of consensus ===
In the most traditional single-value consensus protocols such as Paxos, cooperating nodes agree on a single value such as an integer, which may be of variable size so as to encode useful metadata such as a transaction committed to a database.
A special case of the single-value consensus problem, called binary consensus, restricts the input, and hence the output domain, to a single binary digit {0,1}. While not highly useful by themselves, binary consensus protocols are often useful as building blocks in more general consensus protocols, especially for asynchronous consensus.
In multi-valued consensus protocols such as Multi-Paxos and Raft, the goal is to agree on not just a single value but a series of values over time, forming a progressively-growing history. While multi-valued consensus may be achieved naively by running multiple iterations of a single-valued consensus protocol in succession, many optimizations and other considerations such as reconfiguration support can make multi-valued consensus protocols more efficient in practice.
=== Crash and Byzantine failures ===
There are two types of failures a process may undergo, a crash failure or a Byzantine failure. A crash failure occurs when a process abruptly stops and does not resume. Byzantine failures are failures in which absolutely no conditions are imposed. For example, they may occur as a result of the malicious actions of an adversary. A process that experiences a Byzantine failure may send contradictory or conflicting data to other processes, or it may sleep and then resume activity after a lengthy delay. Of the two types of failures, Byzantine failures are far more disruptive.
Thus, a consensus protocol tolerating Byzantine failures must be resilient to every possible error that can occur.
A stronger version of consensus tolerating Byzantine failures is given by strengthening the Integrity constraint:
Integrity
If a correct process decides
v
{\displaystyle v}
, then
v
{\displaystyle v}
must have been proposed by some correct process.
=== Asynchronous and synchronous systems ===
The consensus problem may be considered in the case of asynchronous or synchronous systems. While real world communications are often inherently asynchronous, it is more practical and often easier to model synchronous systems, given that asynchronous systems naturally involve more issues than synchronous ones.
In synchronous systems, it is assumed that all communications proceed in rounds. In one round, a process may send all the messages it requires, while receiving all messages from other processes. In this manner, no message from one round may influence any messages sent within the same round.
==== The FLP impossibility result for asynchronous deterministic consensus ====
In a fully asynchronous message-passing distributed system, in which at least one process may have a crash failure, it has been proven in the famous 1985 FLP impossibility result by Fischer, Lynch and Paterson that a deterministic algorithm for achieving consensus is impossible. This impossibility result derives from worst-case scheduling scenarios, which are unlikely to occur in practice except in adversarial situations such as an intelligent denial-of-service attacker in the network. In most normal situations, process scheduling has a degree of natural randomness.
In an asynchronous model, some forms of failures can be handled by a synchronous consensus protocol. For instance, the loss of a communication link may be modeled as a process which has suffered a Byzantine failure.
Randomized consensus algorithms can circumvent the FLP impossibility result by achieving both safety and liveness with overwhelming probability, even under worst-case scheduling scenarios such as an intelligent denial-of-service attacker in the network.
=== Permissioned versus permissionless consensus ===
Consensus algorithms traditionally assume that the set of participating nodes is fixed and given at the outset: that is, that some prior (manual or automatic) configuration process has permissioned a particular known group of participants who can authenticate each other as members of the group. In the absence of such a well-defined, closed group with authenticated members, a Sybil attack against an open consensus group can defeat even a Byzantine consensus algorithm, simply by creating enough virtual participants to overwhelm the fault tolerance threshold.
A permissionless consensus protocol, in contrast, allows anyone in the network to join dynamically and participate without prior permission, but instead imposes a different form of artificial cost or barrier to entry to mitigate the Sybil attack threat. Bitcoin introduced the first permissionless consensus protocol using proof of work and a difficulty adjustment function, in which participants compete to solve cryptographic hash puzzles, and probabilistically earn the right to commit blocks and earn associated rewards in proportion to their invested computational effort. Motivated in part by the high energy cost of this approach, subsequent permissionless consensus protocols have proposed or adopted other alternative participation rules for Sybil attack protection, such as proof of stake, proof of space, and proof of authority.
== Equivalency of agreement problems ==
Three agreement problems of interest are as follows.
=== Terminating Reliable Broadcast ===
A collection of
n
{\displaystyle n}
processes, numbered from
0
{\displaystyle 0}
to
n
−
1
,
{\displaystyle n-1,}
communicate by sending messages to one another. Process
0
{\displaystyle 0}
must transmit a value
v
{\displaystyle v}
to all processes such that:
if process
0
{\displaystyle 0}
is correct, then every correct process receives
v
{\displaystyle v}
for any two correct processes, each process receives the same value.
It is also known as The General's Problem.
=== Consensus ===
Formal requirements for a consensus protocol may include:
Agreement: All correct processes must agree on the same value.
Weak validity: For each correct process, its output must be the input of some correct process.
Strong validity: If all correct processes receive the same input value, then they must all output that value.
Termination: All processes must eventually decide on an output value
=== Weak Interactive Consistency ===
For n processes in a partially synchronous system (the system alternates between good and bad periods of synchrony), each process chooses a private value. The processes communicate with each other by rounds to determine a public value and generate a
consensus vector with the following requirements:
if a correct process sends
v
{\displaystyle v}
, then all correct processes receive either
v
{\displaystyle v}
or nothing (integrity property)
all messages sent in a round by a correct process are received in the same round by all correct processes (consistency property).
It can be shown that variations of these problems are equivalent in that the solution for a problem in one type of model may be the solution for another problem in another type of model. For example, a solution to the Weak Byzantine General problem in a synchronous authenticated message passing model leads to a solution for Weak Interactive Consistency. An interactive consistency algorithm can solve the consensus problem by having each process choose the majority value in its consensus vector as its consensus value.
== Solvability results for some agreement problems ==
There is a t-resilient anonymous synchronous protocol which solves the Byzantine Generals problem, if
t
n
<
1
3
{\displaystyle {\tfrac {t}{n}}<{\tfrac {1}{3}}}
and the Weak Byzantine Generals case where
t
{\displaystyle t}
is the number of failures and
n
{\displaystyle n}
is the number of processes.
For systems with
n
{\displaystyle n}
processors, of which
f
{\displaystyle f}
are Byzantine, it has been shown that there exists no algorithm that solves the consensus problem for
n
≤
3
f
{\displaystyle n\leq 3f}
in the oral-messages model. The proof is constructed by first showing the impossibility for the three-node case
n
=
3
{\displaystyle n=3}
and using this result to argue about partitions of processors. In the written-messages model there are protocols that can tolerate
n
=
f
+
1
{\displaystyle n=f+1}
.
In a fully asynchronous system there is no consensus solution that can tolerate one or more crash failures even when only requiring the non triviality property. This result is sometimes called the FLP impossibility proof named after the authors Michael J. Fischer, Nancy Lynch, and Mike Paterson who were awarded a Dijkstra Prize for this significant work. The FLP result has been mechanically verified to hold even under fairness assumptions. However, FLP does not state that consensus can never be reached: merely that under the model's assumptions, no algorithm can always reach consensus in bounded time. In practice it is highly unlikely to occur.
== Some consensus protocols ==
The Paxos consensus algorithm by Leslie Lamport, and variants of it such as Raft, are used pervasively in widely deployed distributed and cloud computing systems. These algorithms are typically synchronous, dependent on an elected leader to make progress, and tolerate only crashes and not Byzantine failures.
An example of a polynomial time binary consensus protocol that tolerates Byzantine failures is the Phase King algorithm by Garay and Berman. The algorithm solves consensus in a synchronous message passing model with n processes and up to f failures, provided n > 4f.
In the phase king algorithm, there are f + 1 phases, with 2 rounds per phase.
Each process keeps track of its preferred output (initially equal to the process's own input value). In the first round of each phase each process broadcasts its own preferred value to all other processes. It then receives the values from all processes and determines which value is the majority value and its count. In the second round of the phase, the process whose id matches the current phase number is designated the king of the phase. The king broadcasts the majority value it observed in the first round and serves as a tie breaker. Each process then updates its preferred value as follows. If the count of the majority value the process observed in the first round is greater than n/2 + f, the process changes its preference to that majority value; otherwise it uses the phase king's value. At the end of f + 1 phases the processes output their preferred values.
Google has implemented a distributed lock service library called Chubby. Chubby maintains lock information in small files which are stored in a replicated database to achieve high availability in the face of failures. The database is implemented on top of a fault-tolerant log layer which is based on the Paxos consensus algorithm. In this scheme, Chubby clients communicate with the Paxos master in order to access/update the replicated log; i.e., read/write to the files.
Many peer-to-peer online real-time strategy games use a modified lockstep protocol as a consensus protocol in order to manage game state between players in a game. Each game action results in a game state delta broadcast to all other players in the game along with a hash of the total game state. Each player validates the change by applying the delta to their own game state and comparing the game state hashes. If the hashes do not agree then a vote is cast, and those players whose game state is in the minority are disconnected and removed from the game (known as a desync.)
Another well-known approach is called MSR-type algorithms which have been used widely in fields from computer science to control theory.
=== Permissionless consensus protocols ===
Bitcoin uses proof of work, a difficulty adjustment function and a reorganization function to achieve permissionless consensus in its open peer-to-peer network. To extend bitcoin's blockchain or distributed ledger, miners attempt to solve a cryptographic puzzle, where probability of finding a solution is proportional to the computational effort expended in hashes per second. The node that first solves such a puzzle has their proposed version of the next block of transactions added to the ledger and eventually accepted by all other nodes. As any node in the network can attempt to solve the proof-of-work problem, a Sybil attack is infeasible in principle unless the attacker has over 50% of the computational resources of the network.
Other cryptocurrencies (e.g. Ethereum, NEO, STRATIS, ...) use proof of stake, in which nodes compete to append blocks and earn associated rewards in proportion to stake, or existing cryptocurrency allocated and locked or staked for some time period. One advantage of a 'proof of stake' over a 'proof of work' system, is the high energy consumption demanded by the latter. As an example, bitcoin mining (2018) is estimated to consume non-renewable energy sources at an amount similar to the entire nations of Czech Republic or Jordan, while the total energy consumption of Ethereum, the largest proof of stake network, is just under that of 205 average US households.
Some cryptocurrencies, such as Ripple, use a system of validating nodes to validate the ledger.
This system used by Ripple, called Ripple Protocol Consensus Algorithm (RPCA), works in rounds:
Step 1: every server compiles a list of valid candidate transactions;
Step 2: each server amalgamates all candidates coming from its Unique Nodes List (UNL) and votes on their veracity;
Step 3: transactions passing the minimum threshold are passed to the next round;
Step 4: the final round requires 80% agreement.
Other participation rules used in permissionless consensus protocols to impose barriers to entry and resist sybil attacks include proof of authority, proof of space, proof of burn, or proof of elapsed time.
Contrasting with the above permissionless participation rules, all of which reward participants in proportion to amount of investment in some action or resource, proof of personhood protocols aim to give each real human participant exactly one unit of voting power in permissionless consensus, regardless of economic investment. Proposed approaches to achieving one-per-person distribution of consensus power for proof of personhood include physical pseudonym parties, social networks, pseudonymized government-issued identities, and biometrics.
== Consensus number ==
To solve the consensus problem in a shared-memory system, concurrent objects must be introduced. A concurrent object, or shared object, is a data structure which helps concurrent processes communicate to reach an agreement. Traditional implementations using critical sections face the risk of crashing if some process dies inside the critical section or sleeps for an intolerably long time. Researchers defined wait-freedom as the guarantee that the algorithm completes in a finite number of steps.
The consensus number of a concurrent object is defined to be the maximum number of processes in the system which can reach consensus by the given object in a wait-free implementation. Objects with a consensus number of
n
{\displaystyle n}
can implement any object with a consensus number of
n
{\displaystyle n}
or lower, but cannot implement any objects with a higher consensus number. The consensus numbers form what is called Herlihy's hierarchy of synchronization objects.
According to the hierarchy, read/write registers cannot solve consensus even in a 2-process system. Data structures like stacks and queues can only solve consensus between two processes. However, some concurrent objects are universal (notated in the table with
∞
{\displaystyle \infty }
), which means they can solve consensus among any number of processes and they can simulate any other objects through an operation sequence.
== See also ==
Uniform consensus
Quantum Byzantine agreement
Byzantine fault
== References ==
== Further reading ==
Herlihy, M.; Shavit, N. (1999). "The topological structure of asynchronous computability". Journal of the ACM. 46 (6): 858. CiteSeerX 10.1.1.78.1455. doi:10.1145/331524.331529. S2CID 5797174.
Saks, M.; Zaharoglou, F. (2000). "Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge". SIAM Journal on Computing. 29 (5): 1449–1483. doi:10.1137/S0097539796307698.
Bashir, Imran. "Blockchain Consensus." Blockchain Consensus - An Introduction to Classical, Blockchain, and Quantum Consensus Protocols. ISBN 978-1-4842-8178-9 Apress, Berkeley, CA, 2022. doi:10.1007/978-1-4842-8179-6 | Wikipedia/Consensus_(computer_science) |
Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown.
In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation.
Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like the British Bombes and Colossus computers at Bletchley Park in World War II, to the mathematically advanced computerized schemes of the present. Methods for breaking modern cryptosystems often involve solving carefully constructed problems in pure mathematics, the best-known being integer factorization.
== Overview ==
In encryption, confidential information (called the "plaintext") is sent securely to a recipient by the sender first converting it into an unreadable form ("ciphertext") using an encryption algorithm. The ciphertext is sent through an insecure channel to the recipient. The recipient decrypts the ciphertext by applying an inverse decryption algorithm, recovering the plaintext. To decrypt the ciphertext, the recipient requires a secret knowledge from the sender, usually a string of letters, numbers, or bits, called a cryptographic key. The concept is that even if an unauthorized person gets access to the ciphertext during transmission, without the secret key they cannot convert it back to plaintext.
Encryption has been used throughout history to send important military, diplomatic and commercial messages, and today is very widely used in computer networking to protect email and internet communication.
The goal of cryptanalysis is for a third party, a cryptanalyst, to gain as much information as possible about the original ("plaintext"), attempting to "break" the encryption to read the ciphertext and learning the secret key so future messages can be decrypted and read. A mathematical technique to do this is called a cryptographic attack. Cryptographic attacks can be characterized in a number of ways:
=== Amount of information available to the attacker ===
Cryptanalytical attacks can be classified based on what type of information the attacker has available. As a basic starting point it is normally assumed that, for the purposes of analysis, the general algorithm is known; this is Shannon's Maxim "the enemy knows the system" – in its turn, equivalent to Kerckhoffs's principle. This is a reasonable assumption in practice – throughout history, there are countless examples of secret algorithms falling into wider knowledge, variously through espionage, betrayal and reverse engineering. (And on occasion, ciphers have been broken through pure deduction; for example, the German Lorenz cipher and the Japanese Purple code, and a variety of classical schemes):
Ciphertext-only: the cryptanalyst has access only to a collection of ciphertexts or codetexts.
Known-plaintext: the attacker has a set of ciphertexts to which they know the corresponding plaintext.
Chosen-plaintext (chosen-ciphertext): the attacker can obtain the ciphertexts (plaintexts) corresponding to an arbitrary set of plaintexts (ciphertexts) of their own choosing.
Adaptive chosen-plaintext: like a chosen-plaintext attack, except the attacker can choose subsequent plaintexts based on information learned from previous encryptions, similarly to the Adaptive chosen ciphertext attack.
Related-key attack: Like a chosen-plaintext attack, except the attacker can obtain ciphertexts encrypted under two different keys. The keys are unknown, but the relationship between them is known; for example, two keys that differ in the one bit.
=== Computational resources required ===
Attacks can also be characterised by the resources they require. Those resources include:
Time – the number of computation steps (e.g., test encryptions) which must be performed.
Memory – the amount of storage required to perform the attack.
Data – the quantity and type of plaintexts and ciphertexts required for a particular approach.
It is sometimes difficult to predict these quantities precisely, especially when the attack is not practical to actually implement for testing. But academic cryptanalysts tend to provide at least the estimated order of magnitude of their attacks' difficulty, saying, for example, "SHA-1 collisions now 252."
Bruce Schneier notes that even computationally impractical attacks can be considered breaks: "Breaking a cipher simply means finding a weakness in the cipher that can be exploited with a complexity less than brute force. Never mind that brute-force might require 2128 encryptions; an attack requiring 2110 encryptions would be considered a break...simply put, a break can just be a certificational weakness: evidence that the cipher does not perform as advertised."
=== Partial breaks ===
The results of cryptanalysis can also vary in usefulness. Cryptographer Lars Knudsen (1998) classified various types of attack on block ciphers according to the amount and quality of secret information that was discovered:
Total break – the attacker deduces the secret key.
Global deduction – the attacker discovers a functionally equivalent algorithm for encryption and decryption, but without learning the key.
Instance (local) deduction – the attacker discovers additional plaintexts (or ciphertexts) not previously known.
Information deduction – the attacker gains some Shannon information about plaintexts (or ciphertexts) not previously known.
Distinguishing algorithm – the attacker can distinguish the cipher from a random permutation.
Academic attacks are often against weakened versions of a cryptosystem, such as a block cipher or hash function with some rounds removed. Many, but not all, attacks become exponentially more difficult to execute as rounds are added to a cryptosystem, so it's possible for the full cryptosystem to be strong even though reduced-round variants are weak. Nonetheless, partial breaks that come close to breaking the original cryptosystem may mean that a full break will follow; the successful attacks on DES, MD5, and SHA-1 were all preceded by attacks on weakened versions.
In academic cryptography, a weakness or a break in a scheme is usually defined quite conservatively: it might require impractical amounts of time, memory, or known plaintexts. It also might require the attacker be able to do things many real-world attackers can't: for example, the attacker may need to choose particular plaintexts to be encrypted or even to ask for plaintexts to be encrypted using several keys related to the secret key. Furthermore, it might only reveal a small amount of information, enough to prove the cryptosystem imperfect but too little to be useful to real-world attackers. Finally, an attack might only apply to a weakened version of cryptographic tools, like a reduced-round block cipher, as a step towards breaking the full system.
== History ==
Cryptanalysis has coevolved together with cryptography, and the contest can be traced through the history of cryptography—new ciphers being designed to replace old broken designs, and new cryptanalytic techniques invented to crack the improved schemes. In practice, they are viewed as two sides of the same coin: secure cryptography requires design against possible cryptanalysis.
=== Classical ciphers ===
Although the actual word "cryptanalysis" is relatively recent (it was coined by William Friedman in 1920), methods for breaking codes and ciphers are much older. David Kahn notes in The Codebreakers that Arab scholars were the first people to systematically document cryptanalytic methods.
The first known recorded explanation of cryptanalysis was given by Al-Kindi (c. 801–873, also known as "Alkindus" in Europe), a 9th-century Arab polymath, in Risalah fi Istikhraj al-Mu'amma (A Manuscript on Deciphering Cryptographic Messages). This treatise contains the first description of the method of frequency analysis. Al-Kindi is thus regarded as the first codebreaker in history. His breakthrough work was influenced by Al-Khalil (717–786), who wrote the Book of Cryptographic Messages, which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels.
Frequency analysis is the basic tool for breaking most classical ciphers. In natural languages, certain letters of the alphabet appear more often than others; in English, "E" is likely to be the most common letter in any sample of plaintext. Similarly, the digraph "TH" is the most likely pair of letters in English, and so on. Frequency analysis relies on a cipher failing to hide these statistics. For example, in a simple substitution cipher (where each letter is simply replaced with another), the most frequent letter in the ciphertext would be a likely candidate for "E". Frequency analysis of such a cipher is therefore relatively easy, provided that the ciphertext is long enough to give a reasonably representative count of the letters of the alphabet that it contains.
Al-Kindi's invention of the frequency analysis technique for breaking monoalphabetic substitution ciphers was the most significant cryptanalytic advance until World War II. Al-Kindi's Risalah fi Istikhraj al-Mu'amma described the first cryptanalytic techniques, including some for polyalphabetic ciphers, cipher classification, Arabic phonetics and syntax, and most importantly, gave the first descriptions on frequency analysis. He also covered methods of encipherments, cryptanalysis of certain encipherments, and statistical analysis of letters and letter combinations in Arabic. An important contribution of Ibn Adlan (1187–1268) was on sample size for use of frequency analysis.
In Europe, Italian scholar Giambattista della Porta (1535–1615) was the author of a seminal work on cryptanalysis, De Furtivis Literarum Notis.
Successful cryptanalysis has undoubtedly influenced history; the ability to read the presumed-secret thoughts and plans of others can be a decisive advantage. For example, in England in 1587, Mary, Queen of Scots was tried and executed for treason as a result of her involvement in three plots to assassinate Elizabeth I of England. The plans came to light after her coded correspondence with fellow conspirators was deciphered by Thomas Phelippes.
In Europe during the 15th and 16th centuries, the idea of a polyalphabetic substitution cipher was developed, among others by the French diplomat Blaise de Vigenère (1523–96). For some three centuries, the Vigenère cipher, which uses a repeating key to select different encryption alphabets in rotation, was considered to be completely secure (le chiffre indéchiffrable—"the indecipherable cipher"). Nevertheless, Charles Babbage (1791–1871) and later, independently, Friedrich Kasiski (1805–81) succeeded in breaking this cipher. During World War I, inventors in several countries developed rotor cipher machines such as Arthur Scherbius' Enigma, in an attempt to minimise the repetition that had been exploited to break the Vigenère system.
=== Ciphers from World War I and World War II ===
In World War I, the breaking of the Zimmermann Telegram was instrumental in bringing the United States into the war. In World War II, the Allies benefitted enormously from their joint success cryptanalysis of the German ciphers – including the Enigma machine and the Lorenz cipher – and Japanese ciphers, particularly 'Purple' and JN-25. 'Ultra' intelligence has been credited with everything between shortening the end of the European war by up to two years, to determining the eventual result. The war in the Pacific was similarly helped by 'Magic' intelligence.
Cryptanalysis of enemy messages played a significant part in the Allied victory in World War II. F. W. Winterbotham, quoted the western Supreme Allied Commander, Dwight D. Eisenhower, at the war's end as describing Ultra intelligence as having been "decisive" to Allied victory. Sir Harry Hinsley, official historian of British Intelligence in World War II, made a similar assessment about Ultra, saying that it shortened the war "by not less than two years and probably by four years"; moreover, he said that in the absence of Ultra, it is uncertain how the war would have ended.
In practice, frequency analysis relies as much on linguistic knowledge as it does on statistics, but as ciphers became more complex, mathematics became more important in cryptanalysis. This change was particularly evident before and during World War II, where efforts to crack Axis ciphers required new levels of mathematical sophistication. Moreover, automation was first applied to cryptanalysis in that era with the Polish Bomba device, the British Bombe, the use of punched card equipment, and in the Colossus computers – the first electronic digital computers to be controlled by a program.
==== Indicator ====
With reciprocal machine ciphers such as the Lorenz cipher and the Enigma machine used by Nazi Germany during World War II, each message had its own key. Usually, the transmitting operator informed the receiving operator of this message key by transmitting some plaintext and/or ciphertext before the enciphered message. This is termed the indicator, as it indicates to the receiving operator how to set his machine to decipher the message.
Poorly designed and implemented indicator systems allowed first Polish cryptographers and then the British cryptographers at Bletchley Park to break the Enigma cipher system. Similar poor indicator systems allowed the British to identify depths that led to the diagnosis of the Lorenz SZ40/42 cipher system, and the comprehensive breaking of its messages without the cryptanalysts seeing the cipher machine.
==== Depth ====
Sending two or more messages with the same key is an insecure process. To a cryptanalyst the messages are then said to be "in depth." This may be detected by the messages having the same indicator by which the sending operator informs the receiving operator about the key generator initial settings for the message.
Generally, the cryptanalyst may benefit from lining up identical enciphering operations among a set of messages. For example, the Vernam cipher enciphers by bit-for-bit combining plaintext with a long key using the "exclusive or" operator, which is also known as "modulo-2 addition" (symbolized by ⊕ ):
Plaintext ⊕ Key = Ciphertext
Deciphering combines the same key bits with the ciphertext to reconstruct the plaintext:
Ciphertext ⊕ Key = Plaintext
(In modulo-2 arithmetic, addition is the same as subtraction.) When two such ciphertexts are aligned in depth, combining them eliminates the common key, leaving just a combination of the two plaintexts:
Ciphertext1 ⊕ Ciphertext2 = Plaintext1 ⊕ Plaintext2
The individual plaintexts can then be worked out linguistically by trying probable words (or phrases), also known as "cribs," at various locations; a correct guess, when combined with the merged plaintext stream, produces intelligible text from the other plaintext component:
Cyphertext1 ⊕ Cyphertext2 ⊕ Plaintext1 = Plaintext2
The recovered fragment of the second plaintext can often be extended in one or both directions, and the extra characters can be combined with the merged plaintext stream to extend the first plaintext. Working back and forth between the two plaintexts, using the intelligibility criterion to check guesses, the analyst may recover much or all of the original plaintexts. (With only two plaintexts in depth, the analyst may not know which one corresponds to which ciphertext, but in practice this is not a large problem.) When a recovered plaintext is then combined with its ciphertext, the key is revealed:
Plaintext1 ⊕ Ciphertext1 = Key
Knowledge of a key then allows the analyst to read other messages encrypted with the same key, and knowledge of a set of related keys may allow cryptanalysts to diagnose the system used for constructing them.
=== Development of modern cryptography ===
Governments have long recognized the potential benefits of cryptanalysis for intelligence, both military and diplomatic, and established dedicated organizations devoted to breaking the codes and ciphers of other nations, for example, GCHQ and the NSA, organizations which are still very active today.
Even though computation was used to great effect in the cryptanalysis of the Lorenz cipher and other systems during World War II, it also made possible new methods of cryptography orders of magnitude more complex than ever before. Taken as a whole, modern cryptography has become much more impervious to cryptanalysis than the pen-and-paper systems of the past, and now seems to have the upper hand against pure cryptanalysis. The historian David Kahn notes:
Many are the cryptosystems offered by the hundreds of commercial vendors today that cannot be broken by any known methods of cryptanalysis. Indeed, in such systems even a chosen plaintext attack, in which a selected plaintext is matched against its ciphertext, cannot yield the key that unlock[s] other messages. In a sense, then, cryptanalysis is dead. But that is not the end of the story. Cryptanalysis may be dead, but there is – to mix my metaphors – more than one way to skin a cat.
Kahn goes on to mention increased opportunities for interception, bugging, side channel attacks, and quantum computers as replacements for the traditional means of cryptanalysis. In 2010, former NSA technical director Brian Snow said that both academic and government cryptographers are "moving very slowly forward in a mature field."
However, any postmortems for cryptanalysis may be premature. While the effectiveness of cryptanalytic methods employed by intelligence agencies remains unknown, many serious attacks against both academic and practical cryptographic primitives have been published in the modern era of computer cryptography:
The block cipher Madryga, proposed in 1984 but not widely used, was found to be susceptible to ciphertext-only attacks in 1998.
FEAL-4, proposed as a replacement for the DES standard encryption algorithm but not widely used, was demolished by a spate of attacks from the academic community, many of which are entirely practical.
The A5/1, A5/2, CMEA, and DECT systems used in mobile and wireless phone technology can all be broken in hours, minutes or even in real-time using widely available computing equipment.
Brute-force keyspace search has broken some real-world ciphers and applications, including single-DES (see EFF DES cracker), 40-bit "export-strength" cryptography, and the DVD Content Scrambling System.
In 2001, Wired Equivalent Privacy (WEP), a protocol used to secure Wi-Fi wireless networks, was shown to be breakable in practice because of a weakness in the RC4 cipher and aspects of the WEP design that made related-key attacks practical. WEP was later replaced by Wi-Fi Protected Access.
In 2008, researchers conducted a proof-of-concept break of SSL using weaknesses in the MD5 hash function and certificate issuer practices that made it possible to exploit collision attacks on hash functions. The certificate issuers involved changed their practices to prevent the attack from being repeated.
Thus, while the best modern ciphers may be far more resistant to cryptanalysis than the Enigma, cryptanalysis and the broader field of information security remain quite active.
== Symmetric ciphers ==
Boomerang attack
Brute-force attack
Davies' attack
Differential cryptanalysis
Harvest now, decrypt later
Impossible differential cryptanalysis
Improbable differential cryptanalysis
Integral cryptanalysis
Linear cryptanalysis
Meet-in-the-middle attack
Mod-n cryptanalysis
Related-key attack
Sandwich attack
Slide attack
XSL attack
== Asymmetric ciphers ==
Asymmetric cryptography (or public-key cryptography) is cryptography that relies on using two (mathematically related) keys; one private, and one public. Such ciphers invariably rely on "hard" mathematical problems as the basis of their security, so an obvious point of attack is to develop methods for solving the problem. The security of two-key cryptography depends on mathematical questions in a way that single-key cryptography generally does not, and conversely links cryptanalysis to wider mathematical research in a new way.
Asymmetric schemes are designed around the (conjectured) difficulty of solving various mathematical problems. If an improved algorithm can be found to solve the problem, then the system is weakened. For example, the security of the Diffie–Hellman key exchange scheme depends on the difficulty of calculating the discrete logarithm. In 1983, Don Coppersmith found a faster way to find discrete logarithms (in certain groups), and thereby requiring cryptographers to use larger groups (or different types of groups). RSA's security depends (in part) upon the difficulty of integer factorization – a breakthrough in factoring would impact the security of RSA.
In 1980, one could factor a difficult 50-digit number at an expense of 1012 elementary computer operations. By 1984 the state of the art in factoring algorithms had advanced to a point where a 75-digit number could be factored in 1012 operations. Advances in computing technology also meant that the operations could be performed much faster. Moore's law predicts that computer speeds will continue to increase. Factoring techniques may continue to do so as well, but will most likely depend on mathematical insight and creativity, neither of which has ever been successfully predictable. 150-digit numbers of the kind once used in RSA have been factored. The effort was greater than above, but was not unreasonable on fast modern computers. By the start of the 21st century, 150-digit numbers were no longer considered a large enough key size for RSA. Numbers with several hundred digits were still considered too hard to factor in 2005, though methods will probably continue to improve over time, requiring key size to keep pace or other methods such as elliptic curve cryptography to be used.
Another distinguishing feature of asymmetric schemes is that, unlike attacks on symmetric cryptosystems, any cryptanalysis has the opportunity to make use of knowledge gained from the public key.
== Attacking cryptographic hash systems ==
Birthday attack
Hash function security summary
Rainbow table
== Side-channel attacks ==
Black-bag cryptanalysis
Man-in-the-middle attack
Power analysis
Replay attack
Rubber-hose cryptanalysis
Timing analysis
== Quantum computing applications for cryptanalysis ==
Quantum computers, which are still in the early phases of research, have potential use in cryptanalysis. For example, Shor's Algorithm could factor large numbers in polynomial time, in effect breaking some commonly used forms of public-key encryption.
By using Grover's algorithm on a quantum computer, brute-force key search can be made quadratically faster. However, this could be countered by doubling the key length.
== See also ==
Economics of security
Global surveillance – Mass surveillance across national borders
Information assurance – Multi-disciplinary methods for decision support systems security, a term for information security often used in government
Information security – Protecting information by mitigating risk, the overarching goal of most cryptography
National Cipher Challenge – annual cryptographic competitionPages displaying wikidata descriptions as a fallback
Security engineering – Process of incorporating security controls into an information system, the design of applications and protocols
Security vulnerability – Exploitable weakness in a computer systemPages displaying short descriptions of redirect targets; vulnerabilities can include cryptographic or other flaws
Topics in cryptography
Zendian Problem – Exercise in communication intelligencePages displaying short descriptions of redirect targets
=== Historic cryptanalysts ===
Conel Hugh O'Donel Alexander
Charles Babbage
Fredson Bowers
Lambros D. Callimahos
Joan Clarke
Alastair Denniston
Agnes Meyer Driscoll
Elizebeth Friedman
William F. Friedman
Meredith Gardner
Friedrich Kasiski
Al-Kindi
Dilly Knox
Solomon Kullback
Marian Rejewski
Joseph Rochefort, whose contributions affected the outcome of the Battle of Midway
Frank Rowlett
Abraham Sinkov
Giovanni Soro, the Renaissance's first outstanding cryptanalyst
John Tiltman
Alan Turing
William T. Tutte
John Wallis – 17th-century English mathematician
William Stone Weedon – worked with Fredson Bowers in World War II
Herbert Yardley
== References ==
=== Citations ===
=== Sources ===
== Further reading ==
Bard, Gregory V. (2009). Algebraic Cryptanalysis. Springer. ISBN 978-1-4419-1019-6.
Hinek, M. Jason (2009). Cryptanalysis of RSA and Its Variants. CRC Press. ISBN 978-1-4200-7518-2.
Joux, Antoine (2009). Algorithmic Cryptanalysis. CRC Press. ISBN 978-1-4200-7002-6.
Junod, Pascal; Canteaut, Anne (2011). Advanced Linear Cryptanalysis of Block and Stream Ciphers. IOS Press. ISBN 978-1-60750-844-1.
Stamp, Mark; Low, Richard (2007). Applied Cryptanalysis: Breaking Ciphers in the Real World. John Wiley & Sons. ISBN 978-0-470-11486-5.
Swenson, Christopher (2008). Modern cryptanalysis: techniques for advanced code breaking. John Wiley & Sons. ISBN 978-0-470-13593-8.
Wagstaff, Samuel S. (2003). Cryptanalysis of number-theoretic ciphers. CRC Press. ISBN 978-1-58488-153-7.
== External links ==
Basic Cryptanalysis (files contain 5 line header, that has to be removed first)
Distributed Computing Projects
List of tools for cryptanalysis on modern cryptography
Simon Singh's crypto corner
The National Museum of Computing
UltraAnvil tool for attacking simple substitution ciphers
How Alan Turing Cracked The Enigma Code Imperial War Museums | Wikipedia/Cryptographic_attack |
The Lightning Network (LN) is a payment protocol built on the bitcoin blockchain. It is intended to enable fast transactions among participating nodes (independently run members of the network) and has been proposed as a solution to the bitcoin scalability problem.
== History ==
Joseph Poon and Thaddeus Dryja published a Lightning Network white paper in February 2015.
Lightning Labs launched the Lightning Network in 2018 with the goal of reducing the cost and time required for cryptocurrency transaction. Specifically, the bitcoin blockchain can only process around 7 transactions per second (compared to Visa Inc., which can process around 24,000 transactions per second). Despite initial enthusiasm for the Lightning Network, reports on social media of failed transactions, security vulnerabilities, and over-complication lead to a decline in interest.
On January 19, 2019, pseudonymous Twitter user hodlonaut began a game-like promotional test of the Lightning Network by sending 100,000 satoshis (0.001 bitcoin) to a trusted recipient where each recipient added 10,000 satoshis ($0.34 at the time) to send to the next trusted recipient. The "lightning torch" payment reached notable personalities including former Twitter A.K.A X CEO Jack Dorsey, Litecoin Creator Charlie Lee, Lightning Labs CEO Elizabeth Stark, and Binance CEO "CZ" Changpeng Zhao, among others.
== Design ==
Andreas Antonopoulos calls the Lightning Network a second layer routing network. The payment channels allow participants to transfer money to each other without having to make all their transactions public on the blockchain. This is secured by penalizing uncooperative participants. When opening a channel, participants must commit an amount on the blockchain (a funding transaction). Time-based script extensions like CheckSequenceVerify and CheckLockTimeVerify make the penalties possible.
Transacting parties use the Lightning Network by opening a payment channel and transferring (committing) funds to the relevant layer-1 blockchain (e.g. bitcoin) under a smart contract. The parties then make any number of off-chain Lightning Network transactions that update the tentative distribution of the channel's funds, without broadcasting to the blockchain. Whenever the parties have finished their transaction session, they close the payment channel, and the smart contract distributes the committed funds according to the transaction record.
To initiate closing, one node first broadcasts the current state of the transaction record to the network, including a proposed settlement, a distribution of the committed funds. If both parties confirm the proposal, the funds are immediately paid on-chain. The other option is uncooperative closure, for example if one node has dropped from the network, or if it is broadcasting an incorrect (possibly fraudulent) transaction state. In this case settlement is delayed during a dispute period, when nodes may contest the proposal. If the second node broadcasts a more up-to-date timestamped distribution, including some transactions omitted by the first proposal, then all committed funds are transferred to the second node: this punitive breach remedy transaction thwarts attempts to defraud the other node by broadcasting out-of-date transactions.
== Implementations ==
=== Benefits ===
According to bitcoin advocate Andreas Antonopoulos, the Lightning Network provides several advantages over on-chain transactions:
Granularity – According to Andreas Antonopoulos, some implementations of the Lightning Network allow for payments that are smaller than a satoshi, the smallest unit on the base layer of bitcoin.
Privacy – Lightning network payments may be routed through many sequential channels where each node operator will be able to see payments across their channels, but they will not be able to see the source nor destination of those funds if they are non-adjacent.
Speed – Settlement time for lightning network transactions is under a minute and can occur in milliseconds. Confirmation time on the bitcoin blockchain, for comparison, occurs every ten minutes, on average.
Transaction throughput – There are no fundamental limits to the amount of payments per second that can occur under the protocol. The amount of transactions are only limited by the capacity and speed of each node.
=== Limitations ===
The Lightning Network (LN) operates through bidirectional payment channels between two nodes, forming smart contracts that facilitate off-chain transactions. If either party closes a channel, the final state is settled on the Bitcoin blockchain. While this design enables faster and cheaper transactions, the necessity of on-chain transactions to open and close channels introduces scalability constraints. These limitations can be partially mitigated when multiple users who trust each other share a Lightning node.
Lightning Network's dispute resolution mechanism requires participants to monitor the blockchain to detect and respond to potential fraud. This responsibility can be delegated to "watchtower" nodes—trusted third parties that oversee the network on behalf of users. A standard time window, typically 24 hours, is allocated for a participant to contest an attempted fraud once a channel closure is broadcast.
=== Routing ===
When a direct payment channel between two parties is unavailable, the Lightning Network facilitates transactions through multi-hop routing. In this process, payments are forwarded across a series of intermediary nodes, each connected via bidirectional channels. To preserve privacy and security, the network employs an onion routing protocol, wherein each node in the path decrypts only enough information to determine the next hop, without knowledge of the payment's origin or final destination .
This routing mechanism relies on Hashed Timelock Contracts (HTLCs), which ensure that payments are either completed in full or fail entirely, preventing partial transfers. HTLCs use cryptographic hashes and time constraints to secure the transaction across multiple hops.
For successful routing, both the sender and receiver must maintain channels with sufficient liquidity. The sender's node constructs a route by analyzing the network graph to find a viable path that meets criteria such as channel capacity and fee rates. However, due to the private nature of channel balances, the sender may not have complete information about the liquidity available in each channel, leading to potential payment failures
To mitigate this, some implementations incorporate probing mechanisms and probabilistic scoring to estimate the reliability of potential routes based on historical data . Additionally, strategies like multi-path payments (MPP) allow larger transactions to be split into smaller parts, increasing the likelihood of successful routing.
Overall, the Lightning Network's routing protocol enables scalable and private off-chain transactions, though it requires careful management of channel liquidity and network connectivity to ensure optimal performance.
=== Developer Tools and Simplification Efforts ===
To address the inherent complexities of operating on the Lightning Network—such as channel management, liquidity allocation, and routing reliability—several initiatives have emerged offering tools and platforms designed to abstract or automate these technical challenges.
==== Lightspark ====
Founded in 2022, Lightspark provides enterprise-grade infrastructure for the Lightning Network. It aims to simplify onboarding and scale Bitcoin payment capabilities for institutions and developers. The platform offers:
Lightspark Connect – a tool for automated Lightning node deployment.
Lightspark Predict – a smart routing engine that improves payment reliability by optimizing liquidity paths.
Developer SDKs and APIs – allowing businesses to integrate Lightning payments into their products without managing underlying node operations. These tools collectively reduce the operational complexity for enterprises, supporting broader adoption of Lightning payments.
==== Breez SDK ====
The Breez SDK offers developers a comprehensive solution to integrate self-custodial Lightning payments into applications. It abstracts the complexities of channel management, liquidity provisioning, and node operations, facilitating seamless Bitcoin payment integration.
===== Nodeless (Liquid Implementation) =====
The Nodeless implementation leverages the Liquid Network, a Bitcoin sidechain, to facilitate Lightning payments without requiring users to manage channels or operate nodes. Key features include:
Submarine Swaps: Utilizes submarine and reverse submarine swaps to convert between Liquid BTC (L-BTC) and Lightning Network sats, enabling seamless fund movement between networks.
Protocol Support: Supports various payment protocols, including BOLT11, BOLT12, LNURL-Pay, LNURL-Withdraw, Lightning Address, and on-chain BTC addresses.
Multi-Asset Support: Offers compatibility with assets like USDT on the Liquid Network.
User Experience: Eliminates the need for channel management and setup fees, providing a frictionless experience for end-users.
==== Native (Greenlight Implementation) ====
The Native implementation integrates with Blockstream's Greenlight, a cloud-based, non-custodial Lightning node service. This setup provides each user with a dedicated Lightning node, managed in the cloud but controlled by the user's device. Key features include:
Dedicated Nodes: Each user operates a personal Lightning node hosted on Greenlight's infrastructure, ensuring autonomy and security.
Protocol Support: Facilitates payments via BOLT11, LNURL-Pay, Lightning Address, and on-chain BTC addresses.
Integrated Watchtower: Includes a built-in watchtower service to monitor the blockchain for potential fraud, enhancing security.
Fiat On-Ramps: Supports third-party fiat on-ramps, allowing users to convert between fiat currencies and Bitcoin seamlessly.
Developer Tools: Provides SDK bindings for various programming languages, including Kotlin, Swift, Python, and React Native, facilitating integration across platforms.
===== Voltage =====
Voltage is a Lightning-as-a-Service (LaaS) provider that launched in 2020. Its mission is to provide enterprises with a Lightning Network solution that enables the settlement of real-time payments with near-zero fees, enabling organizations to send and receive payments while creating new experiences and business models
===== Lightning Dev Kit (LDK) =====
LDK is a flexible Lightning implementation with supporting modules. It provides a multi-language native API, allowing developers to run a Lightning node on mobile, web, hardware security modules (HSMs), Lightning Service Providers (LSPs), or existing infrastructure.
===== Amboss Technologies =====
Amboss harnesses machine learning, including reinforcement learning on network graphs, to develop intelligent tools for the Lightning Network. With over five years of data-driven insights, Amboss drives network growth and unlocks new opportunities as Bitcoin scales globally.
===== Strike =====
Strike is a mobile payments app that enables instant transactions via the Lightning Network. It facilitates swift, peer-to-peer micropayments in Bitcoin, aiming to make digital assets more accessible to the general public.
== Compatible Wallets ==
Several cryptocurrency wallets offer support for the Lightning Network, enabling instant, low-cost, and scalable Bitcoin transactions. Available options include custodial, non-custodial, and hybrid models, each offering different levels of technical complexity and user control. Below are some of the main wallets currently compatible with the Lightning Network:
Electrum One of the most traditional wallets in the Bitcoin ecosystem, Electrum offers desktop support for the Lightning Network. It is a non-custodial wallet designed for advanced users, providing full control over funds and a wide range of customization options.
Phoenix (ACINQ) A non-custodial mobile wallet focused on simplicity. Phoenix manages channel and liquidity configuration automatically, eliminating the need for manual setup. It is developed by ACINQ, a leading company in the Lightning ecosystem.
Misty Breez A self-custodial wallet built for everyday use. Misty Breez includes features such as point-of-sale (POS) support, podcast streaming with Lightning-based monetization, and automatic backups. It also handles channel and liquidity management without user intervention.
Muun A hybrid wallet that balances security and ease of use. Muun enables Lightning payments with automatic fallback to on-chain transactions. It is particularly popular in Brazil, especially among beginners.
BlueWallet A mobile wallet that supports the Lightning Network through connections with external nodes. BlueWallet operates as a custodial wallet by default but can be configured to connect to private nodes. Although no longer actively maintained, it remains functional.
Cash App A widely used payment app in the United States, with direct integration of the Lightning Network. Cash App is custodial and focuses on ease of use for mainstream users.
Klever Wallet A multi-blockchain wallet that supports the Lightning Network. Klever Wallet eliminates the need for manual channel, node (nodeless), and liquidity setup, making it suitable for users interacting with multiple blockchain networks beyond Bitcoin.
Wallet of Satoshi One of the simplest ways to use the Lightning Network. Wallet of Satoshi is fully custodial and ideal for beginners or scenarios where convenience is a priority — such as events, demos, or educational use cases.
== Use cases ==
Since its inception, Bitcoin has been envisioned as a peer-to-peer electronic cash system. A notable early example occurred in May 2010 when Laszlo Hanyecz paid 10,000 BTC for two pizzas—an event now noted annually as Bitcoin Pizza Day . As Bitcoin’s value and network congestion increased, its use shifted more towards a store of value. However, the development of the Lightning Network (LN) has revitalized Bitcoin’s potential for fast, low-cost, and scalable payments.
The Lightning Network is utilized globally for various practical applications:
Micropayments and Everyday Commerce: LN enables low-fee transactions suitable for small purchases, from buying digital goods to paying for coffee. Innovative use cases, such as triggering actions like feeding goats via Lightning payments, have demonstrated its versatility.
Grassroots Economic Initiatives: In El Zonte, El Salvador—also known as "Bitcoin Beach"—local communities began using LN to transact in Bitcoin for groceries, school fees, and services, showcasing how LN could support circular economies in developing regions.
Global Remittances and Cross-Border Payments: Lightning offers an efficient alternative to traditional remittance services by enabling near-instant global transfers without intermediaries or high fees.
Mobile and Point-of-Sale Payments: Mobile wallets integrating Lightning make it feasible to use Bitcoin in physical stores and daily purchases.
Tipping and Content Monetization: LN is also used for micro-tipping on social media platforms and blogs, offering an alternative to traditional ad-driven or subscription-based models.
In Brazil, several communities have adopted the Lightning Network to enhance local economies:
Rolante, Rio Grande do Sul: This town has become a leader in Bitcoin adoption, with over 200 businesses accepting Bitcoin payments. The initiative, led by the "Bitcoin é Aqui" project, has transformed Rolante into a model for integrating cryptocurrency into daily life.
Jericoacoara, Ceará: Known as "Bitcoin Beach Brazil," this coastal village has implemented LN to facilitate transactions among residents and tourists. The community has also engaged in educational initiatives, such as distributing Bitcoin wallets to students and teachers.
Santo Antônio do Pinhal, São Paulo: Inspired by Rolante's success, this town has embraced Bitcoin adoption, with numerous establishments accepting Bitcoin payments via Lightning Network , aiming to promote cryptocurrency tourism.
São Thomé das Letras, Minas Gerais: This tourist destination has integrated Lightning Network into its local economy, with businesses accepting Bitcoin and educational programs teaching residents about cryptocurrency.
As Lightning infrastructure continues to improve, adoption is expanding across both emerging economies and industrialized nations, reinforcing its role in Bitcoin’s usability for day-to-day transactions and financial empowerment.
== References ==
== External links ==
lightning.network | Wikipedia/Lightning_Network |
Hedera Hashgraph, commonly known as Hedera, is a distributed ledger which uses a variant of proof of stake to reach consensus. The native cryptocurrency of the Hedera Hashgraph system is HBAR.
== History ==
Hashgraph was invented in the mid-2010s by the American computer scientist Leemon Baird. Baird is the co-founder and chief technical officer of Swirlds, a company that holds patents covering the hashgraph algorithm. Hashgraph were described as a continuation or successor to the blockchain concept, which provides increased speed, fairness, low cost, and security constraints.
Based on Hashgraph protocol, Hedera Hashgraph mainnet was launched in 2019. The Hedera white paper co-authored by Baird explained that "at the end of each round, each node calculates the shared state after processing all transactions that were received in that round and before," and it "digitally signs a hash of that shared state, puts it in a transaction, and gossips it out to the community."
In 2020, Google Cloud joined Hedera Governing Council. A year later, EFTPOS joined the governing council.
In September 2024 Hedera has transferred all source code of the Hedera Hashgraph to the Linux Foundation. The sources are now available as the open-source and vendor-neutral project Hiero.
== Distributed ledger ==
Hedera Hashgraph is a public distributed ledger based on the Hashgraph algorithm. Hedera Hashgraph is developed by a company of the same name, Hedera, based in Dallas, Texas. Hedera was founded by Hashgraph inventor Leemon Baird and his business partner Mance Harmon, and Andrew Masanto, adding significant contribution to the team. Previously, Hedera had an exclusive license to the Hashgraph patents held by their company, Swirlds. The Hedera Governing Council voted to purchase the patent rights to Hashgraph and make the algorithm open source under the Apache License in 2022.
Hedera mainnet is maintained by governing council members which include companies such as Deutsche Telekom, IBM, Neuron, FIS Global, and Tata Communications.
== Hashgraphs ==
Unlike blockchains, hashgraphs do not bundle data into blocks or use miners to validate transactions. Instead, hashgraphs use a "gossip about gossip" protocol where the individual nodes on the network "gossip" about transactions to create directed acyclic graphs that time-sequence transactions. Each "gossip" message contains one or more transactions plus a timestamp, a digital signature, and cryptographic hashes of two earlier events. This makes Hashgraph form an asynchronous Byzantine Fault-Tolerant (aBFT) consensus algorithm.
== Criticism ==
It has been claimed that hashgraphs are less technically constrained than blockchains proper. Cornell Professor Emin Gün Sirer notes that "The correctness of the entire Hashgraph protocol seems to hinge on every participant knowing and agreeing upon N, the total number of participants in the system," which is "a difficult number to determine in an open distributed system." Baird responded that "All of the nodes at a given time know how many nodes there are."
== References == | Wikipedia/Hashgraph |
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a hash function are called hash values, hash codes, (hash/message) digests, or simply hashes. The values are usually used to index a fixed-size table called a hash table. Use of a hash function to index a hash table is called hashing or scatter-storage addressing.
Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally- and storage-space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often-exponential storage requirements of direct access of state spaces of large or variable-length keys.
Use of hash functions relies on statistical properties of key and function interaction: worst-case behavior is intolerably bad but rare, and average-case behavior can be nearly optimal (minimal collision).: 527
Hash functions are related to (and often confused with) checksums, check digits, fingerprints, lossy compression, randomization functions, error-correcting codes, and ciphers. Although the concepts overlap to some extent, each one has its own uses and requirements and is designed and optimized differently. The hash function differs from these concepts mainly in terms of data integrity. Hash tables may use non-cryptographic hash functions, while cryptographic hash functions are used in cybersecurity to secure sensitive data such as passwords.
== Overview ==
In a hash table, a hash function takes a key as an input, which is associated with a datum or record and used to identify it to the data storage and retrieval application. The keys may be fixed-length, like an integer, or variable-length, like a name. In some cases, the key is the datum itself. The output is a hash code used to index a hash table holding the data or records, or pointers to them.
A hash function may be considered to perform three functions:
Convert variable-length keys into fixed-length (usually machine-word-length or less) values, by folding them by words or other units using a parity-preserving operator like ADD or XOR,
Scramble the bits of the key so that the resulting values are uniformly distributed over the keyspace, and
Map the key values into ones less than or equal to the size of the table.
A good hash function satisfies two basic properties: it should be very fast to compute, and it should minimize duplication of output values (collisions). Hash functions rely on generating favorable probability distributions for their effectiveness, reducing access time to nearly constant. High table loading factors, pathological key sets, and poorly designed hash functions can result in access times approaching linear in the number of items in the table. Hash functions can be designed to give the best worst-case performance, good performance under high table loading factors, and in special cases, perfect (collisionless) mapping of keys into hash codes. Implementation is based on parity-preserving bit operations (XOR and ADD), multiply, or divide. A necessary adjunct to the hash function is a collision-resolution method that employs an auxiliary data structure like linked lists, or systematic probing of the table to find an empty slot.
== Hash tables ==
Hash functions are used in conjunction with hash tables to store and retrieve data items or data records. The hash function translates the key associated with each datum or record into a hash code, which is used to index the hash table. When an item is to be added to the table, the hash code may index an empty slot (also called a bucket), in which case the item is added to the table there. If the hash code indexes a full slot, then some kind of collision resolution is required: the new item may be omitted (not added to the table), or replace the old item, or be added to the table in some other location by a specified procedure. That procedure depends on the structure of the hash table. In chained hashing, each slot is the head of a linked list or chain, and items that collide at the slot are added to the chain. Chains may be kept in random order and searched linearly, or in serial order, or as a self-ordering list by frequency to speed up access. In open address hashing, the table is probed starting from the occupied slot in a specified manner, usually by linear probing, quadratic probing, or double hashing until an open slot is located or the entire table is probed (overflow). Searching for the item follows the same procedure until the item is located, an open slot is found, or the entire table has been searched (item not in table).
=== Specialized uses ===
Hash functions are also used to build caches for large data sets stored in slow media. A cache is generally simpler than a hashed search table, since any collision can be resolved by discarding or writing back the older of the two colliding items.
Hash functions are an essential ingredient of the Bloom filter, a space-efficient probabilistic data structure that is used to test whether an element is a member of a set.
A special case of hashing is known as geometric hashing or the grid method. In these applications, the set of all inputs is some sort of metric space, and the hashing function can be interpreted as a partition of that space into a grid of cells. The table is often an array with two or more indices (called a grid file, grid index, bucket grid, and similar names), and the hash function returns an index tuple. This principle is widely used in computer graphics, computational geometry, and many other disciplines, to solve many proximity problems in the plane or in three-dimensional space, such as finding closest pairs in a set of points, similar shapes in a list of shapes, similar images in an image database, and so on.
Hash tables are also used to implement associative arrays and dynamic sets.
== Properties ==
=== Uniformity ===
A good hash function should map the expected inputs as evenly as possible over its output range. That is, every hash value in the output range should be generated with roughly the same probability. The reason for this last requirement is that the cost of hashing-based methods goes up sharply as the number of collisions—pairs of inputs that are mapped to the same hash value—increases. If some hash values are more likely to occur than others, then a larger fraction of the lookup operations will have to search through a larger set of colliding table entries.
This criterion only requires the value to be uniformly distributed, not random in any sense. A good randomizing function is (barring computational efficiency concerns) generally a good choice as a hash function, but the converse need not be true.
Hash tables often contain only a small subset of the valid inputs. For instance, a club membership list may contain only a hundred or so member names, out of the very large set of all possible names. In these cases, the uniformity criterion should hold for almost all typical subsets of entries that may be found in the table, not just for the global set of all possible entries.
In other words, if a typical set of m records is hashed to n table slots, then the probability of a bucket receiving many more than m/n records should be vanishingly small. In particular, if m < n, then very few buckets should have more than one or two records. A small number of collisions is virtually inevitable, even if n is much larger than m—see the birthday problem.
In special cases when the keys are known in advance and the key set is static, a hash function can be found that achieves absolute (or collisionless) uniformity. Such a hash function is said to be perfect. There is no algorithmic way of constructing such a function—searching for one is a factorial function of the number of keys to be mapped versus the number of table slots that they are mapped into. Finding a perfect hash function over more than a very small set of keys is usually computationally infeasible; the resulting function is likely to be more computationally complex than a standard hash function and provides only a marginal advantage over a function with good statistical properties that yields a minimum number of collisions. See universal hash function.
=== Testing and measurement ===
When testing a hash function, the uniformity of the distribution of hash values can be evaluated by the chi-squared test. This test is a goodness-of-fit measure: it is the actual distribution of items in buckets versus the expected (or uniform) distribution of items. The formula is
∑
j
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0
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1
(
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(
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/
2
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,
{\displaystyle {\frac {\sum _{j=0}^{m-1}(b_{j})(b_{j}+1)/2}{(n/2m)(n+2m-1)}},}
where n is the number of keys, m is the number of buckets, and bj is the number of items in bucket j.
A ratio within one confidence interval (such as 0.95 to 1.05) is indicative that the hash function evaluated has an expected uniform distribution.
Hash functions can have some technical properties that make it more likely that they will have a uniform distribution when applied. One is the strict avalanche criterion: whenever a single input bit is complemented, each of the output bits changes with a 50% probability. The reason for this property is that selected subsets of the keyspace may have low variability. For the output to be uniformly distributed, a low amount of variability, even one bit, should translate into a high amount of variability (i.e. distribution over the tablespace) in the output. Each bit should change with a probability of 50% because, if some bits are reluctant to change, then the keys become clustered around those values. If the bits want to change too readily, then the mapping is approaching a fixed XOR function of a single bit. Standard tests for this property have been described in the literature. The relevance of the criterion to a multiplicative hash function is assessed here.
=== Efficiency ===
In data storage and retrieval applications, the use of a hash function is a trade-off between search time and data storage space. If search time were unbounded, then a very compact unordered linear list would be the best medium; if storage space were unbounded, then a randomly accessible structure indexable by the key-value would be very large and very sparse, but very fast. A hash function takes a finite amount of time to map a potentially large keyspace to a feasible amount of storage space searchable in a bounded amount of time regardless of the number of keys. In most applications, the hash function should be computable with minimum latency and secondarily in a minimum number of instructions.
Computational complexity varies with the number of instructions required and latency of individual instructions, with the simplest being the bitwise methods (folding), followed by the multiplicative methods, and the most complex (slowest) are the division-based methods.
Because collisions should be infrequent, and cause a marginal delay but are otherwise harmless, it is usually preferable to choose a faster hash function over one that needs more computation but saves a few collisions.
Division-based implementations can be of particular concern because a division requires multiple cycles on nearly all processor microarchitectures. Division (modulo) by a constant can be inverted to become a multiplication by the word-size multiplicative-inverse of that constant. This can be done by the programmer, or by the compiler. Division can also be reduced directly into a series of shift-subtracts and shift-adds, though minimizing the number of such operations required is a daunting problem; the number of machine-language instructions resulting may be more than a dozen and swamp the pipeline. If the microarchitecture has hardware multiply functional units, then the multiply-by-inverse is likely a better approach.
We can allow the table size n to not be a power of 2 and still not have to perform any remainder or division operation, as these computations are sometimes costly. For example, let n be significantly less than 2b. Consider a pseudorandom number generator function P(key) that is uniform on the interval [0, 2b − 1]. A hash function uniform on the interval [0, n − 1] is n P(key) / 2b. We can replace the division by a (possibly faster) right bit shift: n P(key) >> b.
If keys are being hashed repeatedly, and the hash function is costly, then computing time can be saved by precomputing the hash codes and storing them with the keys. Matching hash codes almost certainly means that the keys are identical. This technique is used for the transposition table in game-playing programs, which stores a 64-bit hashed representation of the board position.
=== Universality ===
A universal hashing scheme is a randomized algorithm that selects a hash function h among a family of such functions, in such a way that the probability of a collision of any two distinct keys is 1/m, where m is the number of distinct hash values desired—independently of the two keys. Universal hashing ensures (in a probabilistic sense) that the hash function application will behave as well as if it were using a random function, for any distribution of the input data. It will, however, have more collisions than perfect hashing and may require more operations than a special-purpose hash function.
=== Applicability ===
A hash function that allows only certain table sizes or strings only up to a certain length, or cannot accept a seed (i.e. allow double hashing) is less useful than one that does.
A hash function is applicable in a variety of situations. Particularly within cryptography, notable applications include:
Integrity checking: Identical hash values for different files imply equality, providing a reliable means to detect file modifications.
Key derivation: Minor input changes result in a random-looking output alteration, known as the diffusion property. Thus, hash functions are valuable for key derivation functions.
Message authentication codes (MACs): Through the integration of a confidential key with the input data, hash functions can generate MACs ensuring the genuineness of the data, such as in HMACs.
Password storage: The password's hash value does not expose any password details, emphasizing the importance of securely storing hashed passwords on the server.
Signatures: Message hashes are signed rather than the whole message.
=== Deterministic ===
A hash procedure must be deterministic—for a given input value, it must always generate the same hash value. In other words, it must be a function of the data to be hashed, in the mathematical sense of the term. This requirement excludes hash functions that depend on external variable parameters, such as pseudo-random number generators or the time of day. It also excludes functions that depend on the memory address of the object being hashed, because the address may change during execution (as may happen on systems that use certain methods of garbage collection), although sometimes rehashing of the item is possible.
The determinism is in the context of the reuse of the function. For example, Python adds the feature that hash functions make use of a randomized seed that is generated once when the Python process starts in addition to the input to be hashed. The Python hash (SipHash) is still a valid hash function when used within a single run, but if the values are persisted (for example, written to disk), they can no longer be treated as valid hash values, since in the next run the random value might differ.
=== Defined range ===
It is often desirable that the output of a hash function have fixed size (but see below). If, for example, the output is constrained to 32-bit integer values, then the hash values can be used to index into an array. Such hashing is commonly used to accelerate data searches. Producing fixed-length output from variable-length input can be accomplished by breaking the input data into chunks of specific size. Hash functions used for data searches use some arithmetic expression that iteratively processes chunks of the input (such as the characters in a string) to produce the hash value.
=== Variable range ===
In many applications, the range of hash values may be different for each run of the program or may change along the same run (for instance, when a hash table needs to be expanded). In those situations, one needs a hash function which takes two parameters—the input data z, and the number n of allowed hash values.
A common solution is to compute a fixed hash function with a very large range (say, 0 to 232 − 1), divide the result by n, and use the division's remainder. If n is itself a power of 2, this can be done by bit masking and bit shifting. When this approach is used, the hash function must be chosen so that the result has fairly uniform distribution between 0 and n − 1, for any value of n that may occur in the application. Depending on the function, the remainder may be uniform only for certain values of n, e.g. odd or prime numbers.
=== Variable range with minimal movement (dynamic hash function) ===
When the hash function is used to store values in a hash table that outlives the run of the program, and the hash table needs to be expanded or shrunk, the hash table is referred to as a dynamic hash table.
A hash function that will relocate the minimum number of records when the table is resized is desirable. What is needed is a hash function H(z,n) (where z is the key being hashed and n is the number of allowed hash values) such that H(z,n + 1) = H(z,n) with probability close to n/(n + 1).
Linear hashing and spiral hashing are examples of dynamic hash functions that execute in constant time but relax the property of uniformity to achieve the minimal movement property. Extendible hashing uses a dynamic hash function that requires space proportional to n to compute the hash function, and it becomes a function of the previous keys that have been inserted. Several algorithms that preserve the uniformity property but require time proportional to n to compute the value of H(z,n) have been invented.
A hash function with minimal movement is especially useful in distributed hash tables.
=== Data normalization ===
In some applications, the input data may contain features that are irrelevant for comparison purposes. For example, when looking up a personal name, it may be desirable to ignore the distinction between upper and lower case letters. For such data, one must use a hash function that is compatible with the data equivalence criterion being used: that is, any two inputs that are considered equivalent must yield the same hash value. This can be accomplished by normalizing the input before hashing it, as by upper-casing all letters.
== Hashing integer data types ==
There are several common algorithms for hashing integers. The method giving the best distribution is data-dependent. One of the simplest and most common methods in practice is the modulo division method.
=== Identity hash function ===
If the data to be hashed is small enough, then one can use the data itself (reinterpreted as an integer) as the hashed value. The cost of computing this identity hash function is effectively zero. This hash function is perfect, as it maps each input to a distinct hash value.
The meaning of "small enough" depends on the size of the type that is used as the hashed value. For example, in Java, the hash code is a 32-bit integer. Thus the 32-bit integer Integer and 32-bit floating-point Float objects can simply use the value directly, whereas the 64-bit integer Long and 64-bit floating-point Double cannot.
Other types of data can also use this hashing scheme. For example, when mapping character strings between upper and lower case, one can use the binary encoding of each character, interpreted as an integer, to index a table that gives the alternative form of that character ("A" for "a", "8" for "8", etc.). If each character is stored in 8 bits (as in extended ASCII or ISO Latin 1), the table has only 28 = 256 entries; in the case of Unicode characters, the table would have 17 × 216 = 1114112 entries.
The same technique can be used to map two-letter country codes like "us" or "za" to country names (262 = 676 table entries), 5-digit ZIP codes like 13083 to city names (100000 entries), etc. Invalid data values (such as the country code "xx" or the ZIP code 00000) may be left undefined in the table or mapped to some appropriate "null" value.
=== Trivial hash function ===
If the keys are uniformly or sufficiently uniformly distributed over the key space, so that the key values are essentially random, then they may be considered to be already "hashed". In this case, any number of any bits in the key may be extracted and collated as an index into the hash table. For example, a simple hash function might mask off the m least significant bits and use the result as an index into a hash table of size 2m.
=== Mid-squares ===
A mid-squares hash code is produced by squaring the input and extracting an appropriate number of middle digits or bits. For example, if the input is 123456789 and the hash table size 10000, then squaring the key produces 15241578750190521, so the hash code is taken as the middle 4 digits of the 17-digit number (ignoring the high digit) 8750. The mid-squares method produces a reasonable hash code if there is not a lot of leading or trailing zeros in the key. This is a variant of multiplicative hashing, but not as good because an arbitrary key is not a good multiplier.
=== Division hashing ===
A standard technique is to use a modulo function on the key, by selecting a divisor M which is a prime number close to the table size, so h(K) ≡ K (mod M). The table size is usually a power of 2. This gives a distribution from {0, M − 1}. This gives good results over a large number of key sets. A significant drawback of division hashing is that division requires multiple cycles on most modern architectures (including x86) and can be 10 times slower than multiplication. A second drawback is that it will not break up clustered keys. For example, the keys 123000, 456000, 789000, etc. modulo 1000 all map to the same address. This technique works well in practice because many key sets are sufficiently random already, and the probability that a key set will be cyclical by a large prime number is small.
=== Algebraic coding ===
Algebraic coding is a variant of the division method of hashing which uses division by a polynomial modulo 2 instead of an integer to map n bits to m bits.: 512–513 In this approach, M = 2m, and we postulate an mth-degree polynomial Z(x) = xm + ζm−1xm−1 + ⋯ + ζ0. A key K = (kn−1…k1k0)2 can be regarded as the polynomial K(x) = kn−1xn−1 + ⋯ + k1x + k0. The remainder using polynomial arithmetic modulo 2 is K(x) mod Z(x) = hm−1xm−1 + ⋯ h1x + h0. Then h(K) = (hm−1…h1h0)2. If Z(x) is constructed to have t or fewer non-zero coefficients, then keys which share fewer than t bits are guaranteed to not collide.
Z is a function of k, t, and n (the last of which is a divisor of 2k − 1) and is constructed from the finite field GF(2k). Knuth gives an example: taking (n,m,t) = (15,10,7) yields Z(x) = x10 + x8 + x5 + x4 + x2 + x + 1. The derivation is as follows:
Let S be the smallest set of integers such that {1,2,…,t} ⊆ S and (2j mod n) ∈ S ∀j ∈ S.
Define
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{\displaystyle P(x)=\prod _{j\in S}(x-\alpha ^{j})}
where α ∈n GF(2k) and where the coefficients of P(x) are computed in this field. Then the degree of P(x) = |S|. Since α2j is a root of P(x) whenever αj is a root, it follows that the coefficients pi of P(x) satisfy p2i = pi, so they are all 0 or 1. If R(x) = rn−1xn−1 + ⋯ + r1x + r0 is any nonzero polynomial modulo 2 with at most t nonzero coefficients, then R(x) is not a multiple of P(x) modulo 2. If follows that the corresponding hash function will map keys with fewer than t bits in common to unique indices.: 542–543
The usual outcome is that either n will get large, or t will get large, or both, for the scheme to be computationally feasible. Therefore, it is more suited to hardware or microcode implementation.: 542–543
=== Unique permutation hashing ===
Unique permutation hashing has a guaranteed best worst-case insertion time.
=== Multiplicative hashing ===
Standard multiplicative hashing uses the formula ha(K) = ⌊(aK mod W) / (W/M)⌋, which produces a hash value in {0, …, M − 1}. The value a is an appropriately chosen value that should be relatively prime to W; it should be large, and its binary representation a random mix of 1s and 0s. An important practical special case occurs when W = 2w and M = 2m are powers of 2 and w is the machine word size. In this case, this formula becomes ha(K) = ⌊(aK mod 2w) / 2w−m⌋. This is special because arithmetic modulo 2w is done by default in low-level programming languages and integer division by a power of 2 is simply a right-shift, so, in C, for example, this function becomes
and for fixed m and w this translates into a single integer multiplication and right-shift, making it one of the fastest hash functions to compute.
Multiplicative hashing is susceptible to a "common mistake" that leads to poor diffusion—higher-value input bits do not affect lower-value output bits. A transmutation on the input which shifts the span of retained top bits down and XORs or ADDs them to the key before the multiplication step corrects for this. The resulting function looks like:
=== Fibonacci hashing ===
Fibonacci hashing is a form of multiplicative hashing in which the multiplier is 2w / ϕ, where w is the machine word length and ϕ (phi) is the golden ratio (approximately 1.618). A property of this multiplier is that it uniformly distributes over the table space, blocks of consecutive keys with respect to any block of bits in the key. Consecutive keys within the high bits or low bits of the key (or some other field) are relatively common. The multipliers for various word lengths are:
16: a = 9E3716 = 4050310
32: a = 9E3779B916 = 265443576910
48: a = 9E3779B97F4B16 = 17396110258977110
64: a = 9E3779B97F4A7C1516 = 1140071481932319848510
The multiplier should be odd, so the least significant bit of the output is invertible modulo 2w. The last two values given above are rounded (up and down, respectively) by more than 1/2 of a least-significant bit to achieve this.
=== Zobrist hashing ===
Tabulation hashing, more generally known as Zobrist hashing after Albert Zobrist, is a method for constructing universal families of hash functions by combining table lookup with XOR operations. This algorithm has proven to be very fast and of high quality for hashing purposes (especially hashing of integer-number keys).
Zobrist hashing was originally introduced as a means of compactly representing chess positions in computer game-playing programs. A unique random number was assigned to represent each type of piece (six each for black and white) on each space of the board. Thus a table of 64×12 such numbers is initialized at the start of the program. The random numbers could be any length, but 64 bits was natural due to the 64 squares on the board. A position was transcribed by cycling through the pieces in a position, indexing the corresponding random numbers (vacant spaces were not included in the calculation) and XORing them together (the starting value could be 0 (the identity value for XOR) or a random seed). The resulting value was reduced by modulo, folding, or some other operation to produce a hash table index. The original Zobrist hash was stored in the table as the representation of the position.
Later, the method was extended to hashing integers by representing each byte in each of 4 possible positions in the word by a unique 32-bit random number. Thus, a table of 28×4 random numbers is constructed. A 32-bit hashed integer is transcribed by successively indexing the table with the value of each byte of the plain text integer and XORing the loaded values together (again, the starting value can be the identity value or a random seed). The natural extension to 64-bit integers is by use of a table of 28×8 64-bit random numbers.
This kind of function has some nice theoretical properties, one of which is called 3-tuple independence, meaning that every 3-tuple of keys is equally likely to be mapped to any 3-tuple of hash values.
=== Customized hash function ===
A hash function can be designed to exploit existing entropy in the keys. If the keys have leading or trailing zeros, or particular fields that are unused, always zero or some other constant, or generally vary little, then masking out only the volatile bits and hashing on those will provide a better and possibly faster hash function. Selected divisors or multipliers in the division and multiplicative schemes may make more uniform hash functions if the keys are cyclic or have other redundancies.
== Hashing variable-length data ==
When the data values are long (or variable-length) character strings—such as personal names, web page addresses, or mail messages—their distribution is usually very uneven, with complicated dependencies. For example, text in any natural language has highly non-uniform distributions of characters, and character pairs, characteristic of the language. For such data, it is prudent to use a hash function that depends on all characters of the string—and depends on each character in a different way.
=== Middle and ends ===
Simplistic hash functions may add the first and last n characters of a string along with the length, or form a word-size hash from the middle 4 characters of a string. This saves iterating over the (potentially long) string, but hash functions that do not hash on all characters of a string can readily become linear due to redundancies, clustering, or other pathologies in the key set. Such strategies may be effective as a custom hash function if the structure of the keys is such that either the middle, ends, or other fields are zero or some other invariant constant that does not differentiate the keys; then the invariant parts of the keys can be ignored.
=== Character folding ===
The paradigmatic example of folding by characters is to add up the integer values of all the characters in the string. A better idea is to multiply the hash total by a constant, typically a sizable prime number, before adding in the next character, ignoring overflow. Using exclusive-or instead of addition is also a plausible alternative. The final operation would be a modulo, mask, or other function to reduce the word value to an index the size of the table. The weakness of this procedure is that information may cluster in the upper or lower bits of the bytes; this clustering will remain in the hashed result and cause more collisions than a proper randomizing hash. ASCII byte codes, for example, have an upper bit of 0, and printable strings do not use the last byte code or most of the first 32 byte codes, so the information, which uses the remaining byte codes, is clustered in the remaining bits in an unobvious manner.
The classic approach, dubbed the PJW hash based on the work of Peter J. Weinberger at Bell Labs in the 1970s, was originally designed for hashing identifiers into compiler symbol tables as given in the "Dragon Book". This hash function offsets the bytes 4 bits before adding them together. When the quantity wraps, the high 4 bits are shifted out and if non-zero, xored back into the low byte of the cumulative quantity. The result is a word-size hash code to which a modulo or other reducing operation can be applied to produce the final hash index.
Today, especially with the advent of 64-bit word sizes, much more efficient variable-length string hashing by word chunks is available.
=== Word length folding ===
Modern microprocessors will allow for much faster processing if 8-bit character strings are not hashed by processing one character at a time, but by interpreting the string as an array of 32-bit or 64-bit integers and hashing/accumulating these "wide word" integer values by means of arithmetic operations (e.g. multiplication by constant and bit-shifting). The final word, which may have unoccupied byte positions, is filled with zeros or a specified randomizing value before being folded into the hash. The accumulated hash code is reduced by a final modulo or other operation to yield an index into the table.
=== Radix conversion hashing ===
Analogous to the way an ASCII or EBCDIC character string representing a decimal number is converted to a numeric quantity for computing, a variable-length string can be converted as xk−1ak−1 + xk−2ak−2 + ⋯ + x1a + x0. This is simply a polynomial in a radix a > 1 that takes the components (x0,x1,...,xk−1) as the characters of the input string of length k. It can be used directly as the hash code, or a hash function applied to it to map the potentially large value to the hash table size. The value of a is usually a prime number large enough to hold the number of different characters in the character set of potential keys. Radix conversion hashing of strings minimizes the number of collisions. Available data sizes may restrict the maximum length of string that can be hashed with this method. For example, a 128-bit word will hash only a 26-character alphabetic string (ignoring case) with a radix of 29; a printable ASCII string is limited to 9 characters using radix 97 and a 64-bit word. However, alphabetic keys are usually of modest length, because keys must be stored in the hash table. Numeric character strings are usually not a problem; 64 bits can count up to 1019, or 19 decimal digits with radix 10.
=== Rolling hash ===
In some applications, such as substring search, one can compute a hash function h for every k-character substring of a given n-character string by advancing a window of width k characters along the string, where k is a fixed integer, and n > k. The straightforward solution, which is to extract such a substring at every character position in the text and compute h separately, requires a number of operations proportional to k·n. However, with the proper choice of h, one can use the technique of rolling hash to compute all those hashes with an effort proportional to mk + n where m is the number of occurrences of the substring.
The most familiar algorithm of this type is Rabin-Karp with best and average case performance O(n+mk) and worst case O(n·k) (in all fairness, the worst case here is gravely pathological: both the text string and substring are composed of a repeated single character, such as t="AAAAAAAAAAA", and s="AAA"). The hash function used for the algorithm is usually the Rabin fingerprint, designed to avoid collisions in 8-bit character strings, but other suitable hash functions are also used.
=== Fuzzy hash ===
=== Perceptual hash ===
== Analysis ==
Worst case results for a hash function can be assessed two ways: theoretical and practical. The theoretical worst case is the probability that all keys map to a single slot. The practical worst case is the expected longest probe sequence (hash function + collision resolution method). This analysis considers uniform hashing, that is, any key will map to any particular slot with probability 1/m, a characteristic of universal hash functions.
While Knuth worries about adversarial attack on real time systems, Gonnet has shown that the probability of such a case is "ridiculously small". His representation was that the probability of k of n keys mapping to a single slot is αk / (eα k!), where α is the load factor, n/m.
== History ==
The term hash offers a natural analogy with its non-technical meaning (to chop up or make a mess out of something), given how hash functions scramble their input data to derive their output.: 514 In his research for the precise origin of the term, Donald Knuth notes that, while Hans Peter Luhn of IBM appears to have been the first to use the concept of a hash function in a memo dated January 1953, the term itself did not appear in published literature until the late 1960s, in Herbert Hellerman's Digital Computer System Principles, even though it was already widespread jargon by then.: 547–548
== See also ==
== Notes ==
== References ==
== External links ==
The Goulburn Hashing Function (PDF) by Mayur Patel
Hash Function Construction for Textual and Geometrical Data Retrieval (PDF) Latest Trends on Computers, Vol.2, pp. 483–489, CSCC Conference, Corfu, 2010 | Wikipedia/Hash_algorithm |
Tor is a free overlay network for enabling anonymous communication. It is built on free and open-source software run by over seven thousand volunteer-operated relays worldwide, as well as by millions of users who route their Internet traffic via random paths through these relays.
Using Tor makes it more difficult to trace a user's Internet activity by preventing any single point on the Internet (other than the user's device) from being able to view both where traffic originated from and where it is ultimately going to at the same time. This conceals a user's location and usage from anyone performing network surveillance or traffic analysis from any such point, protecting the user's freedom and ability to communicate confidentially.
== History ==
The core principle of Tor, known as onion routing, was developed in the mid-1990s by United States Naval Research Laboratory employees, mathematician Paul Syverson, and computer scientists Michael G. Reed and David Goldschlag, to protect American intelligence communications online. Onion routing is implemented by means of encryption in the application layer of the communication protocol stack, nested like the layers of an onion. The alpha version of Tor, developed by Syverson and computer scientists Roger Dingledine and Nick Mathewson and then called The Onion Routing project (which was later given the acronym "Tor"), was launched on 20 September 2002. The first public release occurred a year later.
In 2004, the Naval Research Laboratory released the code for Tor under a free license, and the Electronic Frontier Foundation (EFF) began funding Dingledine and Mathewson to continue its development. In 2006, Dingledine, Mathewson, and five others founded The Tor Project, a Massachusetts-based 501(c)(3) research-education nonprofit organization responsible for maintaining Tor. The EFF acted as The Tor Project's fiscal sponsor in its early years, and early financial supporters included the U.S. Bureau of Democracy, Human Rights, and Labor and International Broadcasting Bureau, Internews, Human Rights Watch, the University of Cambridge, Google, and Netherlands-based Stichting NLnet.
Over the course of its existence, various Tor vulnerabilities have been discovered and occasionally exploited. Attacks against Tor are an active area of academic research that is welcomed by The Tor Project itself.
== Usage ==
Tor enables its users to surf the Internet, chat and send instant messages anonymously, and is used by a wide variety of people for both licit and illicit purposes. Tor has, for example, been used by criminal enterprises, hacktivism groups, and law enforcement agencies at cross purposes, sometimes simultaneously; likewise, agencies within the U.S. government variously fund Tor (the U.S. State Department, the National Science Foundation, and – through the Broadcasting Board of Governors, which itself partially funded Tor until October 2012 – Radio Free Asia) and seek to subvert it. Tor was one of a dozen circumvention tools evaluated by a Freedom House-funded report based on user experience from China in 2010, which include Ultrasurf, Hotspot Shield, and Freegate.
Tor is not meant to completely solve the issue of anonymity on the web. Tor is not designed to completely erase tracking but instead to reduce the likelihood for sites to trace actions and data back to the user.
Tor can also be used for illegal activities. These can include privacy protection or censorship circumvention, as well as distribution of child abuse content, drug sales, or malware distribution.
Tor has been described by The Economist, in relation to Bitcoin and Silk Road, as being "a dark corner of the web". It has been targeted by the American National Security Agency and the British GCHQ signals intelligence agencies, albeit with marginal success, and more successfully by the British National Crime Agency in its Operation Notarise. At the same time, GCHQ has been using a tool named "Shadowcat" for "end-to-end encrypted access to VPS over SSH using the Tor network". Tor can be used for anonymous defamation, unauthorized news leaks of sensitive information, copyright infringement, distribution of illegal sexual content, selling controlled substances, weapons, and stolen credit card numbers, money laundering, bank fraud, credit card fraud, identity theft and the exchange of counterfeit currency; the black market utilizes the Tor infrastructure, at least in part, in conjunction with Bitcoin. It has also been used to brick IoT devices.
In its complaint against Ross William Ulbricht of Silk Road, the US Federal Bureau of Investigation acknowledged that Tor has "known legitimate uses". According to CNET, Tor's anonymity function is "endorsed by the Electronic Frontier Foundation (EFF) and other civil liberties groups as a method for whistleblowers and human rights workers to communicate with journalists". EFF's Surveillance Self-Defense guide includes a description of where Tor fits in a larger strategy for protecting privacy and anonymity.
In 2014, the EFF's Eva Galperin told Businessweek that "Tor's biggest problem is press. No one hears about that time someone wasn't stalked by their abuser. They hear how somebody got away with downloading child porn."
The Tor Project states that Tor users include "normal people" who wish to keep their Internet activities private from websites and advertisers, people concerned about cyber-spying, and users who are evading censorship such as activists, journalists, and military professionals. In November 2013, Tor had about four million users. According to the Wall Street Journal, in 2012 about 14% of Tor's traffic connected from the United States, with people in "Internet-censoring countries" as its second-largest user base. Tor is increasingly used by victims of domestic violence and the social workers and agencies that assist them, even though shelter workers may or may not have had professional training on cyber-security matters. Properly deployed, however, it precludes digital stalking, which has increased due to the prevalence of digital media in contemporary online life. Along with SecureDrop, Tor is used by news organizations such as The Guardian, The New Yorker, ProPublica and The Intercept to protect the privacy of whistleblowers.
In March 2015, the Parliamentary Office of Science and Technology released a briefing which stated that "There is widespread agreement that banning online anonymity systems altogether is not seen as an acceptable policy option in the U.K." and that "Even if it were, there would be technical challenges." The report further noted that Tor "plays only a minor role in the online viewing and distribution of indecent images of children" (due in part to its inherent latency); its usage by the Internet Watch Foundation, the utility of its onion services for whistleblowers, and its circumvention of the Great Firewall of China were touted.
Tor's executive director, Andrew Lewman, also said in August 2014 that agents of the NSA and the GCHQ have anonymously provided Tor with bug reports.
The Tor Project's FAQ offers supporting reasons for the EFF's endorsement:
Criminals can already do bad things. Since they're willing to break laws, they already have lots of options available that provide better privacy than Tor provides...
Tor aims to provide protection for ordinary people who want to follow the law. Only criminals have privacy right now, and we need to fix that...
So yes, criminals could in theory use Tor, but they already have better options, and it seems unlikely that taking Tor away from the world will stop them from doing their bad things. At the same time, Tor and other privacy measures can fight identity theft, physical crimes like stalking, and so on.
== Operation ==
Tor aims to conceal its users' identities and their online activity from surveillance and traffic analysis by separating identification and routing. It is an implementation of onion routing, which encrypts and then randomly bounces communications through a network of relays run by volunteers around the globe. These onion routers employ encryption in a multi-layered manner (hence the onion metaphor) to ensure perfect forward secrecy between relays, thereby providing users with anonymity in a network location. That anonymity extends to the hosting of censorship-resistant content by Tor's anonymous onion service feature. Furthermore, by keeping some of the entry relays (bridge relays) secret, users can evade Internet censorship that relies upon blocking public Tor relays.
Because the IP address of the sender and the recipient are not both in cleartext at any hop along the way, anyone eavesdropping at any point along the communication channel cannot directly identify both ends. Furthermore, to the recipient, it appears that the last Tor node (called the exit node), rather than the sender, is the originator of the communication.
=== Originating traffic ===
A Tor user's SOCKS-aware applications can be configured to direct their network traffic through a Tor instance's SOCKS interface, which is listening on TCP port 9050 (for standalone Tor) or 9150 (for Tor Browser bundle) at localhost. Tor periodically creates virtual circuits through the Tor network through which it can multiplex and onion-route that traffic to its destination. Once inside a Tor network, the traffic is sent from router to router along the circuit, ultimately reaching an exit node at which point the cleartext packet is available and is forwarded on to its original destination. Viewed from the destination, the traffic appears to originate at the Tor exit node.
Tor's application independence sets it apart from most other anonymity networks: it works at the Transmission Control Protocol (TCP) stream level. Applications whose traffic is commonly anonymized using Tor include Internet Relay Chat (IRC), instant messaging, and World Wide Web browsing.
=== Onion services ===
Tor can also provide anonymity to websites and other servers. Servers configured to receive inbound connections only through Tor are called onion services (formerly, hidden services). Rather than revealing a server's IP address (and thus its network location), an onion service is accessed through its onion address, usually via the Tor Browser or some other software designed to use Tor. The Tor network understands these addresses by looking up their corresponding public keys and introduction points from a distributed hash table within the network. It can route data to and from onion services, even those hosted behind firewalls or network address translators (NAT), while preserving the anonymity of both parties. Tor is necessary to access these onion services. Because the connection never leaves the Tor network, and is handled by the Tor application on both ends, the connection is always end-to-end encrypted.
Onion services were first specified in 2003 and have been deployed on the Tor network since 2004. They are unlisted by design, and can only be discovered on the network if the onion address is already known, though a number of sites and services do catalog publicly known onion addresses. Popular sources of .onion links include Pastebin, Twitter, Reddit, other Internet forums, and tailored search engines.
While onion services are often discussed in terms of websites, they can be used for any TCP service, and are commonly used for increased security or easier routing to non-web services, such as secure shell remote login, chat services such as IRC and XMPP, or file sharing. They have also become a popular means of establishing peer-to-peer connections in messaging and file sharing applications. Web-based onion services can be accessed from a standard web browser without client-side connection to the Tor network using services like Tor2web, which remove client anonymity.
== Attacks and limitations ==
Like all software with an attack surface, Tor's protections have limitations, and Tor's implementation or design have been vulnerable to attacks at various points throughout its history. While most of these limitations and attacks are minor, either being fixed without incident or proving inconsequential, others are more notable.
=== End-to-end traffic correlation ===
Tor is designed to provide relatively high performance network anonymity against an attacker with a single vantage point on the connection (e.g., control over one of the three relays, the destination server, or the user's internet service provider). Like all current low-latency anonymity networks, Tor cannot and does not attempt to protect against an attacker performing simultaneous monitoring of traffic at the boundaries of the Tor network—i.e., the traffic entering and exiting the network. While Tor does provide protection against traffic analysis, it cannot prevent traffic confirmation via end-to-end correlation.
There are no documented cases of this limitation being used at scale; as of the 2013 Snowden leaks, law enforcement agencies such as the NSA were unable to perform dragnet surveillance on Tor itself, and relied on attacking other software used in conjunction with Tor, such as vulnerabilities in web browsers.
However, targeted attacks have been able to make use of traffic confirmation on individual Tor users, via police surveillance or investigations confirming that a particular person already under suspicion was sending Tor traffic at the exact times the connections in question occurred. The relay early traffic confirmation attack also relied on traffic confirmation as part of its mechanism, though on requests for onion service descriptors, rather than traffic to the destination server.
=== Consensus attacks ===
Like many decentralized systems, Tor relies on a consensus mechanism to periodically update its current operating parameters. For Tor, these include network parameters like which nodes are good and bad relays, exits, guards, and how much traffic each can handle. Tor's architecture for deciding the consensus relies on a small number of directory authority nodes voting on current network parameters. Currently, there are nine directory authority nodes, and their health is publicly monitored. The IP addresses of the authority nodes are hard coded into each Tor client. The authority nodes vote every hour to update the consensus, and clients download the most recent consensus on startup. A compromise of the majority of the directory authorities could alter the consensus in a way that is beneficial to an attacker. Alternatively, a network congestion attack, such as a DDoS, could theoretically prevent the consensus nodes from communicating, and thus prevent voting to update the consensus (though such an attack would be visible).
=== Server-side restrictions ===
Tor makes no attempt to conceal the IP addresses of exit relays, or hide from a destination server the fact that a user is connecting via Tor. Operators of Internet sites therefore have the ability to prevent traffic from Tor exit nodes or to offer reduced functionality for Tor users. For example, Wikipedia generally forbids all editing when using Tor or when using an IP address also used by a Tor exit node, and the BBC blocks the IP addresses of all known Tor exit nodes from its iPlayer service.
Apart from intentional restrictions of Tor traffic, Tor use can trigger defense mechanisms on websites intended to block traffic from IP addresses observed to generate malicious or abnormal traffic. Because traffic from all Tor users is shared by a comparatively small number of exit relays, tools can misidentify distinct sessions as originating from the same user, and attribute the actions of a malicious user to a non-malicious user, or observe an unusually large volume of traffic for one IP address. Conversely, a site may observe a single session connecting from different exit relays, with different Internet geolocations, and assume the connection is malicious, or trigger geo-blocking. When these defense mechanisms are triggered, it can result in the site blocking access, or presenting captchas to the user.
=== Relay early traffic confirmation attack ===
In July 2014, the Tor Project issued a security advisory for a "relay early traffic confirmation" attack, disclosing the discovery of a group of relays attempting to de-anonymize onion service users and operators. A set of onion service directory nodes (i.e., the Tor relays responsible for providing information about onion services) were found to be modifying traffic of requests. The modifications made it so the requesting client's guard relay, if controlled by the same adversary as the onion service directory node, could easily confirm that the traffic was from the same request. This would allow the adversary to simultaneously know the onion service involved in the request, and the IP address of the client requesting it (where the requesting client could be a visitor or owner of the onion service).
The attacking nodes joined the network on 30 January, using a Sybil attack to comprise 6.4% of guard relay capacity, and were removed on 4 July. In addition to removing the attacking relays, the Tor application was patched to prevent the specific traffic modifications that made the attack possible.
In November 2014, there was speculation in the aftermath of Operation Onymous, resulting in 17 arrests internationally, that a Tor weakness had been exploited. A representative of Europol was secretive about the method used, saying: "This is something we want to keep for ourselves. The way we do this, we can't share with the whole world, because we want to do it again and again and again."
A BBC source cited a "technical breakthrough"
that allowed tracking physical locations of servers, and the initial number of infiltrated sites led to the exploit speculation. A Tor Project representative downplayed this possibility, suggesting that execution of more traditional police work was more likely.
In November 2015, court documents suggested a connection between the attack and arrests, and raised concerns about security research ethics. The documents revealed that the FBI obtained IP addresses of onion services and their visitors from a "university-based research institute", leading to arrests. Reporting from Motherboard found that the timing and nature of the relay early traffic confirmation attack matched the description in the court documents. Multiple experts, including a senior researcher with the ICSI of UC Berkeley, Edward Felten of Princeton University, and the Tor Project agreed that the CERT Coordination Center of Carnegie Mellon University was the institute in question. Concerns raised included the role of an academic institution in policing, sensitive research involving non-consenting users, the non-targeted nature of the attack, and the lack of disclosure about the incident.
=== Vulnerable applications ===
Many attacks targeted at Tor users result from flaws in applications used with Tor, either in the application itself, or in how it operates in combination with Tor. E.g., researchers with Inria in 2011 performed an attack on BitTorrent users by attacking clients that established connections both using and not using Tor, then associating other connections shared by the same Tor circuit.
==== Fingerprinting ====
When using Tor, applications may still provide data tied to a device, such as information about screen resolution, installed fonts, language configuration, or supported graphics functionality, reducing the set of users a connection could possibly originate from, or uniquely identifying them. This information is known as the device fingerprint, or browser fingerprint in the case of web browsers. Applications implemented with Tor in mind, such as Tor Browser, can be designed to minimize the amount of information leaked by the application and reduce its fingerprint.
==== Eavesdropping ====
Tor cannot encrypt the traffic between an exit relay and the destination server.
If an application does not add an additional layer of end-to-end encryption between the client and the server, such as Transport Layer Security (TLS, used in HTTPS) or the Secure Shell (SSH) protocol, this allows the exit relay to capture and modify traffic. Attacks from malicious exit relays have recorded usernames and passwords, and modified Bitcoin addresses to redirect transactions.
Some of these attacks involved actively removing the HTTPS protections that would have otherwise been used. To attempt to prevent this, Tor Browser has since made it so only connections via onion services or HTTPS are allowed by default.
==== Firefox/Tor browser attacks ====
In 2011, the Dutch authority investigating child pornography discovered the IP address of a Tor onion service site from an unprotected administrator's account and gave it to the FBI, who traced it to Aaron McGrath. After a year of surveillance, the FBI launched "Operation Torpedo" which resulted in McGrath's arrest and allowed them to install their Network Investigative Technique (NIT) malware on the servers for retrieving information from the users of the three onion service sites that McGrath controlled. The technique exploited a vulnerability in Firefox/Tor Browser that had already been patched, and therefore targeted users that had not updated. A Flash application sent a user's IP address directly back to an FBI server, and resulted in revealing at least 25 US users as well as numerous users from other countries. McGrath was sentenced to 20 years in prison in early 2014, while at least 18 others (including a former Acting HHS Cyber Security Director) were sentenced in subsequent cases.
In August 2013, it was discovered that the Firefox browsers in many older versions of the Tor Browser Bundle were vulnerable to a JavaScript-deployed shellcode attack, as NoScript was not enabled by default. Attackers used this vulnerability to extract users' MAC and IP addresses and Windows computer names. News reports linked this to a FBI operation targeting Freedom Hosting's owner, Eric Eoin Marques, who was arrested on a provisional extradition warrant issued by a United States' court on 29 July. The FBI extradited Marques from Ireland to the state of Maryland on 4 charges: distributing; conspiring to distribute; and advertising child pornography, as well as aiding and abetting advertising of child pornography. The FBI acknowledged the attack in a 12 September 2013 court filing in Dublin; further technical details from a training presentation leaked by Edward Snowden revealed the code name for the exploit as "EgotisticalGiraffe".
In 2022, Kaspersky researchers found that when looking up "Tor Browser" in Chinese on YouTube, one of the URLs provided under the top-ranked Chinese-language video actually pointed to malware disguised as Tor Browser. Once installed, it saved browsing history and form data that genuine Tor forgot by default, and downloaded malicious components if the device's IP addresses was in China. Kaspersky researchers noted that the malware was not stealing data to sell for profit, but was designed to identify users.
==== Onion service configuration ====
Like client applications that use Tor, servers relying on onion services for protection can introduce their own weaknesses. Servers that are reachable through Tor onion services and the public Internet can be subject to correlation attacks, and all onion services are susceptible to misconfigured services (e.g., identifying information included by default in web server error responses), leaking uptime and downtime statistics, intersection attacks, or various user errors. The OnionScan program, written by independent security researcher Sarah Jamie Lewis, comprehensively examines onion services for such flaws and vulnerabilities.
== Software ==
The main implementation of Tor is written primarily in C. Starting in 2020, the Tor Project began development of a full rewrite of the C Tor codebase in Rust. The project, named Arti, was publicly announced in July 2021.
=== Tor Browser ===
The Tor Browser is a web browser capable of accessing the Tor network. It was created as the Tor Browser Bundle by Steven J. Murdoch and announced in January 2008. The Tor Browser consists of a modified Mozilla Firefox ESR web browser, the TorButton, TorLauncher, NoScript and the Tor proxy. Users can run the Tor Browser from removable media. It can operate under Microsoft Windows, macOS, Android and Linux.
The default search engine is DuckDuckGo (until version 4.5, Startpage.com was its default). The Tor Browser automatically starts Tor background processes and routes traffic through the Tor network. Upon termination of a session the browser deletes privacy-sensitive data such as HTTP cookies and the browsing history. This is effective in reducing web tracking and canvas fingerprinting, and it also helps to prevent creation of a filter bubble.
To allow download from places where accessing the Tor Project URL may be risky or blocked, a GitHub repository is maintained with links for releases hosted in other domains.
=== Tor Messenger ===
On 29 October 2015, the Tor Project released Tor Messenger Beta, an instant messaging program based on Instantbird with Tor and OTR built in and used by default. Like Pidgin and Adium, Tor Messenger supports multiple different instant messaging protocols; however, it accomplishes this without relying on libpurple, implementing all chat protocols in the memory-safe language JavaScript instead.
According to Lucian Armasu of Toms Hardware, in April 2018, the Tor Project shut down the Tor Messenger project for three reasons: the developers of "Instabird" [sic] discontinued support for their own software, limited resources and known metadata problems. The Tor Messenger developers explained that overcoming any vulnerabilities discovered in the future would be impossible due to the project relying on outdated software dependencies.
=== Tor Phone ===
In 2016, Tor developer Mike Perry announced a prototype tor-enabled smartphone based on CopperheadOS. It was meant as a direction for Tor on mobile. The project was called 'Mission Improbable'. Copperhead's then lead developer Daniel Micay welcomed the prototype.
=== Third-party applications ===
The Vuze (formerly Azureus) BitTorrent client, Bitmessage anonymous messaging system, and TorChat instant messenger include Tor support. The Briar messenger routes all messaging via Tor by default. OnionShare allows users to share files using Tor.
The Guardian Project is actively developing a free and open-source suite of applications and firmware for the Android operating system to improve the security of mobile communications. The applications include the ChatSecure instant messaging client, Orbot Tor implementation (also available for iOS), Orweb (discontinued) privacy-enhanced mobile browser, Orfox, the mobile counterpart of the Tor Browser, ProxyMob Firefox add-on, and ObscuraCam.
Onion Browser is open-source, privacy-enhancing web browser for iOS, which uses Tor. It is available in the iOS App Store, and source code is available on GitHub.
Brave added support for Tor in its desktop browser's private-browsing mode.
=== Security-focused operating systems ===
In September of 2024, it was announced that Tails, a security-focused operating system, had become part of the Tor Project. Other security-focused operating systems that make or made extensive use of Tor include Hardened Linux From Scratch, Incognito, Liberté Linux, Qubes OS, Subgraph, Parrot OS, Tor-ramdisk, and Whonix.
== Reception, impact, and legislation ==
Tor has been praised for providing privacy and anonymity to vulnerable Internet users such as political activists fearing surveillance and arrest, ordinary web users seeking to circumvent censorship, and people who have been threatened with violence or abuse by stalkers. The U.S. National Security Agency (NSA) has called Tor "the king of high-secure, low-latency Internet anonymity", and BusinessWeek magazine has described it as "perhaps the most effective means of defeating the online surveillance efforts of intelligence agencies around the world". Other media have described Tor as "a sophisticated privacy tool", "easy to use" and "so secure that even the world's most sophisticated electronic spies haven't figured out how to crack it".
Advocates for Tor say it supports freedom of expression, including in countries where the Internet is censored, by protecting the privacy and anonymity of users. The mathematical underpinnings of Tor lead it to be characterized as acting "like a piece of infrastructure, and governments naturally fall into paying for infrastructure they want to use".
The project was originally developed on behalf of the U.S. intelligence community and continues to receive U.S. government funding, and has been criticized as "more resembl[ing] a spook project than a tool designed by a culture that values accountability or transparency". As of 2012, 80% of The Tor Project's $2M annual budget came from the United States government, with the U.S. State Department, the Broadcasting Board of Governors, and the National Science Foundation as major contributors, aiming "to aid democracy advocates in authoritarian states". Other public sources of funding include DARPA, the U.S. Naval Research Laboratory, and the Government of Sweden. Some have proposed that the government values Tor's commitment to free speech, and uses the darknet to gather intelligence. Tor also receives funding from NGOs including Human Rights Watch, and private sponsors including Reddit and Google. Dingledine said that the United States Department of Defense funds are more similar to a research grant than a procurement contract. Tor executive director Andrew Lewman said that even though it accepts funds from the U.S. federal government, the Tor service did not collaborate with the NSA to reveal identities of users.
Critics say that Tor is not as secure as it claims, pointing to U.S. law enforcement's investigations and shutdowns of Tor-using sites such as web-hosting company Freedom Hosting and online marketplace Silk Road. In October 2013, after analyzing documents leaked by Edward Snowden, The Guardian reported that the NSA had repeatedly tried to crack Tor and had failed to break its core security, although it had had some success attacking the computers of individual Tor users. The Guardian also published a 2012 NSA classified slide deck, entitled "Tor Stinks", which said: "We will never be able to de-anonymize all Tor users all the time", but "with manual analysis we can de-anonymize a very small fraction of Tor users". When Tor users are arrested, it is typically due to human error, not to the core technology being hacked or cracked. On 7 November 2014, for example, a joint operation by the FBI, ICE Homeland Security investigations and European Law enforcement agencies led to 17 arrests and the seizure of 27 sites containing 400 pages. A late 2014 report by Der Spiegel using a new cache of Snowden leaks revealed, however, that as of 2012 the NSA deemed Tor on its own as a "major threat" to its mission, and when used in conjunction with other privacy tools such as OTR, Cspace, ZRTP, RedPhone, Tails, and TrueCrypt was ranked as "catastrophic," leading to a "near-total loss/lack of insight to target communications, presence..."
=== 2011 ===
In March 2011, The Tor Project received the Free Software Foundation's 2010 Award for Projects of Social Benefit. The citation read, "Using free software, Tor has enabled roughly 36 million people around the world to experience freedom of access and expression on the Internet while keeping them in control of their privacy and anonymity. Its network has proved pivotal in dissident movements in both Iran and more recently Egypt."
Iran tried to block Tor at least twice in 2011. One attempt simply blocked all servers with 2-hour-expiry security certificates; it was successful for less than 24 hours.
=== 2012 ===
In 2012, Foreign Policy magazine named Dingledine, Mathewson, and Syverson among its Top 100 Global Thinkers "for making the web safe for whistleblowers".
=== 2013 ===
In 2013, Jacob Appelbaum described Tor as a "part of an ecosystem of software that helps people regain and reclaim their autonomy. It helps to enable people to have agency of all kinds; it helps others to help each other and it helps you to help yourself. It runs, it is open and it is supported by a large community spread across all walks of life."
In June 2013, whistleblower Edward Snowden used Tor to send information about PRISM to The Washington Post and The Guardian.
=== 2014 ===
In 2014, the Russian government offered a $111,000 contract to "study the possibility of obtaining technical information about users and users' equipment on the Tor anonymous network".
In September 2014, in response to reports that Comcast had been discouraging customers from using the Tor Browser, Comcast issued a public statement that "We have no policy against Tor, or any other browser or software."
In October 2014, The Tor Project hired the public relations firm Thomson Communications to improve its public image (particularly regarding the terms "Dark Net" and "hidden services," which are widely viewed as being problematic) and to educate journalists about the technical aspects of Tor.
Turkey blocked downloads of Tor Browser from the Tor Project.
=== 2015 ===
In June 2015, the special rapporteur from the United Nations' Office of the High Commissioner for Human Rights specifically mentioned Tor in the context of the debate in the U.S. about allowing so-called backdoors in encryption programs for law enforcement purposes in an interview for The Washington Post.
In July 2015, the Tor Project announced an alliance with the Library Freedom Project to establish exit nodes in public libraries. The pilot program, which established a middle relay running on the excess bandwidth afforded by the Kilton Library in Lebanon, New Hampshire, making it the first library in the U.S. to host a Tor node, was briefly put on hold when the local city manager and deputy sheriff voiced concerns over the cost of defending search warrants for information passed through the Tor exit node. Although the Department of Homeland Security (DHS) had alerted New Hampshire authorities to the fact that Tor is sometimes used by criminals, the Lebanon Deputy Police Chief and the Deputy City Manager averred that no pressure to strong-arm the library was applied, and the service was re-established on 15 September 2015. U.S. Rep. Zoe Lofgren (D-Calif) released a letter on 10 December 2015, in which she asked the DHS to clarify its procedures, stating that "While the Kilton Public Library's board ultimately voted to restore their Tor relay, I am no less disturbed by the possibility that DHS employees are pressuring or persuading public and private entities to discontinue or degrade services that protect the privacy and anonymity of U.S. citizens." In a 2016 interview, Kilton Library IT Manager Chuck McAndrew stressed the importance of getting libraries involved with Tor: "Librarians have always cared deeply about protecting privacy, intellectual freedom, and access to information (the freedom to read). Surveillance has a very well-documented chilling effect on intellectual freedom. It is the job of librarians to remove barriers to information." The second library to host a Tor node was the Las Naves Public Library in Valencia, Spain, implemented in the first months of 2016.
In August 2015, an IBM security research group, called "X-Force", put out a quarterly report that advised companies to block Tor on security grounds, citing a "steady increase" in attacks from Tor exit nodes as well as botnet traffic.
In September 2015, Luke Millanta created OnionView (now defunct), a web service that plots the location of active Tor relay nodes onto an interactive map of the world. The project's purpose was to detail the network's size and escalating growth rate.
In December 2015, Daniel Ellsberg (of the Pentagon Papers), Cory Doctorow (of Boing Boing), Edward Snowden, and artist-activist Molly Crabapple, amongst others, announced their support of Tor.
=== 2016 ===
In March 2016, New Hampshire state representative Keith Ammon introduced a bill allowing public libraries to run privacy software. The bill specifically referenced Tor. The text was crafted with extensive input from Alison Macrina, the director of the Library Freedom Project. The bill was passed by the House 268–62.
Also in March 2016, the first Tor node, specifically a middle relay, was established at a library in Canada, the Graduate Resource Centre (GRC) in the Faculty of Information and Media Studies (FIMS) at the University of Western Ontario. Given that the running of a Tor exit node is an unsettled area of Canadian law, and that in general institutions are more capable than individuals to cope with legal pressures, Alison Macrina of the Library Freedom Project has opined that in some ways she would like to see intelligence agencies and law enforcement attempt to intervene in the event that an exit node were established.
On 16 May 2016, CNN reported on the case of core Tor developer "isis agora lovecruft", who had fled to Germany under the threat of a subpoena by the FBI during the Thanksgiving break of the previous year. The Electronic Frontier Foundation legally represented lovecruft.
On 2 December 2016, The New Yorker reported on burgeoning digital privacy and security workshops in the San Francisco Bay Area, particularly at the hackerspace Noisebridge, in the wake of the 2016 United States presidential election; downloading the Tor browser was mentioned. Also, in December 2016, Turkey has blocked the usage of Tor, together with ten of the most used VPN services in Turkey, which were popular ways of accessing banned social media sites and services.
Tor (and Bitcoin) was fundamental to the operation of the dark web marketplace AlphaBay, which was taken down in an international law enforcement operation in July 2017. Despite federal claims that Tor would not shield a user, however, elementary operational security errors outside of the ambit of the Tor network led to the site's downfall.
=== 2017 ===
In June 2017 the Democratic Socialists of America recommended intermittent Tor usage for politically active organizations and individuals as a defensive mitigation against information security threats. And in August 2017, according to reportage, cybersecurity firms which specialize in monitoring and researching the dark web (which relies on Tor as its infrastructure) on behalf of banks and retailers routinely share their findings with the FBI and with other law enforcement agencies "when possible and necessary" regarding illegal content. The Russian-speaking underground offering a crime-as-a-service model is regarded as being particularly robust.
=== 2018 ===
In June 2018, Venezuela blocked access to the Tor network. The block affected both direct connections to the network and connections being made via bridge relays.
On 20 June 2018, Bavarian police raided the homes of the board members of the non-profit Zwiebelfreunde, a member of torservers.net, which handles the European financial transactions of riseup.net in connection with a blog post there which apparently promised violence against the upcoming Alternative for Germany convention. Tor came out strongly against the raid on its support organization, which provides legal and financial aid for the setting up and maintenance of high-speed relays and exit nodes. According to torservers.net, on 23 August 2018 the German court at Landgericht München ruled that the raid and seizures were illegal. The hardware and documentation seized had been kept under seal, and purportedly were neither analyzed nor evaluated by the Bavarian police.
Since October 2018, Chinese online communities within Tor have begun to dwindle due to increased efforts to stop them by the Chinese government.
=== 2019 ===
In November 2019, Edward Snowden called for a full, unabridged simplified Chinese translation of his autobiography, Permanent Record, as the Chinese publisher had violated their agreement by expurgating all mentions of Tor and other matters deemed politically sensitive by the Chinese Communist Party.
=== 2021 ===
On 8 December 2021, the Russian government agency Roskomnadzor announced it has banned Tor and six VPN services for failing to abide by the Russian Internet blacklist. Russian ISPs unsuccessfully attempted to block Tor's main website as well as several bridges beginning on 1 December 2021. The Tor Project has appealed to Russian courts over this ban.
=== 2022 ===
In response to Internet censorship during the Russian invasion of Ukraine, the BBC and VOA have directed Russian audiences to Tor. The Russian government increased efforts to block access to Tor through technical and political means, while the network reported an increase in traffic from Russia, and increased Russian use of its anti-censorship Snowflake tool.
Russian courts temporarily lifted the blockade on Tor's website (but not connections to relays) on May 24, 2022 due to Russian law requiring that the Tor Project be involved in the case. However, the blockade was reinstated on July 21, 2022.
Iran implemented rolling internet blackouts during the Mahsa Amini protests, and Tor and Snowflake were used to circumvent them.
China, with its highly centralized control of its internet, had effectively blocked Tor.
== Improved security ==
Tor responded to earlier vulnerabilities listed above by patching them and improving security. In one way or another, human (user) errors can lead to detection. The Tor Project website provides the best practices (instructions) on how to properly use the Tor browser. When improperly used, Tor is not secure. For example, Tor warns its users that not all traffic is protected; only the traffic routed through the Tor browser is protected. Users are also warned to use HTTPS versions of websites, not to torrent with Tor, not to enable browser plugins, not to open documents downloaded through Tor while online, and to use safe bridges. Users are also warned that they cannot provide their name or other revealing information in web forums over Tor and stay anonymous at the same time.
Despite intelligence agencies' claims that 80% of Tor users would be de-anonymized within 6 months in the year 2013, that has still not happened. In fact, as late as September 2016, the FBI could not locate, de-anonymize and identify the Tor user who hacked into the email account of a staffer on Hillary Clinton's email server.
The best tactic of law enforcement agencies to de-anonymize users appears to remain with Tor-relay adversaries running poisoned nodes, as well as counting on the users themselves using the Tor browser improperly. For example, downloading a video through the Tor browser and then opening the same file on an unprotected hard drive while online can make the users' real IP addresses available to authorities.
=== Odds of detection ===
When properly used, odds of being de-anonymized through Tor are said to be extremely low. Tor project's co-founder Nick Mathewson explained that the problem of "Tor-relay adversaries" running poisoned nodes means that a theoretical adversary of this kind is not the network's greatest threat:
"No adversary is truly global, but no adversary needs to be truly global," he says. "Eavesdropping on the entire Internet is a several-billion-dollar problem. Running a few computers to eavesdrop on a lot of traffic, a selective denial of service attack to drive traffic to your computers, that's like a tens-of-thousands-of-dollars problem." At the most basic level, an attacker who runs two poisoned Tor nodes—one entry, one exit—is able to analyse traffic and thereby identify the tiny, unlucky percentage of users whose circuit happened to cross both of those nodes. In 2016 the Tor network offers a total of around 7,000 relays, around 2,000 guard (entry) nodes and around 1,000 exit nodes. So the odds of such an event happening are one in two million (1⁄2000 × 1⁄1000), give or take."
Tor does not provide protection against end-to-end timing attacks: if an attacker can watch the traffic coming out of the target computer, and also the traffic arriving at the target's chosen destination (e.g. a server hosting a .onion site), that attacker can use statistical analysis to discover that they are part of the same circuit.
A similar attack has been used by German authorities to track down users related to Boystown.
== Levels of security ==
Depending on individual user needs, Tor browser offers three levels of security located under the Security Level (the small gray shield at the top-right of the screen) icon > Advanced Security Settings. In addition to encrypting the data, including constantly changing an IP address through a virtual circuit comprising successive, randomly selected Tor relays, several other layers of security are at a user's disposal:
=== Standard ===
At this level, all features from the Tor Browser and other websites are enabled.
=== Safer ===
This level eliminates website features that are often pernicious to the user. This may cause some sites to lose functionality. JavaScript is disabled on all non-HTTPS sites; some fonts and mathematical symbols are disabled. Also, audio and video (HTML5 media) are click-to-play.
=== Safest ===
This level only allows website features required for static sites and basic services. These changes affect images, media, and scripts. Javascript is disabled by default on all sites; some fonts, icons, math symbols, and images are disabled; audio and video (HTML5 media) are click-to-play.
=== Introduction of proof-of-work defense for Onion services ===
In 2023, Tor unveiled a new defense mechanism to safeguard its onion services against denial of service (DoS) attacks. With the release of Tor 0.4.8, this proof-of-work (PoW) defense promises to prioritize legitimate network traffic while deterring malicious attacks.
== Notes ==
== See also ==
== Citations ==
== General and cited references ==
== External links ==
Official website | Wikipedia/Tor_(network) |
TON, also known as The Open Network (previously Telegram Open Network), is a decentralized layer-1 blockchain. TON was originally developed by Nikolai Durov who is also known for his role in creating the messaging platform, Telegram.
Telegram had planned to use TON to launch its own cryptocurrency (Gram), but was forced to abandon the project in 2020 following an injunction by US regulators. The network was then renamed and independent developers have created their own cryptocurrencies and decentralized applications (dApps) using TON. Toncoin, the principal token of The Open Network is deeply integrated into the Telegram messaging app, used for paying rewards to creators and developers, buying Telegram ads, hosting giveaways or purchasing services such as Telegram Premium.
== History ==
The Open Network (TON) began in January 2018 when Telegram Messenger Inc. and TON Issuer Inc. started selling “Gram” tokens to finance development of the Telegram Open Network blockchain, ultimately raising US$1.7 billion across two private SAFT rounds.
=== SEC injunction and Telegram’s withdrawal (2019–2020) ===
On 11 October 2019, the U.S. SEC obtained an emergency injunction in the Southern District of New York, alleging the offer and sale of Grams constituted an unregistered securities offering.
Telegram settled the case on 26 June 2020, agreeing to repay US$1.224 billion to investors and pay an US$18.5 million civil penalty, while formally ceasing work on TON.
Telegram then open-sourced its code base under GPL v2, enabling independent developers to continue the project.
=== Community forks: Free TON → Everscale (2020–2021) ===
One group led by TON Labs and dozens of validators launched Free TON on 7 May 2020, emphasizing meritocratic token distribution and on-chain governance.
As protocol upgrades diverged from Telegram’s original design, the network rebranded to Everscale in November 2021 to reflect its new scalability roadmap and EVER token economics.
=== Revival as “New TON” and founding of TON Foundation (2020–present) ===
In parallel, developers Anatoliy Makosov and Kirill Emelyanenko organised a separate community effort—initially nicknamed “New TON”—to continue the canonical Telegram code without altering its core architecture.
Their group incorporated the non-profit TON Foundation in Switzerland in 2021, assumed stewardship of the code repository, and renamed the native asset Toncoin.
Telegram CEO Pavel Durov publicly endorsed the community-run chain on 23 December 2021, calling Toncoin “the continuation of our vision.”
=== Ecosystem expansion (2022–2023) ===
Major infrastructure releases followed: TON DNS, a human-readable naming system, launched in July 2022 with on-chain auctions for “.ton” domains;
TON Storage debuted later that year as a decentralized file-storage layer;
and Telegram integrated Toncoin peer-to-peer transfers via the @wallet bot in April 2022.
In September 2023 Telegram designated TON as its official Web3 infrastructure and added a self-custodial wallet (“TON Space”) for its 900 million-user base.
=== Growth and recent developments (2024–2025) ===
Ecosystem metrics accelerated through 2024: daily on-chain transactions rose from 100,000 to 1.2 million and TVL surpassed US$350 million, according to a Bitget-backed report.
April 2024 saw Tether (USDT) issue a native TON version, further embedding stable-value transfers inside Telegram chats.
In March 2025 a major wallet upgrade introduced integrated trading and staking (“Earn”) features to over 100 million Wallet users on Telegram.
Together, these milestones position TON as a high-throughput, Telegram-native layer-1 with growing DeFi, gaming, and identity applications.
== Architecture ==
=== Overview ===
The Open Network (TON) is a layer-1 blockchain designed to support a wide range of applications, including digital payments, smart contracts, and on-chain governance. It emphasizes scalability, parallelism, and efficiency, enabling millions of smart contracts to operate concurrently across a dynamically sharded, multichain network. TON's architecture is optimized for high transaction throughput and low latency, making it suitable for global-scale decentralized systems.
=== Network Architecture ===
TON’s architecture is built around a hierarchical multi-blockchain model, consisting of a single masterchain, up to
2
32
{\displaystyle 2^{32}}
workchains, and each workchain dynamically splitting into up to
2
60
{\displaystyle 2^{60}}
shardchains based on load. This dynamic sharding mechanism ensures horizontal scalability, allowing the network to process thousands of transactions per second without congestion.
Inter-chain communication is enabled by a hypercube routing protocol, which supports low-latency message transfers between chains in logarithmic time. This design ensures efficient cross-chain contract execution and data synchronization as the network scales globally.
The masterchain maintains critical network-wide metadata, including validator sets, configuration parameters, and references to all workchain blocks. Each workchain can define its own virtual machine and governance rules, enabling a wide range of specialized applications.
=== Consensus and Governance ===
TON employs a modified proof-of-stake (PoS) consensus with Byzantine fault tolerance (BFT). Validators are selected based on the amount of Toncoin staked and participate in block production and validation. Protocol upgrades and parameter changes are implemented via on-chain validator voting, with governance decisions automatically enforced by the consensus engine.
Although the TON Foundation coordinates ecosystem growth and funds development initiatives, it does not hold unilateral control over protocol-level changes. The governance process is decentralized and driven by validator consensus.
=== TON Virtual Machine and Smart Contracts ===
The TON Virtual Machine (TVM) is a high-performance, stack-based execution environment built for the TON blockchain, optimized for resource efficiency, asynchronous processing, and formal verification. It runs smart contracts in TVM-compatible bytecode, compiled from:
Fift: A low-level language for stack manipulation and system-level contract development.
Func: A high-level, statically-typed language for secure and simplified contract creation.
Tact: A concise, modern language for safe and expressive smart contracts.
Tolk: A readability-focused language for simplifying complex contract logic.
TVM smart contracts operate on a message-driven model, where inbound messages trigger execution, and outbound messages enable scalable, parallel interactions across shards. Gas fees are computed based on computation, memory, and storage usage.
The TVM toolchain includes static analysis, formal verification, and debugging tools, ensuring contract security, reliability, and performance before deployment.
=== Security and Auditing ===
The Open Network (TON) implements a multi-layered security framework that integrates economic deterrents, formal verification methodologies, and independent audits. Validator misbehavior, such as double signing or downtime, may result in stake slashing, thus incentivizing honest participation in the consensus process. Additionally, smart contracts on TON are built to support transparency and formal verifiability prior to deployment.
To enhance the reliability and integrity of the ecosystem, TON collaborates with a group of certified Security Assurance Providers (SAPs). These third-party firms specialize in code auditing, vulnerability assessments, and protocol-level reviews. As of 2024, notable SAPs working with TON include CertiK, Quantstamp, SlowMist, Hexens, Vidma, Scalebit, and SoftStack. Their evaluations contribute to the proactive mitigation of security risks across smart contracts and infrastructure layers.
The network also promotes formal verification of smart contracts through its native toolchain, enabling developers to mathematically prove correctness and prevent critical vulnerabilities before deployment.
== TON-based Services ==
The TON ecosystem encompasses a variety of decentralized services and infrastructure protocols aimed at providing scalable and censorship-resistant solutions. These services are natively integrated into the TON blockchain and are facilitated by Toncoin, the network's utility token, which supports transactions, staking, and governance.
=== Toncoin ===
Toncoin is the native utility token of the TON blockchain, used for paying transaction fees, staking to secure the network, executing smart contracts, and participating in protocol governance. It serves as the primary medium of exchange within the TON ecosystem, enabling services such as decentralized file storage (TON Storage), anonymous routing (TON Proxy), and domain registration (TON DNS). Toncoin also incentivizes validators and infrastructure operators through the network's proof-of-stake consensus mechanism. For instance, storage providers in TON Storage and proxy operators in TON Proxy are compensated in Toncoin for their services.
=== TON DNS ===
TON DNS is a decentralized domain name system that allows users to register human-readable .ton domains. These domains can be linked to wallet addresses, smart contracts, or decentralized services, simplifying interactions with blockchain-based resources. Unlike traditional DNS systems, which rely on centralized authorities, TON DNS is fully decentralized and resistant to censorship. Domain ownership is managed through on-chain smart contracts, with domains acquired via auction or direct registration, similar to other blockchain-based domain systems like the Ethereum Name Service.
=== TON Sites and TON Proxy ===
TON Sites enables decentralized web hosting on the TON blockchain using .ton domains registered through TON DNS. Content for these sites can be stored directly on the blockchain for small files or via TON Storage for larger content, ensuring decentralized access without reliance on centralized hosting providers. TON Sites are accessible through compatible browsers and TON-enabled wallets, providing a seamless user experience for decentralized web applications.
TON Proxy is a decentralized anonymity protocol that allows users and nodes to obfuscate their identities and traffic. Inspired by networks like Tor and I2P, TON Proxy supports the creation of privacy-preserving services such as decentralized VPNs and censorship-resistant applications. It offers advantages over traditional anonymity networks through its integration with the TON ecosystem, including Toncoin-based incentives for proxy operators and enhanced performance for TON-based services. TON Proxy also supports standard HTTP Proxy features for broader compatibility.
=== TON Storage ===
TON Storage is a distributed file storage system integrated with the TON blockchain. It enables users to upload large files, which are fragmented into smaller pieces and stored across peer-to-peer nodes for redundancy and fault tolerance. Storage providers are compensated through smart contracts tied to service commitments, with payments made in Toncoin. This system supports various applications, including decentralized website hosting, smart contract metadata storage, and large media content delivery. TON Storage shares similarities with other decentralized storage solutions like IPFS and Filecoin, but is specifically tailored for the TON ecosystem.
=== TON Payments ===
TON Payments is an off-chain payment system designed for micropayments and high-frequency transactions. It utilizes payment channels to enable secure value transfers between users and services without immediately settling each transaction on-chain. This mechanism reduces latency and transaction fees by allowing multiple payments to be aggregated and settled only when the channel is closed—similar to writing multiple checks that are cashed at once. TON Payments incorporates cryptographic proofs to ensure the integrity and security of payment channels, preventing fraud and double-spending. This system is particularly useful for compensating operators in services like TON Proxy and TON Storage, where frequent, small payments are required.
== Decentralized Finance (DeFi) on TON ==
The TON blockchain supports a growing decentralized finance (DeFi) ecosystem, offering high-throughput, low-fee infrastructure suitable for decentralized applications. With native support in the Telegram platform, TON DeFi products aim to improve accessibility and integrate blockchain-based financial services into mainstream user experiences.
=== KTON ===
KTON is a liquid staking protocol deployed on the TON blockchain. It is built using the TON Core Team’s Liquid Staking Contract V2 framework, enabling users to stake Toncoin and receive liquid staking tokens (LSTs) in return. These tokens represent staked positions and can be freely transferred or used in other DeFi applications.
KTON’s architecture emphasizes instant liquidity, non-custodial staking, and future compatibility with on-chain governance. The project has undergone security audits and is positioned as a next-generation staking solution for both institutional and retail users on TON.
=== STON.fi ===
STON.fi is a decentralized exchange (DEX) operating on the TON blockchain. It utilizes an automated market maker (AMM) model to allow users to swap TON-based assets without intermediaries. STON.fi supports the Jetton token standard and enables liquidity provision, yield farming, and permissionless trading.
Launched in 2022, STON.fi has grown to become one of the primary liquidity hubs in the TON ecosystem. It integrates with TON-native wallets such as Tonkeeper and Wallet (Telegram-integrated), and supports seamless interaction for on-chain users.
=== Tonkeeper ===
Tonkeeper is a non-custodial wallet application for the TON blockchain. It allows users to manage Toncoin and Jetton-standard tokens, access DeFi protocols such as STON.fi, and interact with TON smart contracts. Tonkeeper is available on mobile and browser extensions and has become one of the most widely used wallets in the ecosystem.
=== Telegram Wallet and TON Space ===
Telegram has integrated native TON functionality into its messaging app through two products:
Wallet: a custodial solution developed in partnership with the TON ecosystem, enabling in-chat transfers and payments.
TON Space: a self-custodial browser-based wallet embedded in Telegram, giving users full control over their private keys and access to DeFi services directly within the platform.
Telegram’s native support has played a significant role in driving user onboarding to TON-based DeFi products, especially among non-crypto-native audiences.
== Forks and related projects ==
Following Telegram's withdrawal from the development of the TON blockchain in May 2020 due to legal pressure from the U.S. Securities and Exchange Commission (SEC), several independent groups began building on the publicly available TON codebase. One of the earliest and most prominent forks was Free TON, which later rebranded to Everscale.
=== Everscale (formerly Free TON) ===
Launched on May 7, 2020, Free TON was initiated by a decentralized community of developers and validators using the open-source TON code released under the GNU General Public License. The project aimed to continue TON’s technological vision independently from Telegram. In November 2021, it was rebranded as Everscale to reflect the project's evolution and commitment to scalability. The rebranding included changing the network's native token name from TON Crystal to EVER.
Everscale introduced several protocol-level innovations, including dynamic sharding, a transition from C++ to Rust-based nodes, and a new governance structure via the EVER DAO. Its native token, EVER, was distributed through community-based contests and validation rewards, emphasizing a meritocratic distribution model. Unlike Toncoin, which is closely integrated into Telegram’s Web3 strategy, Everscale developed as a parallel ecosystem with its own development roadmap and tools.
== References ==
== External links ==
Official website
Ton-blockchain on GitHub | Wikipedia/The_Open_Network |
In cryptography a universal one-way hash function (UOWHF, often pronounced "woof") is a type of universal hash function of particular importance to cryptography. UOWHFs are proposed as an alternative to collision-resistant hash functions (CRHFs). CRHFs have a strong collision-resistance property: that it is hard, given randomly chosen hash function parameters, to find any collision of the hash function. In contrast, UOWHFs require that it be hard to find a collision where one preimage is chosen independently of the hash function parameters. The primitive was suggested by Moni Naor and Moti Yung and is also known as "target collision resistant" hash functions; it was employed to construct general digital signature schemes without trapdoor functions, and also within chosen-ciphertext secure public key encryption schemes.
The UOWHF family contains a finite number of hash functions with each
having the same probability of being used.
== Definition ==
The security property of a UOWHF is as follows. Let
A
{\displaystyle A}
be an algorithm that operates in two phases:
Initially,
A
{\displaystyle A}
receives no input (or just a security parameter) and chooses a value
x
{\displaystyle x}
.
A hash function
H
{\displaystyle H}
is chosen randomly from the family.
A
{\displaystyle A}
then receives
H
{\displaystyle H}
and must output
y
≠
x
{\displaystyle y\neq x}
such that
H
(
x
)
=
H
(
y
)
{\displaystyle H(x)=H(y)}
.
Then for all polynomial-time
A
{\displaystyle A}
the probability that
A
{\displaystyle A}
succeeds is negligible.
== Applications ==
UOWHFs are thought to be less computationally expensive than CRHFs, and are most often used for efficiency purposes in schemes where the choice of the hash function happens at some stage of execution, rather than beforehand. For instance, the Cramer–Shoup cryptosystem uses a UOWHF as part of the validity check in its ciphertexts.
== See also ==
Preimage attack
== Further reading ==
Goldreich, Oded (2004). Foundations of Cryptography. Vol. 2. Cambridge University Press.
== External links ==
Moni Naor and Moti Yung, "Universal One-Way Hash Functions and their Cryptographic Applications", 1989. | Wikipedia/Universal_one-way_hash_function |
A decentralised application (DApp, dApp, Dapp, or dapp) is an application that can operate autonomously, typically through the use of smart contracts, that run on a decentralized computing, blockchain or other distributed ledger system. Like traditional applications, DApps provide some function or utility to its users. However, unlike traditional applications, DApps operate without human intervention and are not owned by any one entity, rather DApps distribute tokens that represent ownership. These tokens are distributed according to a programmed algorithm to the users of the system, diluting ownership and control of the DApp. Without any one entity controlling the system, the application is therefore decentralised.
Decentralised applications have been popularised by distributed ledger technologies (DLT), such as the Ethereum or Cardano blockchain, on which DApps are built, amongst other public blockchains. In social media the largest decentralized platform is Bluesky.
DApps are divided into numerous categories: exchanges, businesses, gambling, games, finance, development, storage, wallet, governance, property, identity, media, social, security, energy, insurance, health, etc.
== Definition ==
There are a series of criteria that must be met in order for an application to be considered a DApp.
Traditional definitions of a decentralised application require a DApp to be open-source. That is, the application operates autonomously without a centralised entity in control of the majority of the application's associated tokens. DApps also have a public, decentralised blockchain that is used by the application to keep a cryptographic record of data, including historical transactions.
Although traditional DApps are typically open-source, DApps that are fully closed-source and partially closed-source have emerged as the cryptocurrency industry evolves. As of 2019, only 15.7% of DApps are fully open-source while 25% of DApps are closed source. In other words, the proportion of DApps with publicly available code is less than the proportion of Dapps without publicly available code. DApps that are open-source generally have higher transaction volumes than closed-source DApps.
Bitcoin, the first cryptocurrency, is an example of a DApp.
== Usage ==
DApps can be classified based on whether they operate on their own block chain, or whether they operate on the block chain of another DApp.
=== Smart contracts ===
Smart contracts are used by developers to maintain data on the block chain and to execute operations. Multiple smart contracts can be developed for a single DApp to handle more complex operations. Over 75% of DApps are supported by a single smart contract, with the remainder using multiple smart contracts.
DApps incur gas, that is fees paid to the validators of the block chain, due to the cost of deploying and executing the DApp's smart contracts. The amount of gas required of a DApp's functions is dependent on the complexity of its smart contracts. A complex smart contract of a DApp that operates on the Ethereum blockchain may fail to be deployed if it costs too much gas, leading to lower throughput and longer wait times for execution.
=== Operation ===
Consensus mechanisms are used by DApps to establish consensus on the network. The two most common mechanisms to establish consensus are proof-of-work (POW) and proof-of-stake (POS).
Proof-of-work utilises computational power to establish consensus through the process of mining. Bitcoin uses the proof-of-work mechanism. Proof-of-stake is a consensus mechanism that supports DApps through validators that secure the network by having a stake and percent ownership over the application.
DApps distribute their tokens through three main mechanisms: mining, fund-raising and development. In mining, tokens are distributed as per a predetermined algorithm as rewards to miners that secure the network through transaction verification. Tokens can also be distributed through fundraising, whereby tokens are distributed in exchange for funding in the initial development phase of the DApp, as in an initial coin offering. Lastly, the development mechanism distributes tokens that are set aside for the purpose of developing the DApp through a pre-determined schedule.
There are three main steps that always occur in the formation and development of any DApp: the publishing of the DApp's whitepaper, the distribution of initial tokens, and the distribution of ownership. Firstly, the whitepaper is published, describing the DApp's protocols, features and implementation. Then, required software and scripts are made available to the miners and stakeholders that support the validation and fundraising of the network. In exchange, they are rewarded with the initial tokens distributed by the system. Lastly, as greater numbers of participants join the network, either through utilisation of the DApp or through contributions to the DApp's development, token ownership dilutes, and the system becomes less centralised.
== Characteristics ==
DApps have their backend code running on a decentralized peer-to-peer network, as opposed to typical applications where the backend code is running on centralized servers. A DApp can have frontend code and user interfaces written in any language that can make calls to its backend.
DApps have been utilized in decentralized finance (DeFi), in which dapps perform financial functions on blockchains. Decentralized finance protocols validating peer-to-peer transactions, such as Aave Protocol, are expected to disrupt centralized finance and lower costs.
The performance of a DApp is tied to its latency, throughput, and sequential performance. Bitcoin's system for transaction validation is designed so that the average time for a block on bitcoin's blockchain to be mined is 10 minutes. Ethereum offers a reduced latency of one mined block every 12 seconds on average (called Block Time). For comparison, Visa handles approximately 10,000 transactions per second. More recent DApp projects, such as Solana, have attempted to exceed that rate.
Internet connectivity is a core dependency of blockchain systems, which includes DApps. High monetary costs also act as a barrier. Transactions of small monetary values can comprises a large proportion of the transferred amount. Greater demand for the service also leads to increased fees due to increased network traffic. This is an issue for Ethereum, which is attributed to increased network traffic caused by DApps built on the Ethereum blockchain, such as those used by Non-fungible tokens (NFTs). Transaction fees are affected by the complexity of a DApp's smart contracts, and by the particular blockchain.
== Trends ==
Ethereum is the distributed ledger technology (DLT) that has the largest DApp market. The first DApp on the Ethereum blockchain was published on April 22, 2016. From May 2017, the number of DApps being developed have grown at a higher rate. After February 2018, DApps have been published every day. Less than one fifth of DApps capture almost all the DApp users on the Ethereum blockchain. About 5% of DApps capture 80% of Ethereum transactions. 80% of DApps on Ethereum are used by less than 1000 users. On Ethereum, DApps that are exchanges capture 61.5% of transaction volume, finance DApps capture 25.6%, gambling DApps capture 5%, high-risk DApps capture 4.1%, and games capture 2.5%.
DApps have not achieved wide adoption. Potential users may not have the skill or knowledge to be able to effectively analyse the differences between DApps and traditional applications, and also may not value those differences. This skill and information can be difficult to access for mainstream users. Additionally, the user experience for DApps is often poor, as they are often developed to prioritize functionality, maintenance and stability.
Many DApps struggle to attract users, particularly in their founding stages, and even those that attract widespread initial popularity struggle to retain it.
A notable example was the DApp CryptoKitties, which heavily slowed down the Ethereum network at the height of its popularity. CryptoKitties and another similar gaming-based DApp Dice Games have failed to attract similar traction since.
== Examples ==
Augur – prediction market platform.
Cryptokitties – game built on Ethereum. It slowed Ethereum down due to insufficient transaction processing and exposed the scaling limitations of public blockchains.
Stacks project – a platform for developing decentralized applications.
Freelance – platform on smart contract.
Steemit – blogging and social media.
Uniswap – cryptocurrency exchange.
Session – blockchain-based end-to-end encrypted messenger.
== References == | Wikipedia/Decentralized_application |
Bouncy Castle is a collection of APIs used for implementing cryptography in computer programs. It includes APIs for both the Java and the C# programming languages. The APIs are supported by a registered Australian charitable organization: Legion of the Bouncy Castle Inc.
Bouncy Castle is Australian in origin and therefore American restrictions on the export of cryptography from the United States do not apply to it.
== History ==
Bouncy Castle started when two colleagues were tired of having to re-invent a set of cryptography libraries each time they changed jobs working in server-side Java SE. One of the developers was active in Java ME (J2ME at that time) development as a hobby and a design consideration was to include the greatest range of Java VMs for the library, including those on J2ME. This design consideration led to the architecture that exists in Bouncy Castle.
The project, founded in May 2000, was originally written in Java only, but added a C# API in 2004. The original Java API consisted of approximately 27,000 lines of code, including test code and provided support for J2ME, a JCE/JCA provider, and basic X.509 certificate generation. In comparison, the 1.53 release consists of 390,640 lines of code, including test code. It supports the same functionality as the original release with a larger number of algorithms, plus PKCS#10, PKCS#12, CMS, S/MIME, OpenPGP, DTLS, TLS, OCSP, TSP, CMP, CRMF, DVCS, DANE, EST and Attribute Certificates. The C# API is around 145,000 lines of code and supports most of what the Java API does.
Some key properties of the project are:
Strong emphasis on standards compliance and adaptability.
Public support facilities include an issue tracker, dev mailing list and a wiki all available on the website.
Commercial support provided under resources for the relevant API listed on the Bouncy Castle website
On 18 October 2013, a not-for-profit association, the Legion of the Bouncy Castle Inc. was established in the state of Victoria, Australia, by the core developers and others to take ownership of the project and support the ongoing development of the APIs. The association was recognised as an Australian charity with a purpose of advancement in education and a purpose that is beneficial to the community by the Australian Charities and Not-For-Profits Commission on 7 November 2013. The association was authorised to fundraise to support its purposes on 29 November 2013 by Consumer Affairs Victoria.
== Architecture ==
The Bouncy Castle architecture consists of two main components that support the base cryptographic capabilities. These are known as the 'light-weight' API, and the Java Cryptography Extension (JCE) provider. Further components built upon the JCE provider support additional functionality, such as PGP support, S/MIME, etc.
The low-level, or 'light-weight', API is a set of APIs that implement all the underlying cryptographic algorithms. The APIs were designed to be simple enough to use if needed, but provided the basic building blocks for the JCE provider. The intent is to use the low-level API in memory constrained devices (JavaME) or when easy access to the JCE libraries is not possible (such as distribution in an applet). As the light-weight API is just Java code, the Java virtual machine (JVM) does not impose any restrictions on the operation of the code, and at early times of the Bouncy Castle history it was the only way to develop strong cryptography that was not crippled by the Jurisdiction Policy files that prevented JCE providers from performing "strong" encryption.
The JCE-compatible provider is built upon the low-level APIs. As such, the source code for the JCE provider is an example of how to implement many of the "common" crypto problems using the low-level API. Many projects have been built using the JCE provider, including an Open Source Certificate Authority EJBCA.
== Certified releases ==
The C# and Java releases have FIPS 140-2 Level 1 certified streams as well. These differ from the regular releases in that, while the modules are designed in a similar fashion to the regular releases, the low-level APIs are quite different – largely to support the enforcement of controls that FIPS requires when an algorithm is used. In the case of the JCE level of the Java API, the provider is still largely a drop-in replacement for the regular release. The first FIPS-certified releases were made available in November 2016, with the latest Java version being assigned certification number 4616 and the latest C# version being assigned certification number 4416.
== Spongy Castle ==
The Android operating system, as of early 2014, includes a customized version of Bouncy Castle. Due to class name conflicts, this prevents Android applications from including and using the official release of Bouncy Castle as-is. A third-party project called Spongy Castle distributes a renamed version of the library to work around this issue.
== Stripy Castle ==
Originally, it was assumed a FIPS 140-2 version of Spongy Castle could also be done. It turned out due to Android's DEX file processing that for FIPS purposes the provider needs to be installed on the device separate from the application. The FIPS 140-2 release for Android is now called Stripy Castle and is packaged under org.stripycastle. This was needed in order to avoid clashes with Android's version of Bouncy Castle as well as clashes for applications that might be using Spongy Castle and not requiring FIPS 140-2 certified services.
== See also ==
Comparison of cryptography libraries
== References ==
== External links ==
Official website | Wikipedia/Bouncy_Castle_(cryptography) |
The Helium Network is a wireless system composed of two distinct networks: one for Internet of things (IoT) devices using LoRaWAN and another for mobile phone coverage using Wi-Fi hotspots.
Both the IoT and Mobile networks are tied to the cryptocurrency Helium Network Token (symbol HNT). Nodes on the networks may be owned and placed by individuals in places like homes or offices, and owners of nodes are rewarded for their participation in the networks in payments of HNT.
Nova Labs plays a central role in its development and operation, alongside the nonprofit Helium Foundation. Amir Haleem is the founder and CEO of Nova Labs.
== History ==
The Helium Network was begun by Helium, Inc. in 2013, as a network of LoRa gateway hotspots which could be deployed throughout an area by agreements with building owners, typically paid in conventional currency.
In 2017, the company's funds were running low, so it switched to a new strategy: offering individuals payment in cryptocurrency to operate individually owned nodes in their homes or offices. These individually owned nodes were purchased at costs of up to $500 each, and the payments to owners vary based on data usage but can be as low as $.10 a month. Hotspot operators would also have a vote in the operation of the network.
In 2021, Helium partnered with Dish Network to deploy thousands of Helium hotspots across Dish's nationwide cellular network, further expanding Helium's reach.
In March 2022, Helium Inc. rebranded to Nova Labs Inc. and raised $200 million in a funding round led by Tiger Global Management and Andreessen Horowitz.
In August 2022, Helium integrated with the 5G network. Helium 5G utilizes a decentralized approach, building a cellular network powered by new kinds of Helium Hotspots equipped with 5G radios. These hotspots, deployed by individuals or businesses, provide local coverage and relay data within the network.
Reports in July 2022 alleged that Helium falsely had claimed Lime and Salesforce as partners and customers, despite neither company having a formal relationship with Helium. Nova Labs CEO Amir Haleem has disputed these claims.
In 2022, Nova Labs (then operating as Helium Inc.) acquired FreedomFi, a company building open source tools for deploying decentralized 5G networks using CBRS spectrum. The acquisition brought together teams working on community-driven wireless infrastructure, laying the groundwork for Helium’s expansion into cellular networking.
In 2022, the Helium community approved two new tokens: IOT and MOBILE, intended to incentivize participation in the network's IoT and Mobile sub-networks. Both tokens were backed by HNT through a redemption mechanism. Ultimately, the community decided that the arrangement added too much complexity to the network’s economic structure. In January 2025, with the adoption of Helium Improvement Proposal 138 (HIP 138), the network returned to HNT as the primary reward token across all sub-networks, simplifying the system and consolidating utility around a single asset.
In April 2023, the Helium Network migrated from its own proprietary blockchain to the Solana blockchain, following community approval of Helium Improvement Proposal 70 (HIP 70). The move was designed to improve scalability, reduce transaction costs, and enable faster development of new features such as advanced Proof-of-Coverage algorithms.
In 2023, Nova Labs began offering cellular services and related plans under the name Helium Mobile. Helium Mobile users utilize both T-Mobile infrastructure as well as the Helium Network's own Wi-Fi hotspots. Previously focused on building a decentralized 5G network using CBRS spectrum, the Helium community pivoted in 2024 to Wi-Fi hotspots, which integrate more easily with existing technology and enable effective carrier offload.
== Litigation ==
On Jan 17 2025, the US Securities and Exchange Commission (SEC) filed a complaint against Nova Labs Inc., the company that developed the Helium Network, alleging that the company raised “millions of dollars from investors through its unregistered sales of securities in the form of “Hotspots” – electronic devices that “mine” one of three Nova Labs crypto assets.” The lawsuit also alleged that Nova Labs misled investors regarding multiple high-profile partnerships. On April 10, 2025 the SEC agreed to dismiss unregistered security claims and Nova Labs chose to resolve the case efficiently by agreeing to a $200,000 no admit/no deny settlement tied to its Series D equity financing.
== See also ==
LoRa
FreedomFi
== References ==
== External links ==
Official website | Wikipedia/Helium_Network |
Nervos Network is a proof-of-work blockchain platform which consists of multiple blockchain layers that are designed for different functions. The native cryptocurrency of this layer is called CKB. Smart contracts and decentralized applications can be deployed on the Nervos blockchain. The Nervos Network was founded in 2018.
== History ==
According to the organization's website, Nervos Network was founded in 2018 by Jan Xie, Terry Tai, Kevin Wang, Daniel Lv, and Cipher Wang.
== Architecture ==
Nervos Network utilizes multiple blockchain layers to for different functions. The base layer prioritizes security and decentralization, and is optimized to verify transactions. It can settle transactions submitted from upper layers and resolves disputes. Layer 2 and above are designed for smart contract and decentralized applications.
=== NC MAX ===
Layer 1 achieves cryptographic consensus through proof of work, using a modified version of Bitcoin's Nakamoto consensus algorithm: NC-MAX. This algorithm changes the original in three ways: a two-step transaction process (propose, commit) which aims to improve block propagation; dynamic adjustment to block interval based on network performance to keep orphan blocks low and improve transaction throughput; and accounting for all blocks (including orphans) during the difficulty adjustment calculation to resist "selfish mining attacks," whereby one group of miners can increase their own profits at the expense of other miners on the network. NC-MAX was presented at the Internet Society's Network and Distributed System Security (NDSS) Symposium in 2022. The consensus process uses a novel hash function called "Eaglesong."
== References ==
== Further reading ==
Sun, Meng; Lu, Yuteng; Feng, Yichun; Zhang, Qi; Liu, Shaoying (November 2021). "Modeling and Verifying the CKB Blockchain Consensus Protocol". Mathematics. 9 (22): 2954. doi:10.3390/math9222954. ISSN 2227-7390.
Bu, Hao; Sun, Meng (March 2020). "Towards Modeling and Verification of the CKB Block Synchronization Protocol in Coq". Formal Methods and Software Engineering: 22nd International Conference on Formal Engineering Methods, ICFEM 2020, Singapore. Lecture Notes in Computer Science. Vol. 12531. pp. 287–296. doi:10.1007/978-3-030-63406-3_17. ISBN 978-3-030-63405-6.
== External links ==
Official website | Wikipedia/Nervos_Network |
In cryptography, the Double Ratchet Algorithm (previously referred to as the Axolotl Ratchet) is a key management algorithm that was developed by Trevor Perrin and Moxie Marlinspike in 2013. It can be used as part of a cryptographic protocol to provide end-to-end encryption for instant messaging. After an initial key exchange it manages the ongoing renewal and maintenance of short-lived session keys. It combines a cryptographic so-called "ratchet" based on the Diffie–Hellman key exchange (DH) and a ratchet based on a key derivation function (KDF), such as a hash function, and is therefore called a double ratchet.
The algorithm provides forward secrecy for messages, and implicit renegotiation of forward keys; properties for which the protocol is named.
== History ==
The Double Ratchet Algorithm was developed by Trevor Perrin and Moxie Marlinspike (Open Whisper Systems) in 2013 and introduced as part of the Signal Protocol in February 2014. The Double Ratchet Algorithm's design is based on the DH ratchet that was introduced by Off-the-Record Messaging (OTR) and combines it with a symmetric-key ratchet modeled after the Silent Circle Instant Messaging Protocol (SCIMP). The ratchet was initially named after the critically endangered aquatic salamander axolotl, which has extraordinary self-healing capabilities. In March 2016, the developers renamed the Axolotl Ratchet as the Double Ratchet Algorithm to better differentiate between the ratchet and the full protocol, because some had used the name Axolotl when referring to the Signal Protocol.
== Overview ==
The Double Ratchet Algorithm features properties that have been commonly available in end-to-end encryption systems for a long time: encryption of contents on the entire way of transport as well as authentication of the remote peer and protection against manipulation of messages. As a hybrid of DH and KDF ratchets, it combines several desired features of both principles. From OTR messaging it takes the properties of forward secrecy and automatically reestablishing secrecy in case of compromise of a session key, forward secrecy with a compromise of the secret persistent main key, and plausible deniability for the authorship of messages. Additionally, it enables session key renewal without interaction with the remote peer by using secondary KDF ratchets. An additional key-derivation step is taken to enable retaining session keys for out-of-order messages without endangering the following keys.
It is said to detect reordering, deletion, and replay of sent messages, and improve forward secrecy properties against passive eavesdropping in comparison to OTR messaging.
Combined with public key infrastructure for the retention of pregenerated one-time keys (prekeys), it allows for the initialization of messaging sessions without the presence of the remote peer (asynchronous communication). The usage of triple Diffie–Hellman key exchange (3-DH) as initial key exchange method improves the deniability properties. An example of this is the Signal Protocol, which combines the Double Ratchet Algorithm, prekeys, and a 3-DH handshake. The protocol provides confidentiality, integrity, authentication, participant consistency, destination validation, forward secrecy, backward secrecy (aka future secrecy), causality preservation, message unlinkability, message repudiation, participation repudiation, and asynchronicity. It does not provide anonymity preservation, and requires servers for the relaying of messages and storing of public key material.
== Functioning ==
A client attempts to renew session key material interactively with the remote peer using a Diffie-Hellman (DH) ratchet. If this is impossible, the clients renew the session key independently using a hash ratchet. With every message, a client advances one of two hash ratchets—one for sending and one for receiving. These two hash ratchets get seeded with a common secret from a DH ratchet. At the same time it tries to use every opportunity to provide the remote peer with a new public DH value and advance the DH ratchet whenever a new DH value from the remote peer arrives. As soon as a new common secret is established, a new hash ratchet gets initialized.
As cryptographic primitives, the Double Ratchet Algorithm uses
for the DH ratchet
Elliptic curve Diffie-Hellman (ECDH) with Curve25519,
for message authentication codes (MAC, authentication)
Keyed-hash message authentication code (HMAC) based on SHA-256,
for symmetric encryption
the Advanced Encryption Standard (AES), partially in cipher block chaining mode (CBC) with padding as per PKCS #5 and partially in counter mode (CTR) without padding,
for the hash ratchet
HMAC.
== Applications ==
The following is a list of applications that use the Double Ratchet Algorithm or a custom implementation of it:
== Notes ==
== References ==
== Literature ==
== External links ==
Specification by Open Whisper Systems
"Advanced cryptographic ratcheting", abstract description by Moxie Marlinspike
Olm: C++ implementation under the Apache 2.0 license
Vodozemac: Rust implementation of the Olm variation, under the Apache 2.0 license
Double ratchet algorithm: The ping-pong game encrypting Signal and WhatsApp on YouTube (exposition) | Wikipedia/Double_Ratchet_Algorithm |
In cryptographic protocol design, cryptographic agility or crypto-agility is the ability to switch between multiple cryptographic primitives.
A cryptographically agile system implementing a particular standard can choose which combination of primitives to use. The primary goal of cryptographic agility is to enable rapid adaptations of new cryptographic primitives and algorithms without making disruptive changes to the system's infrastructure.
Cryptographic agility acts as a safety measure or an incident response mechanism for when a cryptographic primitive of a system is discovered to be vulnerable. A security system is considered crypto-agile if its cryptographic algorithms or parameters can be replaced with ease and is at least partly automated. The impending arrival of a quantum computer that can break existing asymmetric cryptography is raising awareness of the importance of cryptographic agility.
== Example ==
The X.509 public key certificate illustrates crypto-agility. A public key certificate has cryptographic parameters including key type, key length, and a hash algorithm. X.509 version v.3, with key type RSA, a 1024-bit key length, and the SHA-1 hash algorithm were found by NIST to have a key length that made it vulnerable to attacks, thus prompting the transition to SHA-2.
== Importance ==
With the rise of secure transport layer communication in the end of the 1990s, cryptographic primitives and algorithms have been increasingly popular; for example, by 2019, more than 80% of all websites employed some form of security measures. Furthermore, cryptographic techniques are widely incorporated to protect applications and business transactions.
However, as cryptographic algorithms are deployed, research of their security intensifies, and new attacks against cryptographic primitives (old and new alike) are discovered. Crypto-agility tries to tackle the implied threat to information security by allowing swift deprecation of vulnerable primitives and replacement with new ones.
This threat is not merely theoretical; many algorithms that were once considered secure (DES, 512-bit RSA, RC4) are now known to be vulnerable, some even to amateur attackers. On the other hand, new algorithms (AES, Elliptic curve cryptography) are often both more secure and faster in comparison to old ones. Systems designed to meet crypto-agility criteria are expected to be less affected should current primitives be found vulnerable, and may enjoy better latency or battery usage by using new and improved primitives.
For example, quantum computing, if feasible, is expected to be able to defeat existing public key cryptography algorithms. The overwhelming majority of existing public-key infrastructure relies on the computational hardness of problems such as integer factorization and discrete logarithms (which includes elliptic-curve cryptography as a special case). Quantum computers running Shor's algorithm can solve these problems exponentially faster than the best-known algorithms for conventional computers. Post-quantum cryptography is the subfield of cryptography that aims to replace quantum-vulnerable algorithms with new ones that are believed hard to break even for a quantum computer. The main families of post-quantum alternatives to factoring and discrete logarithms include lattice-based cryptography, multivariate cryptography, hash-based cryptography, and code-based cryptography.
== Awareness ==
System evolution and crypto-agility are not the same. System evolution progresses on the basis of emerging business and technical requirements. Crypto-agility is related instead to computing infrastructure and requires consideration by security experts, system designers, and application developers.
== Best practices ==
Best practices about dealing with crypto-agility include:
All business applications involving any sort of cryptographic technology should incorporate the latest algorithms and techniques.
Crypto-agility requirements must be disseminated to all hardware, software, and service suppliers, who must comply on a timely basis; suppliers who cannot address these requirements must be replaced.
Suppliers must provide timely updates and identify the crypto technology they employ.
Quantum-resistant solutions should be kept in mind.
Symmetric-key algorithms should be flexible in their key lengths.
Hash algorithms should support different lengths of outputs.
Digital certificate and private key rotations must be automated.
Standards and regulations must be complied with.
The names of the algorithms used should be communicated and not assumed or defaulted.
== Other designs ==
Cryptographic agility typically increases the complexity of the applications that rely on it. Developers need to build support for each of the optional cryptographic primitives, introducing more code and increasing the chance of implementation flaws as well as increasing maintenance and support costs. Users of the systems need to select which primitives they wish to use; for example, OpenSSL users can select from dozens of ciphersuites when using TLS. Further, when two parties negotiate the cryptographic primitives for their message exchange, it creates the opportunity for downgrade attacks by intermediaries (such as POODLE), or for the selection of insecure primitives.
One alternative approach is to dramatically limit the choices available to both developers and users, so that there is less scope for implementation or configuration flaws. In this approach, the designers of the library or system choose the primitives and do not offer a choice of cryptographic primitives (or, if they do, it is a very constrained set of choices). Opinionated encryption is visible in tools like Libsodium, where high-level APIs explicitly aim to discourage developers from picking primitives, and in Wireguard, where single primitives are picked to intentionally eliminate crypto-agility.
If opinionated encryption is used and a vulnerability is discovered in one of the primitives in a protocol, there is no way to substitute better primitives. Instead, the solution is to use versioned protocols. A new version of the protocol will include the fixed primitive. As a consequence of this, two parties running different versions of the protocol will not be able to communicate.
== References == | Wikipedia/Cryptographic_agility |
Below is a timeline of notable events related to cryptography.
== B.C. ==
36th century – The Sumerians develop cuneiform writing and the Egyptians develop hieroglyphic writing.
16th century – The Phoenicians develop an alphabet
600-500 – Hebrew scholars make use of simple monoalphabetic substitution ciphers (such as the Atbash cipher)
c. 400 – Spartan use of scytale (alleged)
c. 400 – Herodotus reports use of steganography in reports to Greece from Persia (tattoo on shaved head)
100-1 A.D.- Notable Roman ciphers such as the Caesar cipher.
== 1–1799 A.D. ==
801–873 A.D. – Cryptanalysis and frequency analysis leading to techniques for breaking monoalphabetic substitution ciphers are developed in A Manuscript on Deciphering Cryptographic Messages by the Muslim mathematician, Al-Kindi (Alkindus), who may have been inspired by textual analysis of the Qur'an. He also covers methods of encipherments, cryptanalysis of certain encipherments, and statistical analysis of letters and letter combinations in Arabic.
1450 – The Chinese develop wooden block movable type printing.
1450–1520 – The Voynich manuscript, an example of a possibly encoded illustrated book, is written.
1466 – Leon Battista Alberti invents polyalphabetic cipher, also first known mechanical cipher machine
1518 – Johannes Trithemius' book on cryptology
1553 – Bellaso invents Vigenère cipher
1585 – Vigenère's book on ciphers
1586 – Cryptanalysis used by spymaster Sir Francis Walsingham to implicate Mary, Queen of Scots, in the Babington Plot to murder Elizabeth I of England. Queen Mary was eventually executed.
1641 – Wilkins' Mercury (English book on cryptology)
1793 – Claude Chappe establishes the first long-distance semaphore telegraph line
1795 – Thomas Jefferson invents the Jefferson disk cipher, reinvented over 100 years later by Etienne Bazeries
== 1800–1899 ==
1809–14 George Scovell's work on Napoleonic ciphers during the Peninsular War
1831 – Joseph Henry proposes and builds an electric telegraph
1835 – Samuel Morse develops the Morse code
1854 – Charles Wheatstone invents the Playfair cipher
c. 1854 – Babbage's method for breaking polyalphabetic ciphers (pub 1863 by Kasiski)
1855 – For the English side in Crimean War, Charles Babbage broke Vigenère's autokey cipher (the 'unbreakable cipher' of the time) as well as the much weaker cipher that is called Vigenère cipher today. Due to secrecy it was also discovered and attributed somewhat later to the Prussian Friedrich Kasiski.
1883 – Auguste Kerckhoffs' La Cryptographie militare published, containing his celebrated laws of cryptography
1885 – Beale ciphers published
1894 – The Dreyfus Affair in France involves the use of cryptography, and its misuse, in regard to false documents.
== 1900–1949 ==
1916-1922 – William Friedman and Elizebeth Smith Friedman apply statistics to cryptanalysis (coincidence counting, etc.), write Riverbank Publications
1917 – Gilbert Vernam develops first practical implementation of a teletype cipher, now known as a stream cipher and, later, with Joseph Mauborgne the one-time pad
1917 – Zimmermann telegram intercepted and decrypted, advancing U.S. entry into World War I
1919 – Weimar Germany Foreign Office adopts (a manual) one-time pad for some traffic
1919 – Edward Hebern invents/patents first rotor machine design—Damm, Scherbius and Koch follow with patents the same year
1921 – Washington Naval Conference – U.S. negotiating team aided by decryption of Japanese diplomatic telegrams
c. 1924 – MI8 (Herbert Yardley, et al.) provide breaks of assorted traffic in support of US position at Washington Naval Conference
c. 1932 – first break of German Army Enigma by Marian Rejewski in Poland
1929 – United States Secretary of State Henry L. Stimson shuts down State Department cryptanalysis "Black Chamber", saying "Gentlemen do not read each other's mail."
1931 – The American Black Chamber by Herbert O. Yardley is published, revealing much about American cryptography
1940 – Break of Japan's PURPLE machine cipher by SIS team
December 7, 1941 – attack on Pearl Harbor; U.S. Navy base at Pearl Harbor in Oahu is surprised by Japanese attack, despite U.S. breaking of Japanese codes. U.S. enters World War II.
June 1942 – Battle of Midway where U.S. partial break into Dec 41 edition of JN-25 leads to turning-point victory over Japan
April 1943 – Admiral Yamamoto, architect of Pearl Harbor attack, is assassinated by U.S. forces who know his itinerary from decoded messages
April 1943 – Max Newman, Wynn-Williams, and their team (including Alan Turing) at the secret Government Code and Cypher School ('Station X'), Bletchley Park, Bletchley, England, complete the "Heath Robinson". This is a specialized machine for cipher-breaking, not a general-purpose calculator or computer.
December 1943 – The Colossus computer was built, by Thomas Flowers at The Post Office Research Laboratories in London, to crack the German Lorenz cipher (SZ42). Colossus was used at Bletchley Park during World War II – as a successor to April's 'Robinson's. Although 10 were eventually built, unfortunately they were destroyed immediately after they had finished their work – it was so advanced that there was to be no possibility of its design falling into the wrong hands.
1944 – Patent application filed on SIGABA code machine used by U.S. in World War II. Kept secret, it finally issues in 2001
1946 – The Venona project's first break into Soviet espionage traffic from the early 1940s
1948 – Claude Shannon writes a paper that establishes the mathematical basis of information theory.
1949 – Shannon's Communication Theory of Secrecy Systems published in Bell Labs Technical Journal
== 1950–1999 ==
1951 – U.S. National Security Agency founded. KL-7 rotor machine introduced sometime thereafter.
1957 – First production order for KW-26 electronic encryption system.
August 1964 – Gulf of Tonkin Incident leads U.S. into Vietnam War, possibly due to misinterpretation of signals intelligence by NSA.
1967 – David Kahn's The Codebreakers is published.
1968 – John Anthony Walker walks into the Soviet Union's embassy in Washington and sells information on KL-7 cipher machine. The Walker spy ring operates until 1985.
1969 – The first hosts of ARPANET, Internet's ancestor, are connected.
1970 – Using quantum states to encode information is first proposed: Stephen Wiesner invents conjugate coding and applies it to design “money physically impossible to counterfeit” (still technologically unfeasible today).
1974? – Horst Feistel develops Feistel network block cipher design.
1976 – The Data Encryption Standard published as an official Federal Information Processing Standard (FIPS) for the United States.
1976 – Diffie and Hellman publish New Directions in Cryptography.
1977 – RSA public key encryption invented.
1978 – Robert McEliece invents the McEliece cryptosystem, the first asymmetric encryption algorithm to use randomization in the encryption process.
1981 – Richard Feynman proposed quantum computers. The main application he had in mind was the simulation of quantum systems, but he also mentioned the possibility of solving other problems.
1984 – Based on Stephen Wiesner's idea from the 1970s, Charles Bennett and Gilles Brassard design the first quantum cryptography protocol, BB84.
1985 – Walker spy ring uncovered. Remaining KL-7's withdrawn from service.
1986 – After an increasing number of break-ins to government and corporate computers, United States Congress passes the Computer Fraud and Abuse Act, which makes it a crime to break into computer systems. The law, however, does not cover juveniles.
1988 – African National Congress uses computer-based one-time pads to build a network inside South Africa.
1989 – Tim Berners-Lee and Robert Cailliau built the prototype system which became the World Wide Web at CERN.
1989 – Quantum cryptography experimentally demonstrated in a proof-of-the-principle experiment by Charles Bennett et al.
1991 – Phil Zimmermann releases the public key encryption program PGP along with its source code, which quickly appears on the Internet.
1994 – Bruce Schneier's Applied Cryptography is published.
1994 – Secure Sockets Layer (SSL) encryption protocol released by Netscape.
1994 – Peter Shor devises an algorithm which lets quantum computers determine the factorization of large integers quickly. This is the first interesting problem for which quantum computers promise a significant speed-up, and it therefore generates a lot of interest in quantum computers.
1994 – DNA computing proof of concept on toy travelling salesman problem; a method for input/output still to be determined.
1994 – Russian crackers siphon $10 million from Citibank and transfer the money to bank accounts around the world. Vladimir Levin, the 30-year-old ringleader, uses his work laptop after hours to transfer the funds to accounts in Finland and Israel. Levin stands trial in the United States and is sentenced to three years in prison. Authorities recover all but $400,000 of the stolen money.
1994 – Formerly proprietary, but un-patented, RC4 cipher algorithm is published on the Internet.
1994 – First RSA Factoring Challenge from 1977 is decrypted as The Magic Words are Squeamish Ossifrage.
1995 – NSA publishes the SHA1 hash algorithm as part of its Digital Signature Standard.
July 1997 – OpenPGP specification (RFC 2440) released
1997 – Ciphersaber, an encryption system based on RC4 that is simple enough to be reconstructed from memory, is published on Usenet.
October 1998 – Digital Millennium Copyright Act (DMCA) becomes law in U.S., criminalizing production and dissemination of technology that can circumvent technical measures taken to protect copyright.
October 1999 – DeCSS, a computer program capable of decrypting content on a DVD, is published on the Internet.
== 2000 and beyond ==
January 14, 2000 – U.S. Government announce restrictions on export of cryptography are relaxed (although not removed). This allows many US companies to stop the long running process of having to create US and international copies of their software.
March 2000 – President of the United States Bill Clinton says he doesn't use e-mail to communicate with his daughter, Chelsea Clinton, at college because he doesn't think the medium is secure.
September 6, 2000 – RSA Security Inc. released their RSA algorithm into the public domain, a few days in advance of their U.S. patent 4,405,829 expiring. Following the relaxation of the U.S. government export restrictions, this removed one of the last barriers to the worldwide distribution of much software based on cryptographic systems
2000 – UK Regulation of Investigatory Powers Act requires anyone to supply their cryptographic key to a duly authorized person on request
2001 – Belgian Rijndael algorithm selected as the U.S. Advanced Encryption Standard (AES) after a five-year public search process by National Institute of Standards and Technology (NIST)
2001 – Scott Fluhrer, Itsik Mantin and Adi Shamir publish an attack on WiFi's Wired Equivalent Privacy security layer
September 11, 2001 – U.S. response to terrorist attacks hampered by lack of secure communications
November 2001 – Microsoft and its allies vow to end "full disclosure" of security vulnerabilities by replacing it with "responsible" disclosure guidelines
2002 – NESSIE project releases final report / selections
August 2002, PGP Corporation formed, purchasing assets from NAI.
2003 – CRYPTREC project releases 2003 report / recommendations
2004 – The hash MD5 is shown to be vulnerable to practical collision attack
2004 – The first commercial quantum cryptography system becomes available from id Quantique.
2005 – Potential for attacks on SHA1 demonstrated
2005 – Agents from the U.S. FBI demonstrate their ability to crack WEP using publicly available tools
May 1, 2007 – Users swamp Digg.com with copies of a 128-bit key to the AACS system used to protect HD DVD and Blu-ray video discs. The user revolt was a response to Digg's decision, subsequently reversed, to remove the keys, per demands from the motion picture industry that cited the U.S. DMCA anti-circumvention provisions.
November 2, 2007 – NIST hash function competition announced.
2009 – Bitcoin network was launched.
2010 – The master key for High-bandwidth Digital Content Protection (HDCP) and the private signing key for the Sony PlayStation 3 game console are recovered and published using separate cryptoanalytic attacks. PGP Corp. is acquired by Symantec.
2012 – NIST selects the Keccak algorithm as the winner of its SHA-3 hash function competition.
2013 – Edward Snowden discloses a vast trove of classified documents from NSA. See Global surveillance disclosures (2013–present)
2013 – Dual_EC_DRBG is discovered to have a NSA backdoor.
2013 – NSA publishes Simon and Speck lightweight block ciphers.
2014 – The Password Hashing Competition accepts 24 entries.
2015 – Year by which NIST suggests that 80-bit keys be phased out.
2024 – August 13th 2024 - NIST releases first 3 finalized post-quantum encryption standards.
== See also ==
History of cryptography
== References ==
== External links ==
Timeline of Cipher Machines Archived 2021-10-06 at the Wayback Machine | Wikipedia/Timeline_of_cryptography |
Network Security Services (NSS) is a collection of cryptographic computer libraries designed to support cross-platform development of security-enabled client and server applications with optional support for hardware TLS/SSL acceleration on the server side and hardware smart cards on the client side. NSS provides a complete open-source implementation of cryptographic libraries supporting Transport Layer Security (TLS) / Secure Sockets Layer (SSL) and S/MIME. NSS releases prior to version 3.14 are tri-licensed under the Mozilla Public License 1.1, the GNU General Public License, and the GNU Lesser General Public License. Since release 3.14, NSS releases are licensed under GPL-compatible Mozilla Public License 2.0.
== History ==
NSS originated from the libraries developed when Netscape invented the SSL security protocol.
=== FIPS 140 validation and NISCC testing ===
The NSS software crypto module has been validated five times (in 1997, 1999, 2002, 2007, and 2010) for conformance to FIPS 140 at Security Levels 1 and 2. NSS was the first open source cryptographic library to receive FIPS 140 validation. The NSS libraries passed the NISCC TLS/SSL and S/MIME test suites (1.6 million test cases of invalid input data).
== Applications that use NSS ==
AOL, Red Hat, Sun Microsystems/Oracle Corporation, Google and other companies and individual contributors have co-developed NSS. Mozilla provides the source code repository, bug tracking system, and infrastructure for mailing lists and discussion groups. They and others named below use NSS in a variety of products, including the following:
Mozilla client products, including Firefox, Thunderbird, SeaMonkey, and Firefox for mobile.
AOL Communicator and AOL Instant Messenger (AIM)
Open source client applications such as Evolution, Pidgin, and OpenOffice.org 2.0 onward (and its descendants).
Server products from Red Hat: Red Hat Directory Server, Red Hat Certificate System, and the mod nss SSL module for the Apache web server.
Sun server products from the Sun Java Enterprise System, including Sun Java System Web Server, Sun Java System Directory Server, Sun Java System Portal Server, Sun Java System Messaging Server, and Sun Java System Application Server, open source version of Directory Server OpenDS.
Libreswan IKE/IPsec requires NSS. It is a fork of Openswan which could optionally use NSS.
== Architecture ==
NSS includes a framework to which developers and OEMs can contribute patches, such as assembly code, to optimize performance on their platforms. Mozilla has certified NSS 3.x on 18 platforms. NSS makes use of Netscape Portable Runtime (NSPR), a platform-neutral open-source API for system functions designed to facilitate cross-platform development. Like NSS, NSPR has been used heavily in multiple products.
=== Software development kit ===
In addition to libraries and APIs, NSS provides security tools required for debugging, diagnostics, certificate and key management, cryptography-module management, and other development tasks. NSS comes with an extensive and growing set of documentation, including introductory material, API references, man pages for command-line tools, and sample code.
Programmers can utilize NSS as source and as shared (dynamic) libraries. Every NSS release is backward-compatible with previous releases, allowing NSS users to upgrade to new NSS shared libraries without recompiling or relinking their applications.
=== Interoperability and open standards ===
NSS supports a range of security standards, including the following:
TLS 1.0 (RFC 2246), 1.1 (RFC 4346), 1.2 (RFC 5246), and 1.3 (RFC 8446). The Transport Layer Security (TLS) protocol from the IETF supersedes SSL v3.0 while remaining backward-compatible with SSL v3 implementations.
SSL 3.0. The Secure Sockets Layer (SSL) protocol allows mutual authentication between a client and server and the establishment of an authenticated and encrypted connection.
DTLS 1.0 (RFC 4347) and 1.2 (RFC 6347).
DTLS-SRTP (RFC 5764).
The following PKCS standards:
PKCS #1. RSA standard that governs implementation of public-key cryptography based on the RSA algorithm.
PKCS #3. RSA standard that governs implementation of Diffie–Hellman key agreement.
PKCS #5. RSA standard that governs password-based cryptography, for example to encrypt private keys for storage.
PKCS #7. RSA standard that governs the application of cryptography to data, for example digital signatures and digital envelopes.
PKCS #8. RSA standard that governs the storage and encryption of private keys.
PKCS #9. RSA standard that governs selected attribute types, including those used with PKCS #7, PKCS #8, and PKCS #10.
PKCS #10. RSA standard that governs the syntax for certificate requests.
PKCS #11. RSA standard that governs communication with cryptographic tokens (such as hardware accelerators and smart cards) and permits application independence from specific algorithms and implementations.
PKCS #12. RSA standard that governs the format used to store or transport private keys, certificates, and other secret material.
Cryptographic Message Syntax, used in S/MIME (RFC 2311 and RFC 2633). IETF message specification (based on the popular Internet MIME standard) that provides a consistent way to send and receive signed and encrypted MIME data.
X.509 v3. ITU standard that governs the format of certificates used for authentication in public-key cryptography.
OCSP (RFC 2560). The Online Certificate Status Protocol (OCSP) governs real-time confirmation of certificate validity.
PKIX Certificate and CRL Profile (RFC 3280). The first part of the four-part standard under development by the Public-Key Infrastructure (X.509) working group of the IETF (known as PKIX) for a public-key infrastructure for the Internet.
RSA, DSA, ECDSA, Diffie–Hellman, EC Diffie–Hellman, AES, Triple DES, Camellia, IDEA, SEED, DES, RC2, RC4, SHA-1, SHA-256, SHA-384, SHA-512, MD2, MD5, HMAC: Common cryptographic algorithms used in public-key and symmetric-key cryptography.
FIPS 186-2 pseudorandom number generator.
=== Hardware support ===
NSS supports the PKCS #11 interface for access to cryptographic hardware like TLS/SSL accelerators, hardware security modules and smart cards. Since most hardware vendors such as SafeNet, AEP and Thales also support this interface, NSS-enabled applications can work with high-speed crypto hardware and use private keys residing on various smart cards, if vendors provide the necessary middleware. NSS version 3.13 and above support the Advanced Encryption Standard New Instructions (AES-NI).
=== Java support ===
Network Security Services for Java (JSS) consists of a Java interface to NSS. It supports most of the security standards and encryption technologies supported by NSS. JSS also provides a pure Java interface for ASN.1 types and BER/DER encoding.
== See also ==
Information security
Comparison of TLS implementations
== References ==
== External links ==
Official website | Wikipedia/Network_Security_Services |
Skein is a cryptographic hash function and one of five finalists in the NIST hash function competition. Entered as a candidate to become the SHA-3 standard, the successor of SHA-1 and SHA-2, it ultimately lost to NIST hash candidate Keccak.
The name Skein refers to how the Skein function intertwines the input, similar to a skein of yarn.
== History ==
Skein was created by Bruce Schneier, Niels Ferguson, Stefan Lucks, Doug Whiting, Mihir Bellare, Tadayoshi Kohno, Jon Callas and Jesse Walker.
Skein is based on the Threefish tweakable block cipher compressed using Unique Block Iteration (UBI) chaining mode, a variant of the Matyas–Meyer–Oseas hash mode, while leveraging an optional low-overhead argument-system for flexibility.
Skein's algorithm and a reference implementation was given to public domain.
== Functionality ==
Skein supports internal state sizes of 256, 512 and 1024 bits, and arbitrary output sizes.
The authors claim 6.1 cycles per byte for any output size on an Intel Core 2 Duo in 64-bit mode.
The core of Threefish is based on a MIX function that transforms 2 64-bit words using a single addition, rotation by a constant and XOR. The UBI chaining mode combines an input chaining value with an arbitrary length input string and produces a fixed size output.
Threefish's nonlinearity comes entirely from the combination of addition operations and exclusive-ORs; it does not use S-boxes. The function is optimized for 64-bit processors, and the Skein paper defines optional features such as randomized hashing, parallelizable tree hashing, a stream cipher, personalization, and a key derivation function.
== Cryptanalysis ==
In October 2010, an attack that combines rotational cryptanalysis with the rebound attack was published. The attack finds rotational collisions for 53 of 72 rounds in Threefish-256, and 57 of 72 rounds in Threefish-512. It also affects the Skein hash function. This is a follow-up to the earlier attack published in February, which breaks 39 and 42 rounds respectively.
The Skein team tweaked the key schedule constant for round 3 of the NIST hash function competition, to make this attack less effective, even though they believe the hash would still be secure without these tweaks.
== Examples of Skein hashes ==
Hash values of empty string.
Skein-256-256("")
c8877087da56e072870daa843f176e9453115929094c3a40c463a196c29bf7ba
Skein-512-256("")
39ccc4554a8b31853b9de7a1fe638a24cce6b35a55f2431009e18780335d2621
Skein-512-512("")
bc5b4c50925519c290cc634277ae3d6257212395cba733bbad37a4af0fa06af41fca7903d06564fea7a2d3730dbdb80c1f85562dfcc070334ea4d1d9e72cba7a
Even a small change in the message will (with overwhelming probability) result in a mostly different hash, due to the avalanche effect. For example, adding a period to the end of the sentence:
Skein-512-256("The quick brown fox jumps over the lazy dog")
b3250457e05d3060b1a4bbc1428bc75a3f525ca389aeab96cfa34638d96e492a
Skein-512-256("The quick brown fox jumps over the lazy dog.")
41e829d7fca71c7d7154ed8fc8a069f274dd664ae0ed29d365d919f4e575eebb
Skein-512-512("The quick brown fox jumps over the lazy dog")
94c2ae036dba8783d0b3f7d6cc111ff810702f5c77707999be7e1c9486ff238a7044de734293147359b4ac7e1d09cd247c351d69826b78dcddd951f0ef912713
Skein-512-512("The quick brown fox jumps over the lazy dog.")
658223cb3d69b5e76e3588ca63feffba0dc2ead38a95d0650564f2a39da8e83fbb42c9d6ad9e03fbfde8a25a880357d457dbd6f74cbcb5e728979577dbce5436
== References ==
== External links ==
Official Skein website (dead, Wayback Machine archive)
Bruce Schneier's Skein webpage
=== Implementations ===
SPARKSkein – an implementation of Skein in SPARK, with proofs of type-safety
Botan contains a C++ implementation of Skein-512
nskein – a .NET implementation of Skein with support for all block sizes
pyskein Skein module for Python
PHP-Skein-Hash Skein hash for PHP on GitHub
Digest::Skein, an implementation in C and Perl
skeinfish A C# implementation of Skein and Threefish (based on version 1.3)
Java, Scala, and Javascript implementations of Skein 512-512 (based on version 1.3)
A Java implementation of Skein (based on version 1.1)
An implementation of Skein in Ada
skerl, Skein hash function for Erlang, via NIFs
Skein 512-512 implemented in Bash
Skein implemented in Haskell
VHDL source code developed by the Cryptographic Engineering Research Group (CERG) at George Mason University
skeinr Skein implemented in Ruby
fhreefish An efficient implementation of Skein-256 for 8-bit Atmel AVR microcontrollers, meeting the performance estimates outlined in the official specification | Wikipedia/Skein_hash_function |
Stellar, or Stellar Lumens (XLM) is a cryptocurrency protocol which allows transactions between any pair of currencies.
The Stellar protocol is supported by the nonprofit Stellar Development Foundation (though this organization does not have 501(c)(3) tax-exempt status) which was founded in 2014. The for profit arm, Lightyear.io, was founded in 2017.
== History ==
In 2014, Jed McCaleb, founder of Mt. Gox and co-founder of Ripple, launched the network system Stellar with former lawyer Joyce Kim. Before the official launch, McCaleb formed a website called "Secret Bitcoin Project" seeking alpha testers. The nonprofit Stellar Development Foundation was created in collaboration with Stripe CEO Patrick Collison and the project officially launched that July. Stellar received $3 million in seed funding from Stripe. Stellar was released as a decentralized payment network and protocol with a native currency, stellar. At its launch, the network had 100 billion stellars. 25 percent of those would be given to other non-profits working toward financial inclusion. Stripe received 2 percent or 2 billion of the initial stellar in return for its seed investment. The cryptocurrency, originally known as stellar, was later called Lumens or XLM. In August 2014, Mercado Bitcoin, the first Brazilian bitcoin exchange, announced it would be using the Stellar network. By January 2015, Stellar had approximately 3 million registered user accounts on its platform and its market cap was almost $15 million.
The Stellar Development Foundation released an upgraded protocol with a new consensus algorithm in April 2015 which went live in November 2015. The new algorithm used SCP, a cryptocurrency protocol created by Stanford professor David Mazières.
Lightyear.io, a for-profit entity of Stellar, was launched in May 2017 as the commercial arm of the company. In September 2017, Stellar announced a benefits program, part of its Stellar Partnership Grant Program, which would award partners up to $2 million worth of Lumens for project development. In September 2018, Lightyear Corporation acquired Chain, Inc and the combined company was named Interstellar.
In 2021, Franklin Templeton launched the first tokenised US mutual fund using Stellar.
== Usage ==
In 2015, it was announced that Stellar was releasing an integration into Vumi, the open-sourced messaging platform of the Praekelt Foundation in South Africa. Vumi uses cellphone talk time as currency using the Stellar protocol. Stellar partnered with cloud-based banking software company Oradian in April 2015 to integrate Stellar into Oradian's banking platform to add microfinance institutions (MFIs) in Nigeria.
Deloitte announced its integration with Stellar in 2016 to build a cross-border payments application, Deloitte Digital Bank. In December 2016, it was announced that Stellar's payment network had expanded to include Coins.ph, a mobile payments startup in the Philippines, ICICI Bank in India, African mobile payments firm Flutterwave, and French remittances company Tempo Money Transfer.
In October 2017, Stellar partnered with IBM and KlickEx to facilitate cross-border transactions in the South Pacific region. The cross-border payment system developed by IBM includes partnerships with banks in the area. The Lumens digital currency was ranked 13th in market capitalization at the time of the IBM partnership.
In December 2017, TechCrunch announced Stellar's partnership with SureRemit, a Nigerian-based remittances platform.
On January 6, 2021, the Ministry of Digital Transformation of Ukraine announced cooperation and partnership with Stellar in development of Ukraine digital infrastructure.
== Ecosystem ==
Stellar has an active community ecosystem and supports projects that utilize the Stellar Network with the Stellar Community Fund.
== Overview ==
Stellar is an open-source protocol for exchanging money or tokens using the Stellar Consensus Protocol. The platform's source code is hosted on GitHub.
Servers run a software implementation of the protocol, and use the Internet to connect to and communicate with other Stellar servers. Each server stores a ledger of all the accounts in the network. 3 nodes are operated by the Stellar Development Foundation, in conjunction with 22 other organizations, providing for a total of 77 validator nodes. Transactions among accounts occur not through mining but rather through a consensus process among accounts in a quorum slice.
== See also ==
Remittance
== References ==
== External links ==
Official Website | Wikipedia/Stellar_(payment_network) |
UML (Unified Modeling Language) is a modeling language used by software developers. UML can be used to develop diagrams and provide users (programmers) with ready-to-use, expressive modeling examples. Some UML tools generate program language code from UML. UML can be used for modeling a system independent of a platform language. UML is a graphical language for visualizing, specifying, constructing, and documenting information about software-intensive systems. UML gives a standard way to write a system model, covering conceptual ideas. With an understanding of modeling, the use and application of UML can make the software development process more efficient.
== History ==
UML has applied to various activities since the second half of the 1990s and been used with object-oriented development methods.
== Fields applying UML ==
UML has been used in following areas
UML can also be used to model nonsoftware systems, such as workflow in the legal systems, medical electronics and patient healthcare systems, and the design of hardware.
== Modeling applications of UML using various diagrams ==
The following lists of UML diagrams and functionality summaries enable understanding of UML applications in real-world examples.
=== Structure diagrams and their applications ===
Structuring diagrams show a view of a system that shows the structure of the objects, including their classifiers, relationships, attributes and operations:
Class diagram
Component diagram
Composite structure diagram
Deployment diagram
Object diagram
Package diagram
Profile diagram
=== Behaviour diagrams and their applications ===
Behaviour diagrams are used to illustrate the behavior of a system, they are used extensively to describe the functionality of software systems. Some Behaviour diagrams are:
Activity diagram
State machine diagram
Use case diagram
=== Interaction diagrams and their applications ===
Interaction diagrams are subset of behaviour diagrams and emphasize the flow of control and data among the things in the system being modelled:
Communication diagram
Interaction overview diagram
Sequence diagram
Timing diagram
== Web applications ==
Web applications of UML can be used to model user interfaces of web applications and make the purpose of the website clear.
Web applications are software-intensive systems and UML is among the efficient choice of languages for modeling them. Web software complexity of an application can be minimized using various UML tools.
UML-based web engineering aims at offering a UML profile that matches the needs of web development better. The following are examples:
Representation of web applications using a set of models
Web app use case model
Web app implementation model
Web app deployment model
Web app security model
Web app site map
To model pages, hyperlinks, and dynamic content on the client and server side.
For modeling server side aspects of web page with one class and client side aspect with another and distinguishing the two by using UML's extension mechanism to define stereotype's and icons for each server and client page.
Stereotypes in UML are used to define new semantics for modeling element.
Forms in HTML can also be modeled using various UML constructs.
UML can be used to express the execution of the system’s business logic in those Web-specific elements and technologies.
== Embedded systems ==
Software in embedded systems design needs to be looked carefully for software specification and analysis. Unified Modeling Language and extension proposals in the realtime domain can be used for the development of new design flows. UML can be used for specification, design and implementation of modern embedded systems. UML can also be used for modelling the system from functional requirements through executable specifications and for that purpose it is important to be able to model the context for an embedded system – both environmental and user-driven.
Some key concepts of UML related to embedded systems:
UML is not a single language, but a set of notations, syntax and semantics to allow the creation of families of languages for particular applications.
Extension mechanisms in UML like profiles, stereotypes, tags, and constraints can be used for particular applications.
Use-case modelling to describe system environments, user scenarios, and test cases.
UML has support for object-oriented system specification, design and modelling.
Growing interest in UML from the embedded systems and realtime community.
Support for state-machine semantics which can be used for modelling and synthesis.
UML supports object-based structural decomposition and refinement.
A specific UML profile, called MARTE for Modeling and Analysis of Real-Time and Embedded systems, provides some extensions dedicated to the domain.
== See also ==
Unified Modeling Language
Web application
Embedded system
MARTE
UML tools
== References and notes ==
Notes
Citations
== External links ==
http://www.uml.org/
https://web.archive.org/web/20110906042707/http://www.itmweb.com/essay546.htm
https://web.archive.org/web/20120331162632/http://oss.org.cn/ossdocs/development/rup/webapps.htm
http://www.sereferences.com/uml-tools.php
http://blogs.oracle.com/JavaFundamentals/entry/the_importance_of_using_unified | Wikipedia/Applications_of_UML |
The Graphical Kernel System (GKS) is a 2D computer graphics system using vector graphics, introduced in 1977. It was suitable for making line and bar charts and similar tasks. A key concept was cross-system portability, based on an underlying coordinate system that could be represented on almost any hardware. GKS is best known as the basis for the graphics in the GEM GUI system used on the Atari ST and as part of Ventura Publisher.
A draft international standard was circulated for review in September 1983. Final ratification of the standard was achieved in 1985, making it the first ISO graphics standard.
A 3D system modelled on GKS was introduced as PHIGS, which saw some use in the 1980s and early 1990s.
== Overview ==
GKS provides a set of drawing features for two-dimensional vector graphics suitable for charting and similar duties. The calls are designed to be portable across different programming languages, graphics devices and hardware, so that applications written to use GKS will be readily portable to many platforms and devices.
GKS was fairly common on computer workstations in the 1980s and early 1990s. GKS formed the basis of Digital Research's GSX which evolved into VDI, one of the core components of GEM. GEM was the native GUI on the Atari ST and was occasionally seen on PCs, particularly in conjunction with Ventura Publisher. GKS was little used commercially outside these markets, but remains in use in some scientific visualization packages. It is also the underlying API defining the Computer Graphics Metafile. One popular application based on an implementation of GKS is the GR Framework, a C library for high-performance scientific visualization that has become a common plotting backend among Julia users.
A main developer and promoter of the GKS was José Luis Encarnação, formerly director of the Fraunhofer Institute for Computer Graphics (IGD) in Darmstadt, Germany.
GKS has been standardized in the following documents:
ANSI standard ANSI X3.124 of 1985.
ISO 7942:1985 standard, revised as ISO 7942:1985/Amd 1:1991 and ISO/IEC 7942-1:1994, as well as ISO/IEC 7942-2:1997, ISO/IEC 7942-3:1999 and ISO/IEC 7942-4:1998
The language bindings are ISO standard ISO 8651.
GKS-3D (Graphical Kernel System for Three Dimensions) functional definition is ISO standard ISO 8805, and the corresponding C bindings are ISO/IEC 8806.
The functionality of GKS is wrapped up as a data model standard in the STEP standard, section ISO 10303-46.
== See also ==
General Graphics Interface
GSS-KERNEL
IGES (Initial Graphics Exchange Specification)
NAPLPS
== References ==
== Further reading ==
Hopgood, F. R. A. (1983). Introduction to the Graphical Kernel System (GKS). London: Academic Press. ISBN 0-12-355570-1.
Laflin, Susan (August 1999). "The Graphical Kernel System". SEM307 Computer Graphics II. School of Computer Science, University of Birmingham. Archived from the original on 2015-09-23. Retrieved 2007-02-18.
Encarnação, José L.; Encarnação, L. M.; Herzner, Wolfgang R. (1987). Graphische Datenverarbeitung mit GKS (in German) (1 ed.). München / Wien: Carl Hanser Verlag. ISBN 3446149783.
Bechlars, Jörg; Buhtz, Rainer (1994). GKS in der Praxis (in German) (2 ed.). Heidelberg: Springer Verlag. ISBN 3540567852.
Fellner, Wolf-Dietrich (1992). Computergrafik (in German) (2 ed.). Mannheim: BI Wissenschaftsverlag. ISBN 3411151226.
Gawehn, Wilfried (1991). Grafikprogrammierung mit C und GKS (in German). Mannheim: BI Wissenschaftsverlag. ISBN 3-411-14981-7.
== External links ==
Unofficial source of current implementation information
GKS at FOLDOC | Wikipedia/Graphical_Kernel_System |
DOT is a graph description language, developed as a part of the Graphviz project. DOT graphs are typically stored as files with the .gv or .dot filename extension — .gv is preferred, to avoid confusion with the .dot extension used by versions of Microsoft Word before 2007. dot is also the name of the main program to process DOT files in the Graphviz package.
Various programs can process DOT files. Some, such as dot, neato, twopi, circo, fdp, and sfdp, can read a DOT file and render it in graphical form. Others, such as gvpr, gc, acyclic, ccomps, sccmap, and tred, read DOT files and perform calculations on the represented graph. Finally, others, such as lefty, dotty, and grappa, provide an interactive interface. The GVedit tool combines a text editor and a non-interactive viewer. Most programs are part of the Graphviz package or use it internally.
DOT is historically an acronym for "DAG of tomorrow", as the successor to a DAG format and a dag program which handled only directed acyclic graphs.
== Syntax ==
=== Graph types ===
==== Undirected graphs ====
At its simplest, DOT can be used to describe an undirected graph. An undirected graph shows simple relations between objects, such as reciprocal friendship between people. The graph keyword is used to begin a new graph, and nodes are described within curly braces. A double-hyphen (--) is used to show relations between the nodes.
==== Directed graphs ====
Similar to undirected graphs, DOT can describe directed graphs, such as flowcharts and dependency trees. The syntax is the same as for undirected graphs, except the digraph keyword is used to begin the graph, and an arrow (->) is used to show relationships between nodes.
=== Attributes ===
Various attributes can be applied to graphs, nodes and edges in DOT files. These attributes can control aspects such as color, shape, and line styles. For nodes and edges, one or more attribute–value pairs are placed in square brackets [] after a statement and before the semicolon (which is optional). Graph attributes are specified as direct attribute–value pairs under the graph element, where multiple attributes are separated by a comma or using multiple sets of square brackets, while node attributes are placed after a statement containing only the name of the node, but not the relations between the dots.
HTML-like labels are supported, although initially Graphviz did not handle them.
=== Comments ===
DOT supports C and C++ style single line and multiple line comments. In addition, it ignores lines with a number sign symbol # as their first character, like many interpreted languages.
== Layout programs ==
The DOT language defines a graph, but does not provide facilities for rendering the graph. There are several programs that can be used to render, view, and manipulate graphs in the DOT language:
=== General ===
Graphviz – a collection of CLI utilities and libraries to manipulate and render graphs into different formats like SVG, PDF, PNG etc.
dot – CLI tool for conversion between .dot and other formats
=== JavaScript ===
Canviz – a JavaScript library for rendering DOT files
d3-graphviz – a JavaScript library based on Viz.js and D3.js that renders DOT graphs and supports animated transitions between graphs and interactive graph manipulation
Vis.js – a JavaScript library that accept DOT as input for network graphs.
Viz.js – a JavaScript port of Graphviz that provides a simple wrapper for using it in the browser.
hpcc-js/wasm Graphviz – a fast WASM library for Graphviz similar to Viz.js
=== Java ===
Gephi – an interactive visualization and exploration platform for all kinds of networks and complex systems, dynamic and hierarchical graphs
Grappa – a partial port of Graphviz to Java
graphviz-java – an open source partial port of Graphviz to Java available from github.com
ZGRViewer – a DOT viewer
=== Other ===
Beluging – a Python- & Google Cloud Platform-based viewer of DOT and Beluga extensions
Delineate – a Rust application for Linux than can edit fully-featured DOT graph with interactive preview, and export as PNG, SVG, or JPEG
dot2tex – a program to convert files from DOT to PGF/TikZ or PSTricks, both of which are rendered in LaTeX
OmniGraffle – a digital illustration application for macOS that can import a subset of DOT, producing an editable document (but the result cannot be exported back to DOT)
Tulip – a software framework in C++ that can import DOT files for analysis
VizierFX – an Apache Flex graph rendering library in ActionScript
== Notes ==
== See also ==
=== External links ===
DOT tutorial and specification
Drawing graphs with dot
Node, Edge and Graph Attributes
Node Shapes
Gallery of examples
Graphviz Online: instant conversion and visualization of DOT descriptions
Boost Graph Library
lisp2dot or tree2dot: convert Lisp programming language-like program trees to DOT language (designed for use with genetic programming) | Wikipedia/DOT_(graph_description_language) |
Computer Graphics Metafile (CGM) is a free and open international standard file format for 2D vector graphics, raster graphics, and text, and is defined by ISO/IEC 8632.
== Overview ==
All graphical elements can be specified in a textual source file that can be compiled into a binary file or one of two text representations. CGM provides a means of graphics data interchange for computer representation of 2D graphical information independent from any particular application, system, platform, or device.
As a metafile, i.e., a file containing information that describes or specifies another file, the CGM format has numerous elements to provide functions and to represent entities, so that a wide range of graphical information and geometric primitives can be accommodated. Rather than establish an explicit graphics file format, CGM contains the instructions and data for reconstructing graphical components to render an image using an object-oriented approach.
Although CGM is not widely supported for web pages and has been supplanted by other formats in the graphic arts, it is still prevalent in engineering, aviation, and other technical applications.
The initial CGM implementation was effectively a streamed representation of a sequence of Graphical Kernel System (GKS) primitive operations. It has been adopted to some extent in the areas of technical illustration and professional design, but has largely been superseded by formats such as SVG and DXF.
The World Wide Web Consortium has developed WebCGM, a profile of CGM intended for the use of CGM on the Web.
== History ==
1986 – ANSI X3 122-1986 (ANSI X3 committee)
1987 – ISO 8632-1987 (ISO)
1991 – ANSI/ISO 8632-1987 (ANSI and ISO)
1992 – ISO 8632:1992, a.k.a. CGM:1992 (ISO)
1999 – ISO/IEC 8632:1999, 2nd Edition (ISO/IEC JTC1/SC24)
December 17, 2001 – WebCGM (W3C)
January 30, 2007 – WebCGM 2.0 (W3C)
March 1, 2010 – WebCGM 2.1 (W3C Recommendation)
== Further reading ==
Arnold, D.B. and P.R. Bono, CGM and CGI: Metafile and Interface Standards for Computer Graphics, Springer-Verlag, New York, NY, 1988.
Henderson, L.R., and Gebhardt, CGM: SGML for Graphics, The Gilbane Report, Fall 1994.
Henderson, L.R., and A.M. Mumford, The CGM Handbook, Academic Press, San Diego, CA, 1993.
Bono, P.R., J.L. Encarnacao, L.M. Encarnacao, and W.R. Herzner, PC Graphics With GKS, Prentice-Hall, Englewood Cliffs, NJ, 1990.
Vaughan Tay (2001) Making It Work, 5th ed
== See also ==
Comparison of graphics file formats
== References ==
== External links ==
=== General ===
Overview of CGM Standards
CGM File Format Summary
WebCGM Resource Page
Technology Reports: WebCGM
Use of CGM as a Scalable Graphics Format
CGM Open - Reference documents & related materials for CGM and WebCGM
=== Standards ===
WebCGM 1.0, W3C Recommendation, 17 December 2001
WebCGM 2.0, W3C Recommendation, 30 January 2007
WebCGM 2.1, W3C Recommendation, 1 March 2010
ISO/IEC 8632-1:1999 Part 1: Functional specification
ISO/IEC 8632-1:1999 Part 1: Technical Corrigendum 1
ISO/IEC 8632-1:1999 Part 1: Technical Corrigendum 2
ISO/IEC 8632-3:1999 Part 3: Binary encoding
ISO/IEC 8632-4:1999 Part 4: Clear text encoding
=== Other ===
WebCGM and SVG: A Comparison
CGM Examples | Wikipedia/Computer_Graphics_Metafile |
Object-oriented role analysis and modeling (OOram) is a method, based on the concept of role, for performing object-oriented modeling.
Originally (1989) coined Object Oriented Role Analysis, Synthesis and Structuring (OORASS), the method focuses on describing patterns of interaction without connecting the interaction to particular objects/instances. OOram was originally developed by Trygve Reenskaug (1996), a professor at the University of Oslo and the founder of the Norwegian IT company Taskon. The use of "roles" in OOram is similar in application to that of agent-oriented programming.
Enterprise models created according to OOram may have a number of views, with each view presenting certain aspects of a model. The following ten views are proposed:
Area of concern view: Textual description of a phenomenon represented in the role model.
Stimulus-response view: Describes how environment roles may trigger activities in the organization (stimulus), together with the effect (response).
Role list view: List describing all roles of a role model together with attributes and textual explanation.
Semantic view: Describes meaning of roles and relationships between roles.
Collaboration view: Describes patterns of roles and message paths.
Interface view: Describes all messages that can be sent along a message path.
Scenario view: Provides a sample sequence of messages flowing between roles (a concrete example).
Process view: Describes data flow between roles and associated activities performed by the roles.
State diagram view: For each role, the legal states can be described together with messages that trigger transitions.
Method specification view: Describes what messages to send for each method belonging to a role. May also specify procedures to perform.
OOram suggests a varied mix of formal and informal notations and languages for representing and communicating models. Which view to use depends upon the needs in a particular situation.
== See also ==
Object modeling language
View model
Unified modeling language
i*
== References ==
== Further reading ==
Reenskaug, Trygve; P. Wold; O. A. Lehne (1996). Working with Objects: The OOram Software Engineering Method. Manning/Prentice Hall.
Rebecca J. Wirfs-Brock and Ralph E. Johnson (1990). Surveying Current Research in Object-Oriented Design. Communications of the ACM, vol. 33, no. 9 (September 1990), pp. 105–124. OORASS on pp. 113–116. | Wikipedia/Object-oriented_role_analysis_and_modeling |
Knowledge Discovery Metamodel (KDM) is a publicly available specification from the Object Management Group (OMG). KDM is a common intermediate representation for existing software systems and their operating environments, that defines common metadata required for deep semantic integration of Application Lifecycle Management tools. KDM was designed as the OMG's foundation for software modernization, IT portfolio management and software assurance. KDM uses OMG's Meta-Object Facility to define an XMI interchange format between tools that work with existing software as well as an abstract interface (API) for the next-generation assurance and modernization tools. KDM standardizes existing approaches to knowledge discovery in software engineering artifacts, also known as software mining.
== History ==
In November 2003, the OMG's Architecture-Driven Modernization Task Force recommended, and the Platform Technical Committee issued, the Knowledge Discovery Metamodel (KDM) RFP. The objective of this RFP was to provide a common repository structure to represent information about existing software assets and their operating environment. The goal of KDM was defined as exchanging information related to transformation of existing software assets. The RFP stated that KDM shall provide the ability to document existing systems, discover reusable components in existing software, support transformations to other languages and to MDA, or enable other potential transformations. The Knowledge Discovery Metamodel will also enable information about existing software artifacts to be exchanged among different tools. This will enable vendors that specialize on certain languages, platforms or types of transformations to deliver customer solutions in conjunction with other vendors.
The original KDM RFP is available to OMG members for download.
Throughout 2004 and 2005 12 companies collaborated to prepare a joint response to the KDM RFP. More than 30 organizations from 5 countries have contributed to the development and review of the KDM specification.
In May 2006, the Team's submission—the Knowledge Discovery Metamodel (KDM) -- moved into the finalization stage of the OMG's standards adoption process. The OMG adopted Specification for KDM became publicly available (OMG document ptc/06-06-07).
In March 2007 the KDM Finalization Task Force finished the finalization stage of the OMG's standards adoption process. The formal KDM specification KDM 1.0 is available from OMG.
The latest version of the spec was finalized in July 2011, making KDM 1.3 the most recent version.
KDM Analytics maintains open portal for KDM news, reference and education materials and tools
== Overview ==
The goal of KDM is to ensure interoperability between tools for maintenance, evolution, assessment and modernization. KDM is defined as a metamodel that can be also viewed as an ontology for describing the key aspects of knowledge related to the various facets of enterprise software. KDM support means investment into the KDM ecosystem – a growing open-standard based cohesive community of tool vendors, service providers, and commercial components.
KDM represents entire enterprise software systems, not just code. KDM is a wide-spectrum entity-relationship representation for describing existing software. KDM represents structural and behavior elements of existing software systems. The key concept of KDM is a container: an entity that owns other entities. This allows KDM to represent existing systems at various degrees of granularity.
KDM defines precise semantic foundation for representing behavior, the so-called micro-KDM. It provides a high-fidelity intermediate representation which can be used, for example, for performing static analysis of existing software systems. micro-KDM is similar in purpose to a virtual machine for KDM, although KDM is not an executable model, or a constraint model, but a representation of existing artifacts for analysis purposes.
KDM facilitates incremental analysis of existing software systems, where the initial KDM representation is analyzed and more pieces of knowledge are extracted and made explicit as KDM to KDM transformation performed entirely within the KDM technology space. The steps of the knowledge extraction process can be performed by tools, and may involve the analyst.
KDM is the uniform language- and platform- independent representation. Its extensibility mechanism allows addition of domain-, application- and implementation-specific knowledge.
== Architecture ==
KDM packages are arranged into the following four layers:
=== Infrastructure Layer ===
The KDM Infrastructure Layer consists of the Core, kdm, and Source packages which provide a small common core for all other packages, the inventory model of the artifacts of the existing system and full traceability between the meta-model elements as links back to the source code of the artifacts, as well as the uniform extensibility mechanism. The Core package determines several of the patterns that are reused by other KDM packages. Although KDM is a meta-model that uses Meta-Object Facility, there is an alignment between the KDM Core and Resource Description Framework (RDF).
=== Program Elements Layer ===
The Program Elements Layer consists of the Code and Action packages.
The Code package represents programming elements as determined by programming languages, for example data types, procedures, classes, methods, variables, etc. This package is similar in purpose to the Common Application Meta-model (CAM) from another OMG specification, called Enterprise Application Integration (EAI). KDM Code package provides greater level of detail and is seamlessly integrated with the architecturally significant views of the software system. Representation of datatypes in KDM is aligned with ISO standard ISO/IEC 11404 (see also General Purpose Datatypes).
The Action package captures the low level behavior elements of applications, including detailed control- and data flow between statements. Code and Action package in combination provide a high-fidelity intermediate representation of each component of the enterprise software system
=== Resource Layer ===
The Resource Layer represents the operational environment of the existing software system. It is related to the area of Enterprise Application Integration (EAI).
Platform package represents the operating environment of the software, related to the operating system, middleware, etc. including the control flows between components as they are determined by the runtime platform
UI package represents the knowledge related to the user interfaces of the existing software system
Event package represents the knowledge related to events and state-transition behavior of the existing software system
Data package represents the artifacts related to persistent data, such as indexed files, relational databases, and other kinds of data storage. These assets are key to enterprise software as they represent the enterprise metadata. The KDM Data package is aligned with another OMG specification, called Common Warehouse Metamodel (CWM)
=== Abstractions Layer ===
The Abstraction Layer represents domain and application abstractions.
Conceptual package represent business domain knowledge and business rules, insofar as this information can be mined from existing applications. These packages are aligned with another OMG specification, called Semantics of Business Vocabulary and Business Rules (SBVR)
Structure package describes the meta-model elements for representing the logical organization of the software system into subsystems, layers and components
Build package represents the engineering view of the software system
== See also ==
Object Management Group
Software Metrics Metamodel is a metric specification that is based on the KDM
== References ==
== External links ==
OMG KDM Specification
Object Management Group (OMG)
Open KDM portal and tools from KDM Analytics
OMG Architecture-Driven Modernization Task Force
DSTC initial submission
SBVR link
Software Hypermodel Blueprint Portal for Open Source Software - TSRI's instantiations of ASTM+KDM+SMM
Open Source Components from MoDisco Eclipse project | Wikipedia/Knowledge_Discovery_Metamodel |
GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC.
== History ==
The GQL project is the culmination of converging initiatives dating back to 2016, particularly a private proposal from Neo4j to other database vendors in July 2016, and a proposal from Oracle technical staff within the ISO/IEC JTC 1 standards process later that year.
=== 2019 GQL project proposal ===
In September 2019 a proposal for a project to create a new standard graph query language (ISO/IEC 39075 Information Technology — Database Languages — GQL) was approved by a vote of national standards bodies which are members of ISO/IEC Joint Technical Committee 1(ISO/IEC JTC 1). JTC 1 is responsible for international Information Technology standards. GQL is intended to be a declarative database query language, like SQL.
The 2019 GQL project proposal states:
"Using graph as a fundamental representation for data modeling is an emerging approach in data management. In this approach, the data set is modeled as a graph, representing each data entity as a vertex (also called a node) of the graph and each relationship between two entities as an edge between corresponding vertices. The graph data model has been drawing attention for its unique advantages.
Firstly, the graph model can be a natural fit for data sets that have hierarchical, complex, or even arbitrary structures. Such structures can be easily encoded into the graph model as edges. This can be more convenient than the relational model, which requires the normalization of the data set into a set of tables with fixed row types.
Secondly, the graph model enables efficient execution of expensive queries or data analytic functions that need to observe multi-hop relationships among data entities, such as reachability queries, shortest or cheapest path queries, or centrality analysis. There are two graph models in current use: the Resource Description Framework (RDF) model and the Property Graph model. The RDF model has been standardized by W3C in a number of specifications. The Property Graph model, on the other hand, has a multitude of implementations in graph databases, graph algorithms, and graph processing facilities. However, a common, standardized query language for property graphs (like SQL for relational database systems) is missing. GQL is proposed to fill this void."
==== Official ISO standard ====
The GQL standard, ISO/IEC 39075:2024 Information technology – Database languages – GQL, was officially published by ISO on
12 April 2024.
=== GQL project organisation ===
The GQL project is led by Stefan Plantikow (who was the first lead engineer of Neo4j's Cypher for Apache Spark project) and Stephen Cannan (Technical Corrigenda editor of SQL). They are also the editors of the initial early working drafts of the GQL specification.
As originally motivated, the GQL project aims to complement the work of creating an implementable normative natural-language specification with supportive community efforts that enable contributions from those who are unable or uninterested in taking part in the formal process of defining a JTC 1 International Standard. In July 2019 the Linked Data Benchmark Council (LDBC) agreed to become the umbrella organization for the efforts of community technical working groups. The Existing Languages and the Property Graph Schema working groups formed in late 2018 and early 2019 respectively. A working group to define formal denotational semantics for GQL was proposed at the third GQL Community Update in October 2019.
=== ISO/IEC JTC 1/SC 32 WG3 ===
Seven national standards bodies (those of the United States, China, Korea, the Netherlands, the United Kingdom, Denmark and Sweden) have nominated national subject-matter experts to work on the project, which is conducted by Working Group 3 (Database Languages) of ISO/IEC JTC 1's Subcommittee 32 (Data Management and Interchange), usually abbreviated as ISO/IEC JTC 1/SC 32 WG3, or just WG3 for short. WG3 (and its direct predecessor committees within JTC 1) has been responsible for the SQL standard since 1987.
=== ISO stages ===
ISO stages by date
2019-09-10 : 10.99 New project approved
2019-09-10 : 20.00 New project registered in TC/SC work programme
2021-11-22 : 30.00 Committee draft (CD) registered
2021-11-23 : 30.20 CD study initiated
2022-02-25 : 30.60 Close of comment period
2022-08-29 : 30.92 CD referred back to Working Group
2022-08-29 : 30.00 Committee draft (CD) registered
2022-08-30 : 30.20 CD study initiated
2022-10-26 : 30.60 Close of comment period
2023-03-22 : 30.99 CD approved for registration as DIS
2023-03-24 : 40.00 DIS registered
2023-05-24 : 40.20 DIS ballot initiated: 12 weeks
2023-08-17 : 40.60 Close of voting
2023-11-28 : 40.99 Full report circulated: DIS approved for registration as FDIS
2023-12-11 : 50.00 Final text received or FDIS registered for formal approval
2024-01-26 : 50.20 Proof sent to secretariat or FDIS ballot initiated: 8 weeks
2024-03-23 : 50.60 Close of voting. Proof returned by secretariat
2024-03-23 : 60.00 International Standard under publication
2024-04-12 : 60.60 International Standard published
== GQL property graph data model ==
GQL is a query language specifically for property graphs. A property graph closely resembles a conceptual data model, as expressed in an entity–relationship model or in a UML class diagram (although it does not include n-ary relationships linking more than two entities). Entities are modelled as nodes, and relationships as edges, in a graph. Property graphs are multigraphs: there can be many edges between the same pair of nodes. GQL graphs can be mixed: they can contain directed edges, where one of the endpoint nodes of an edge is the tail (or source) and the other node is the head (or target or destination), but they can also contain undirected (bidirectional or reflexive) edges.
Nodes and edges, collectively known as elements, have attributes. Those attributes may be data values, or labels (tags). Values of properties cannot be elements of graphs, nor can they be whole graphs: these restrictions intentionally force a clean separation between the topology of a graph, and the attributes carrying data values in the context of a graph topology. The property graph data model therefore deliberately prevents nesting of graphs, or treating nodes in one graph as edges in another. Each property graph may have a set of labels and a set of properties that are associated with the graph as a whole.
Current graph database products and projects often support a limited version of the model described here. For example, Apache Tinkerpop forces each node and each edge to have a single label; Cypher allows nodes to have zero to many labels, but relationships only have a single label (called a reltype). Neo4j's database supports undocumented graph-wide properties, Tinkerpop has graph values which play the same role, and also supports "metaproperties" or properties on properties. Oracle's PGQL supports zero to many labels on nodes and on edges, whereas SQL/PGQ supports one to many labels for each kind of element. The NGSI-LD information model specified by ETSI is an attempt at formally specifying property graphs, with node and relationship (edge) types that may play the role of labels in previously mentioned models and support semantic referencing by inheriting classes defined in shared ontologies.
The GQL project will define a standard data model, which is likely to be the superset of these variants, and at least the first version of GQL is likely to permit vendors to decide on the cardinalities of labels in each implementation, as does SQL/PGQ, and to choose whether to support undirected relationships.
Additional aspects of the ERM or UML models (like generalization or subtyping, or entity or relationship cardinalities) may be captured by GQL schemas or types that describe possible instances of the general data model.
== Implementations ==
The first in-memory graph database that can interpret GQL is available. Aside from the implementation, one can also find a formalization and read the syntax of the specific subset of GQL.
== Extending existing graph query languages ==
The GQL project draws on multiple sources or inputs, notably existing industrial languages and a new section of the SQL standard. In preparatory discussions within WG3 surveys of the history and comparative content of some of these inputs were presented. GQL is a declarative language with its own distinct syntax, playing a similar role to SQL in the building of a database application. Other graph query languages have been defined which offer direct procedural features such as branching and looping (Apache Tinkerpop's Gremlin), and GSQL, making it possible to traverse a graph iteratively to perform a class of graph algorithms, but GQL will not directly incorporate such features. However, GQL is envisaged as a specific case of a more general class of graph languages, which share a graph type system and a calling interface for procedures that process graphs.
=== SQL/PGQ Property Graph Query ===
Prior work by WG3 and SC32 mirror bodies, particularly in INCITS Data Management (formerly INCITS DM32), has helped to define a new planned Part 16 of the SQL Standard, which allows a read-only graph query to be called inside a SQL SELECT statement, matching a graph pattern using syntax which is very close to Cypher, PGQL and G-CORE, and returning a table of data values as the result. SQL/PGQ also contains DDL to allow SQL tables to be mapped to a graph view schema object with nodes and edges associated to sets of labels and set of data properties. The GQL project coordinates closely with the SQL/PGQ "project split" of (extension to) ISO 9075 SQL, and the technical working groups in the U.S. (INCITS DM32) and at the international level (SC32/WG3) have several expert contributors who work on both projects. The GQL project proposal mandates close alignment of SQL/PGQ and GQL, indicating that GQL will in general be a superset of SQL/PGQ.
More details about the pattern matching language can be found in the paper "Graph Pattern Matching in GQL and SQL/PGQ"
=== Cypher ===
Cypher is a language originally designed by Andrés Taylor and colleagues at Neo4j Inc., and first implemented by that company in 2011. Since 2015 it has been made available as an open source language description with grammar tooling, a JVM front-end that parses Cypher queries, and a Technology Compatibility Kit (TCK) of over 2000 test scenarios, using Cucumber for implementation language portability. The TCK reflects the language description and an enhancement for temporal datatypes and functions documented in a Cypher Improvement Proposal.
Cypher allows creation, reading, updating and deleting of graph elements, and is a language that can therefore be used for analytics engines and transactional databases.
==== Querying with visual path patterns ====
Cypher uses compact fixed- and variable-length patterns which combine visual representations of node and relationship (edge) topologies, with label existence and property value predicates. (These patterns are usually referred to as "ASCII art" patterns, and arose originally as a way of commenting programs which used a lower-level graph API.) By matching such a pattern against graph data elements, a query can extract references to nodes, relationships and paths of interest. Those references are emitted as a "binding table" where column names are bound to a multiset of graph elements. The name of a column becomes the name of a "binding variable", whose value is a specific graph element reference for each row of the table.
For example, a pattern MATCH (p:Person)-[:LIVES_IN]->(c:City) will generate a two-column output table. The first column named p will contain references to nodes with a label Person . The second column named c will contain references to nodes with a label City , denoting the city where the person lives.
The binding variables p and c can then be dereferenced to obtain access to property values associated with the elements referred to by a variable. The example query might be terminated with a RETURN, resulting in a complete query like this:
This would result in a final four-column table listing the names of the residents of the cities stored in the graph.
Pattern-based queries are able to express joins, by combining multiple patterns which use the same binding variable to express a natural join using the MATCH clause:
This query would return the residential location only of EU nationals.
An outer join can be expressed by MATCH ... OPTIONAL MATCH :
This query would return the city of residence of each person in the graph with residential information, and, if an EU national, which country they come from.
Queries are therefore able to first project a sub-graph of the graph input into the query, and then extract the data values associated with that subgraph. Data values can also be processed by functions, including aggregation functions, leading to the projection of computed values which render the information held in the projected graph in various ways. Following the lead of G-CORE and Morpheus, GQL aims to project the sub-graphs defined by matching patterns (and graphs then computed over those sub-graphs) as new graphs to be returned by a query.
Patterns of this kind have become pervasive in property graph query languages, and are the basis for the advanced pattern sub-language being defined in SQL/PGQ, which is likely to become a subset of the GQL language. Cypher also uses patterns for insertion and modification clauses ( CREATE and MERGE ), and proposals have been made in the GQL project for collecting node and edge patterns to describe graph types.
==== Cypher 9 and Cypher 10 ====
The current version of Cypher (including the temporal extension) is referred to as Cypher 9. Prior to the GQL project it was planned to create a new version, Cypher 10 [REF HEADING BELOW], that would incorporate features like schema and composable graph queries and views. The first designs for Cypher 10, including graph construction and projection, were implemented in the Cypher for Apache Spark project starting in 2016.
=== PGQL ===
PGQL
is a language designed and implemented by Oracle Inc., but made available as an open source specification, along with JVM parsing software. PGQL combines familiar SQL SELECT syntax including SQL expressions and result ordering and aggregation with a pattern matching language very similar to that of Cypher. It allows the specification of the graph to be queried, and includes a facility for macros to capture "pattern views", or named sub-patterns. It does not support insertion or updating operations, having been designed primarily for an analytics environment, such as Oracle's PGX product. PGQL has also been implemented in Oracle Big Data Spatial and Graph, and in a research project, PGX.D/Async.
=== G-CORE ===
G-CORE is a research language designed by a group of academic and industrial researchers and language designers which draws on features of Cypher, PGQL and SPARQL. The project was conducted under the auspices of the Linked Data Benchmark Council (LDBC), starting with the formation of a Graph Query Language task force in late 2015, with the bulk of the work of paper writing occurring in 2017. G-CORE is a composable language which is closed over graphs: graph inputs are processed to create a graph output, using graph projections and graph set operations to construct the new graph. G-CORE queries are pure functions over graphs, having no side effects, which mean that the language does not define operations which mutate (update or delete) stored data. G-CORE introduces views (named queries). It also incorporates paths as elements in a graph ("paths as first class citizens"), which can be queried independently of projected paths (which are computed at query time over node and edge elements). G-CORE has been partially implemented in open-source research projects in the LDBC GitHub organization.
=== GSQL ===
GSQL is a language designed for TigerGraph Inc.'s proprietary graph database. Since October 2018 TigerGraph language designers have been promoting and working on the GQL project. GSQL is a Turing-complete language that incorporates procedural flow control and iteration, and a facility for gathering and modifying computed values associated with a program execution for the whole graph or for elements of a graph called accumulators. These features are designed to enable iterative graph computations to be combined with data exploration and retrieval. GSQL graphs must be described by a schema of vertexes and edges, which constrains all insertions and updates. This schema therefore has the closed world property of an SQL schema, and this aspect of GSQL (also reflected in design proposals deriving from the Morpheus project) is proposed as an important optional feature of GSQL.
Vertexes and edges are named schema objects which contain data but also define an imputed type, much as SQL tables are data containers, with an associated implicit row type. GSQL graphs are then composed from these vertex and edge sets, and multiple named graphs can include the same vertex or edge set. GSQL has developed new features since its release in September 2017, most notably introducing variable-length edge pattern matching using a syntax related to that seen in Cypher, PGQL and SQL/PGQ, but also close in style to the fixed-length patterns offered by Microsoft SQL/Server Graph
GSQL also supports the concept of Multigraphs
which allow subsets of a graph to have role-based access control. Multigraphs are important for enterprise-scale graphs that need fine-grain access control for different users.
=== Morpheus: multiple graphs and composable graph queries in Apache Spark ===
The opencypher Morpheus project implements Cypher for Apache Spark users. Commencing in 2016, this project originally ran alongside three related efforts, in which Morpheus designers also took part: SQL/PGQ, G-CORE and design of Cypher extensions for querying and constructing multiple graphs. The Morpheus project acted as a testbed for extensions to Cypher (known as "Cypher 10") in the two areas of graph DDL and query language extensions.
Graph DDL features include
definition of property graph views over JDBC-connected SQL tables and Spark DataFrames
definition of graph schemas or types defined by assembling node type and edge type patterns, with subtyping
constraining the content of a graph by a closed or fixed schema
creating catalog entries for multiple named graphs in a hierarchically organized catalog
graph data sources to form a federated, heterogeneous catalog
creating catalog entries for named queries (views)
Graph query language extensions include
graph union
projection of graphs computed from the results of pattern matches on multiple input graphs
support for tables (Spark DataFrames) as inputs to queries ("driving tables")
views which accept named or projected graphs as parameters.
These features have been proposed as inputs to the standardization of property graph query languages in the GQL project.
== See also ==
Graph Modeling Language (GML)
GraphQL
Cypher (query language)
Graph database
Graph (abstract data type)
Graph traversal
Regular path query
== References ==
== External links ==
GQL Standard (Official website) | Wikipedia/Graph_Query_Language |
The C4 model is a lean graphical notation technique for modeling the architecture of software systems. It is based on a structural decomposition (a hierarchical tree structure) of a system into containers and components and relies on existing modelling techniques such as Unified Modeling Language (UML) or entity–relationship diagrams (ERDs) for the more detailed decomposition of the architectural building blocks.
== History ==
The C4 model was created by the software architect Simon Brown between 2006 and 2011 on the roots of Unified Modelling Language (UML) and the 4+1 architectural view model. The launch of an official website under a Creative Commons license and an article published in 2018 popularised the emerging technique.
== Overview ==
The C4 model documents the architecture of a software system, by showing multiple points of view that explain the decomposition of a system into containers and components, the relationship between these elements, and, where appropriate, the relation with its users.
The viewpoints are organized according to their hierarchical level:
Context diagrams (level 1): show the system in scope and its relationship with users and other systems;
Container diagrams (level 2): decompose a system into interrelated containers. A container represents an application or a data store;
Component diagrams (level 3): decompose containers into interrelated components, and relate the components to other containers or other systems;
Code diagrams (level 4): provide additional details about the design of the architectural elements that can be mapped to code. The C4 model relies at this level on existing notations such as Unified Modelling Language (UML), Entity Relation Diagrams (ERD) or diagrams generated by Integrated Development Environments (IDE).
For level 1 to 3, the C4 model uses 5 basic diagramming elements: persons, software systems, containers, components and relationships. The technique is not prescriptive for the layout, shape, colour and style of these elements. Instead, the C4 model recommends using simple diagrams based on nested boxes in order to facilitate interactive collaborative drawing. The technique also promotes good modelling practices such as providing a title and legend on every diagram, and clear unambiguous labelling in order to facilitate the understanding by the intended audience.
The C4 model facilitates collaborative visual architecting and evolutionary architecture in the context of agile teams where more formal documentation methods and up-front architectural design are not desired.
== See also ==
Software architecture
== References ==
== External links ==
Official site | Wikipedia/C4_model |
In software engineering, a software development process or software development life cycle (SDLC) is a process of planning and managing software development. It typically involves dividing software development work into smaller, parallel, or sequential steps or sub-processes to improve design and/or product management. The methodology may include the pre-definition of specific deliverables and artifacts that are created and completed by a project team to develop or maintain an application.
Most modern development processes can be vaguely described as agile. Other methodologies include waterfall, prototyping, iterative and incremental development, spiral development, rapid application development, and extreme programming.
A life-cycle "model" is sometimes considered a more general term for a category of methodologies and a software development "process" is a particular instance as adopted by a specific organization. For example, many specific software development processes fit the spiral life-cycle model. The field is often considered a subset of the systems development life cycle.
== History ==
The software development methodology framework did not emerge until the 1960s. According to Elliott (2004), the systems development life cycle can be considered to be the oldest formalized methodology framework for building information systems. The main idea of the software development life cycle has been "to pursue the development of information systems in a very deliberate, structured and methodical way, requiring each stage of the life cycle––from the inception of the idea to delivery of the final system––to be carried out rigidly and sequentially" within the context of the framework being applied. The main target of this methodology framework in the 1960s was "to develop large scale functional business systems in an age of large scale business conglomerates. Information systems activities revolved around heavy data processing and number crunching routines."
Requirements gathering and analysis:
The first phase of the custom software development process involves understanding the client's requirements and objectives. This stage typically involves engaging in thorough discussions and conducting interviews with stakeholders to identify the desired features, functionalities, and overall scope of the software. The development team works closely with the client to analyze existing systems and workflows, determine technical feasibility, and define project milestones.
Planning and design:
Once the requirements are understood, the custom software development team proceeds to create a comprehensive project plan. This plan outlines the development roadmap, including timelines, resource allocation, and deliverables. The software architecture and design are also established during this phase. User interface (UI) and user experience (UX) design elements are considered to ensure the software's usability, intuitiveness, and visual appeal.
Development:
With the planning and design in place, the development team begins the coding process. This phase involves writing, testing, and debugging the software code. Agile methodologies, such as scrum or kanban, are often employed to promote flexibility, collaboration, and iterative development. Regular communication between the development team and the client ensures transparency and enables quick feedback and adjustments.
Testing and quality assurance:
To ensure the software's reliability, performance, and security, rigorous testing and quality assurance (QA) processes are carried out. Different testing techniques, including unit testing, integration testing, system testing, and user acceptance testing, are employed to identify and rectify any issues or bugs. QA activities aim to validate the software against the predefined requirements, ensuring that it functions as intended.
Deployment and implementation:
Once the software passes the testing phase, it is ready for deployment and implementation. The development team assists the client in setting up the software environment, migrating data if necessary, and configuring the system. User training and documentation are also provided to ensure a smooth transition and enable users to maximize the software's potential.
Maintenance and support:
After the software is deployed, ongoing maintenance and support become crucial to address any issues, enhance performance, and incorporate future enhancements. Regular updates, bug fixes, and security patches are released to keep the software up-to-date and secure. This phase also involves providing technical support to end users and addressing their queries or concerns.
Methodologies, processes, and frameworks range from specific prescriptive steps that can be used directly by an organization in day-to-day work, to flexible frameworks that an organization uses to generate a custom set of steps tailored to the needs of a specific project or group. In some cases, a "sponsor" or "maintenance" organization distributes an official set of documents that describe the process. Specific examples include:
1970s
Structured programming since 1969
Cap Gemini SDM, originally from PANDATA, the first English translation was published in 1974. SDM stands for System Development Methodology
1980s
Structured systems analysis and design method (SSADM) from 1980 onwards
Information Requirement Analysis/Soft systems methodology
1990s
Object-oriented programming (OOP) developed in the early 1960s and became a dominant programming approach during the mid-1990s
Rapid application development (RAD), since 1991
Dynamic systems development method (DSDM), since 1994
Scrum, since 1995
Team software process, since 1998
Rational Unified Process (RUP), maintained by IBM since 1998
Extreme programming, since 1999
2000s
Agile Unified Process (AUP) maintained since 2005 by Scott Ambler
Disciplined agile delivery (DAD) Supersedes AUP
2010s
Scaled Agile Framework (SAFe)
Large-Scale Scrum (LeSS)
DevOps
Since DSDM in 1994, all of the methodologies on the above list except RUP have been agile methodologies - yet many organizations, especially governments, still use pre-agile processes (often waterfall or similar). Software process and software quality are closely interrelated; some unexpected facets and effects have been observed in practice.
Among these, another software development process has been established in open source. The adoption of these best practices known and established processes within the confines of a company is called inner source.
== Prototyping ==
Software prototyping is about creating prototypes, i.e. incomplete versions of the software program being developed.
The basic principles are:
Prototyping is not a standalone, complete development methodology, but rather an approach to try out particular features in the context of a full methodology (such as incremental, spiral, or rapid application development (RAD)).
Attempts to reduce inherent project risk by breaking a project into smaller segments and providing more ease of change during the development process.
The client is involved throughout the development process, which increases the likelihood of client acceptance of the final implementation.
While some prototypes are developed with the expectation that they will be discarded, it is possible in some cases to evolve from prototype to working system.
A basic understanding of the fundamental business problem is necessary to avoid solving the wrong problems, but this is true for all software methodologies.
== Methodologies ==
=== Agile development ===
"Agile software development" refers to a group of software development frameworks based on iterative development, where requirements and solutions evolve via collaboration between self-organizing cross-functional teams. The term was coined in the year 2001 when the Agile Manifesto was formulated.
Agile software development uses iterative development as a basis but advocates a lighter and more people-centric viewpoint than traditional approaches. Agile processes fundamentally incorporate iteration and the continuous feedback that it provides to successively refine and deliver a software system.
The Agile model also includes the following software development processes:
Dynamic systems development method (DSDM)
Kanban
Scrum
Lean software development
=== Continuous integration ===
Continuous integration is the practice of merging all developer working copies to a shared mainline several times a day.
Grady Booch first named and proposed CI in his 1991 method, although he did not advocate integrating several times a day. Extreme programming (XP) adopted the concept of CI and did advocate integrating more than once per day – perhaps as many as tens of times per day.
=== Incremental development ===
Various methods are acceptable for combining linear and iterative systems development methodologies, with the primary objective of each being to reduce inherent project risk by breaking a project into smaller segments and providing more ease-of-change during the development process.
There are three main variants of incremental development:
A series of mini-waterfalls are performed, where all phases of the waterfall are completed for a small part of a system, before proceeding to the next increment, or
Overall requirements are defined before proceeding to evolutionary, mini-waterfall development of individual increments of a system, or
The initial software concept, requirements analysis, and design of architecture and system core are defined via waterfall, followed by incremental implementation, which culminates in installing the final version, a working system.
=== Rapid application development ===
Rapid application development (RAD) is a software development methodology, which favors iterative development and the rapid construction of prototypes instead of large amounts of up-front planning. The "planning" of software developed using RAD is interleaved with writing the software itself. The lack of extensive pre-planning generally allows software to be written much faster and makes it easier to change requirements.
The rapid development process starts with the development of preliminary data models and business process models using structured techniques. In the next stage, requirements are verified using prototyping, eventually to refine the data and process models. These stages are repeated iteratively; further development results in "a combined business requirements and technical design statement to be used for constructing new systems".
The term was first used to describe a software development process introduced by James Martin in 1991. According to Whitten (2003), it is a merger of various structured techniques, especially data-driven information technology engineering, with prototyping techniques to accelerate software systems development.
The basic principles of rapid application development are:
Key objective is for fast development and delivery of a high-quality system at a relatively low investment cost.
Attempts to reduce inherent project risk by breaking a project into smaller segments and providing more ease of change during the development process.
Aims to produce high-quality systems quickly, primarily via iterative Prototyping (at any stage of development), active user involvement, and computerized development tools. These tools may include graphical user interface (GUI) builders, Computer Aided Software Engineering (CASE) tools, Database Management Systems (DBMS), fourth-generation programming languages, code generators, and object-oriented techniques.
Key emphasis is on fulfilling the business need, while technological or engineering excellence is of lesser importance.
Project control involves prioritizing development and defining delivery deadlines or “timeboxes”. If the project starts to slip, the emphasis is on reducing requirements to fit the timebox, not on increasing the deadline.
Generally includes joint application design (JAD), where users are intensely involved in system design, via consensus building in either structured workshops, or electronically facilitated interaction.
Active user involvement is imperative.
Iteratively produces production software, as opposed to a throwaway prototype.
Produces documentation necessary to facilitate future development and maintenance.
Standard systems analysis and design methods can be fitted into this framework.
=== Waterfall development ===
The waterfall model is a sequential development approach, in which development is seen as flowing steadily downwards (like a waterfall) through several phases, typically:
Requirements analysis resulting in a software requirements specification
Software design
Implementation
Testing
Integration, if there are multiple subsystems
Deployment (or Installation)
Maintenance
The first formal description of the method is often cited as an article published by Winston W. Royce in 1970, although Royce did not use the term "waterfall" in this article. Royce presented this model as an example of a flawed, non-working model.
The basic principles are:
The Project is divided into sequential phases, with some overlap and splashback acceptable between phases.
Emphasis is on planning, time schedules, target dates, budgets, and implementation of an entire system at one time.
Tight control is maintained over the life of the project via extensive written documentation, formal reviews, and approval/signoff by the user and information technology management occurring at the end of most phases before beginning the next phase. Written documentation is an explicit deliverable of each phase.
The waterfall model is a traditional engineering approach applied to software engineering. A strict waterfall approach discourages revisiting and revising any prior phase once it is complete. This "inflexibility" in a pure waterfall model has been a source of criticism by supporters of other more "flexible" models. It has been widely blamed for several large-scale government projects running over budget, over time and sometimes failing to deliver on requirements due to the big design up front approach. Except when contractually required, the waterfall model has been largely superseded by more flexible and versatile methodologies developed specifically for software development. See Criticism of waterfall model.
=== Spiral development ===
In 1988, Barry Boehm published a formal software system development "spiral model," which combines some key aspects of the waterfall model and rapid prototyping methodologies, in an effort to combine advantages of top-down and bottom-up concepts. It provided emphasis on a key area many felt had been neglected by other methodologies: deliberate iterative risk analysis, particularly suited to large-scale complex systems.
The basic principles are:
Focus is on risk assessment and on minimizing project risk by breaking a project into smaller segments and providing more ease-of-change during the development process, as well as providing the opportunity to evaluate risks and weigh consideration of project continuation throughout the life cycle.
"Each cycle involves a progression through the same sequence of steps, for each part of the product and for each of its levels of elaboration, from an overall concept-of-operation document down to the coding of each individual program."
Each trip around the spiral traverses four basic quadrants: (1) determine objectives, alternatives, and constraints of the iteration, and (2) evaluate alternatives; Identify and resolve risks; (3) develop and verify deliverables from the iteration; and (4) plan the next iteration.
Begin each cycle with an identification of stakeholders and their "win conditions", and end each cycle with review and commitment.
=== Shape Up ===
Shape Up is a software development approach introduced by Basecamp in 2018. It is a set of principles and techniques that Basecamp developed internally to overcome the problem of projects dragging on with no clear end. Its primary target audience is remote teams. Shape Up has no estimation and velocity tracking, backlogs, or sprints, unlike waterfall, agile, or scrum. Instead, those concepts are replaced with appetite, betting, and cycles. As of 2022, besides Basecamp, notable organizations that have adopted Shape Up include UserVoice and Block.
=== Advanced methodologies ===
Other high-level software project methodologies include:
Behavior-driven development and business process management.
Chaos model - The main rule always resolves the most important issue first.
Incremental funding methodology - an iterative approach
Lightweight methodology - a general term for methods that only have a few rules and practices
Structured systems analysis and design method - a specific version of waterfall
Slow programming, as part of the larger Slow Movement, emphasizes careful and gradual work without (or minimal) time pressures. Slow programming aims to avoid bugs and overly quick release schedules.
V-Model (software development) - an extension of the waterfall model
Unified Process (UP) is an iterative software development methodology framework, based on Unified Modeling Language (UML). UP organizes the development of software into four phases, each consisting of one or more executable iterations of the software at that stage of development: inception, elaboration, construction, and guidelines.
== Process meta-models ==
Some "process models" are abstract descriptions for evaluating, comparing, and improving the specific process adopted by an organization.
ISO/IEC 12207 is the international standard describing the method to select, implement, and monitor the life cycle for software.
The Capability Maturity Model Integration (CMMI) is one of the leading models and is based on best practices. Independent assessments grade organizations on how well they follow their defined processes, not on the quality of those processes or the software produced. CMMI has replaced CMM.
ISO 9000 describes standards for a formally organized process to manufacture a product and the methods of managing and monitoring progress. Although the standard was originally created for the manufacturing sector, ISO 9000 standards have been applied to software development as well. Like CMMI, certification with ISO 9000 does not guarantee the quality of the end result, only that formalized business processes have been followed.
ISO/IEC 15504 Information technology—Process assessment is also known as Software Process Improvement Capability Determination (SPICE), is a "framework for the assessment of software processes". This standard is aimed at setting out a clear model for process comparison. SPICE is used much like CMMI. It models processes to manage, control, guide, and monitor software development. This model is then used to measure what a development organization or project team actually does during software development. This information is analyzed to identify weaknesses and drive improvement. It also identifies strengths that can be continued or integrated into common practice for that organization or team.
ISO/IEC 24744 Software Engineering—Metamodel for Development Methodologies, is a power type-based metamodel for software development methodologies.
Soft systems methodology - a general method for improving management processes.
Method engineering - a general method for improving information system processes.
== See also ==
Systems development life cycle
Computer-aided software engineering (some of these tools support specific methodologies)
List of software development philosophies
Outline of software engineering
Software Project Management
Software development
Software development effort estimation
Software documentation
Software release life cycle
Top-down and bottom-up design#Computer science
== References ==
== External links ==
Selecting a development approach Archived January 2, 2019, at the Wayback Machine at cms.hhs.gov.
Gerhard Fischer, "The Software Technology of the 21st Century: From Software Reuse to Collaborative Software Design" Archived September 15, 2009, at the Wayback Machine, 2001 | Wikipedia/Software_development_methodologies |
The input–process–output (IPO) model, or input-process-output pattern, is a widely used approach in systems analysis and software engineering for describing the structure of an information processing program or other process. Many introductory programming and systems analysis texts introduce this as the most basic structure for describing a process.
== Overview ==
A computer program is useful for another sort of process using the input-process-output model receives inputs from a user or other source, does some computations on the inputs, and returns the results of the computations. In essence the system separates itself from the environment, thus defining both inputs and outputs as one united mechanism.
The system would divide the work into three categories:
A requirement from the environment (input)
A computation based on the requirement (process)
A provision for the environment (output)
In other words, such inputs may be materials, human resources, money or information, transformed into outputs, such as consumables, services, new information or money.
As a consequence, an input-process-output system becomes very vulnerable to misinterpretation. This is because, theoretically, it contains all the data, in regards to the environment outside the system. Yet, in practice, the environment contains a significant variety of objects that a system is unable to comprehend, as it exists outside the system's control. As a result, it is very important to understand where the boundary lies between the system and the environment, which is beyond the system's understanding. Various analysts often set their own boundaries, favoring their point of view, thus creating much confusion.
== Systems at work ==
The views differ, in regards to systems thinking. One of such definitions would outline the Input-process-output system, as a structure, would be:
"Systems thinking is the art and science of making reliable inferences about behaviour by developing an increasingly deep understanding of the understanding of the underlying structure"
Alternatively, it was also suggested that systems are not 'holistic' in the sense of bonding with remote objects (for example: trying to connect a crab, ozone layer and capital life cycle together).
== Types of systems ==
There are five major categories that are the most cited in information systems literature:
=== Natural systems ===
A system which has not been created as a result of human interference. Examples of such would be the Solar System as well as the human body, evolving into its current form
=== Designed physical systems ===
A system which has been created as a result of human interference, and is physically identifiable. Examples of such would be various computing machines, created by human mind for some specific purpose.
=== Designed abstract systems ===
A system which has been created as a result of human interference, and is not physically identifiable. Examples of such would be mathematical and philosophical systems, which have been created by human minds, for some specific purpose.
There are also some social systems, which allow humans to collectively achieve a specific
=== Social systems ===
A system created by humans, and derived from intangible purposes. For example: a family, that is a hierarchy of human relationships, which in essence create the boundary between natural and human systems.
=== Human activity systems ===
An organisation with hierarchy, created by humans for a specific purpose. For example: a company, which organises humans together to collaborate and achieve a specific purpose. The result of this system is physically identifiable. There are, however, some significant links between with previous types. It is clear that the idea of human activity system (HAS), would consist of a variety of smaller social system, with its unique development and organisation. Moreover, arguably HASes can include designed systems - computers and machinery. Majority of previous systems would overlap.
== System characteristics ==
There are several key characteristics, when it comes to the fundamental behaviour of any system.
Systems can be classified as open or closed:'
Those that interact with their environment, in form of money, data, energy or exchange materials, are generally understood as open. Openness of the system can vary significantly. This is because, a system would be classified as open, if it receives even a single input from the environment, yet a system that merely interacts with the environment, would be classified as open as well. The more open the system is, the more complex it normally would be, due to lower predictability of its components.
Those that have no interactions with the environment at all are closed. In practice, however, a completely closed system is merely liveable, due to loss of practical usage of the output. As a result, most of the systems would be open or open to a certain extent.
Systems can be classified as deterministic or stochastic:
Well-defined and clearly structured system in terms of behavioural patterns becomes predictable, thus becoming deterministic. In other words, it would only use empirical data. For example: mathematics or physics are set around specific laws, which make the results of calculation predictable. Deterministic systems would have simplistic interactions between inner components.
More complex, and often more open systems, would have relatively lower extent of predictability, due to absence of clearly structured behavioural patterns. Analysing such system, is therefore much harder. Such systems would be stochastic, or probabilistic, this is because of the stochastic nature of human beings whilst performing various activities. Having said that, designed systems would still be considered as deterministic, due to a rigid structure of rules incorporated into the design.
Systems can be classified as static or dynamic
Most systems would be known as dynamic, because of the constant evolution in computing power, yet some systems could find it hard to balance between being created and ceasing to exist. An example of such could be a printed map, which is not evolving, in contrast to a dynamic map, provided from constantly updating developers.
Systems can be classified as self-regulating or non-self-regulating
The greater the extent of self-control of systems activity is, the greater is the liveability of the final system is. It is vital for any system to be able to control its activities in order to remain stable.
== Real life applications ==
=== Corporate business ===
A manufacturing processes that take raw materials as inputs, applies a manufacturing process, and produces manufactured goods as output. The usage of such systems could help to create stronger human organisations, in terms of company operations in each and every department of the firm, no matter the size, which . IPOs can also restructure existing static and non-self-regulating systems, which in real world would be used in form of outsourcing the product fulfilment, due to inefficiency of current fulfilment.
=== Programming ===
The majority of existing programs for coding, such as Java, Python, C++, would be based upon a deterministic IPO model, with clear inputs coming from the coder, converting into outputs, such as applications.
A batch transaction processing system, which accepts large volumes of homogeneous transactions, processes it (possibly updating a database), and produces output such as reports or computations.
An interactive computer program, which accepts simple requests from a user and responds to them after some processing and/or database accesses.
=== Scientific ===
A calculator, which uses inputs, provided by the operator, and processes them into outputs to be used by the operator.
A thermostat, which senses the temperature (input), decides on an action (heat on/off), and executes the action (output).
== See also ==
Read–eval–print loop
Extract, transform, load
CIPO-model
== References == | Wikipedia/IPO_model |
A conglomerate () is a type of multi-industry company that consists of several different and unrelated business entities that operate in various industries. A conglomerate usually has a parent company that owns and controls many subsidiaries, which are legally independent but financially and strategically dependent on the parent company. Conglomerates are often large and multinational corporations that have a global presence and a diversified portfolio of products and services. Conglomerates can be formed by merger and acquisitions, spin-offs, or joint ventures.
Conglomerates are common in many countries and sectors, such as media, banking, energy, mining, manufacturing, retail, defense, and transportation. This type of organization aims to achieve economies of scale, market power, risk diversification, and financial synergy. However, they also face challenges such as complexity, bureaucracy, agency problems, and regulation.
The popularity of conglomerates has varied over time and across regions. In the United States, conglomerates became popular in the 1960s as a form of economic bubble driven by low interest rates and leveraged buyouts. However, many of them collapsed or were broken up in the 1980s due to poor performance, accounting scandals, and antitrust regulation. In contrast, conglomerates have remained prevalent in Asia, especially in China, Japan, South Korea, and India. In mainland China, many state-affiliated enterprises have gone through high value mergers and acquisitions, resulting in some of the highest value business transactions of all time. These conglomerates have strong ties with the government and preferential policies and access to capital.
== United States ==
=== The conglomerate fad of the 1960s ===
During the 1960s, the United States was caught up in a "conglomerate fad" which turned out to be a form of an economic bubble.
Due to a combination of low interest rates and a repeating bear-bull market, conglomerates were able to buy smaller companies in leveraged buyouts (sometimes at temporarily deflated values). Famous examples from the 1960s include Gulf and Western Industries, Ling-Temco-Vought, ITT Corporation, Litton Industries, Textron, and Teledyne. The trick was to look for acquisition targets with solid earnings and much lower price–earnings ratios than the acquirer. The conglomerate would make a tender offer to the target's shareholders at a princely premium to the target's current stock price. Upon obtaining shareholder approval, the conglomerate usually settled the transaction in something other than cash, like debentures, bonds, warrants or convertible debentures (issuing the latter two would effectively dilute its shareholders down the road, but many shareholders at the time were not thinking that far ahead). The conglomerate would then add the target's earnings to its earnings, thereby increasing the conglomerate's overall earnings per share. In finance jargon, the transaction was "accretive to earnings."
The relatively lax accounting standards of the time meant that accountants were often able to get away with creative mathematics in calculating the conglomerate's post-acquisition consolidated earnings numbers. In turn, the price of the conglomerate's stock would go up, thereby re-establishing its previous price-earnings ratio, and then it could repeat the whole process with a new target. In plain English, conglomerates were using rapid acquisitions to create the illusion of rapid growth. In 1968, the peak year of the conglomerate fad, U.S. corporations completed a record number of mergers: approximately 4,500. In that year, at least 26 of the country's 500 largest corporations were acquired, of which 12 had assets above $250 million.
All this complex company reorganization had very real consequences for people who worked for companies that were either acquired by conglomerates or were seen as likely to be acquired by them. Acquisitions were a disorienting and demoralizing experience for executives at acquired companies—those who were not immediately laid off found themselves at the mercy of the conglomerate's executives in some other distant city. Most conglomerates' headquarters were located on the West Coast or East Coast, while many of their acquisitions were located in the country's interior. Many interior cities were devastated by repeatedly losing the headquarters of corporations to mergers, in which independent ventures were reduced to subsidiaries of conglomerates based in New York or Los Angeles. Pittsburgh, for example, lost about a dozen. The terror instilled by the mere prospect of such harsh consequences for executives and their home cities meant that fending off takeovers, real or imagined, was a constant distraction for executives at all corporations seen as choice acquisition targets during this era.
The chain reaction of rapid growth through acquisitions could not last forever. When interest rates rose to offset rising inflation, conglomerate profits began to fall. The beginning of the end came in January 1968, when Litton shocked Wall Street by announcing a quarterly profit of only 21 cents per share, versus 63 cents for the previous year's quarter. This was "just a decline in earnings of about 19 percent", not an actual loss or a corporate scandal, and "yet the stock was crushed, plummeting from $90 to $53". It would take two more years before it was clear that the conglomerate fad was on its way out. The stock market eventually figured out that the conglomerates' bloated and inefficient businesses were as cyclical as any others—indeed, it was that cyclical nature that had caused such businesses to be such undervalued acquisition targets in the first place—and their descent put "the lie to the claim that diversification allowed them to ride out a downturn." A major selloff of conglomerate shares ensued. To keep going, many conglomerates were forced to shed the new businesses they had recently purchased, and by the mid-1970s most conglomerates had been reduced to shells. The conglomerate fad was subsequently replaced by newer ideas like focusing on a company's core competency and unlocking shareholder value (which often translate into spin-offs).
=== Genuine diversification ===
In other cases, conglomerates are formed for genuine interests of diversification rather than manipulation of paper return on investment. Companies with this orientation would only make acquisitions or start new branches in other sectors when they believed this would increase profitability or stability by sharing risks. Flush with cash during the 1980s, General Electric also moved into financing and financial services, which in 2005 accounted for about 45% of the company's net earnings. GE formerly owned a minority interest in NBCUniversal, which owns the NBC television network and several other cable networks. United Technologies was also a successful conglomerate until it was dismantled in the late 2010s.
=== Mutual funds ===
With the spread of mutual funds (especially index funds since 1976), investors could more easily obtain diversification by owning a small slice of many companies in a fund rather than owning shares in a conglomerate. Another example of a successful conglomerate is Warren Buffett's Berkshire Hathaway, a holding company which used surplus capital from its insurance subsidiaries to invest in businesses across a variety of industries.
== International ==
The end of the First World War caused a brief economic crisis in Weimar Germany, permitting entrepreneurs to buy businesses at rock-bottom prices. The most successful, Hugo Stinnes, established the most powerful private economic conglomerate in 1920s Europe – Stinnes Enterprises – which embraced sectors as diverse as manufacturing, mining, shipbuilding, hotels, newspapers, and other enterprises.
The best-known British conglomerate was Hanson plc. It followed a rather different timescale than the U.S. examples mentioned above, as it was founded in 1964 and ceased to be a conglomerate when it split itself into four separate listed companies between 1995 and 1997.
In Hong Kong, some of the well-known conglomerates such as:
Swire Group (AD1816) (or Swire Pacific) Started by Liverpool natives the Swire family, which controls a wide range of businesses, including property (Swire Properties), aviation (i.e. Cathay Pacific), beverages (bottler of Coca-Cola), shipping and trading.
Jardine Matheson (AD1824) operates businesses in the fields of property (Hongkong Land), finance (Jardine Lloyd Thompson), trading, retail (Dairy Farm) and hotels (i.e. Mandarin Oriental).
CK Hutchison Holdings Limited: Telecoms, Infrastructure, Ports (i.e. Hongkong International Terminals, River Trade Terminal), Health and Beauty Retail (i.e. AS Watson), Energy, Finance
The Wharf (Holdings): Telecoms (formerly i-Cable Communications), Retail, Transportation (i.e. Modern Terminals), Finance, Hotels (i.e. Marco Polo Hotels)
In Japan, a different model of conglomerate, the keiretsu, evolved. Whereas the Western model of conglomerate consists of a single corporation with multiple subsidiaries controlled by that corporation, the companies in a keiretsu are linked by interlocking shareholdings and a central role of a bank. Mitsui, Mitsubishi, Sumitomo are some of Japan's best-known keiretsu, reaching from automobile manufacturing to the production of electronics such as televisions. While not a keiretsu, Sony is an example of a modern Japanese conglomerate with operations in consumer electronics, video games, the music industry, television and film production and distribution, financial services, and telecommunications.
In China, many of the country's conglomerates are state-owned enterprises, but there is a substantial number of private conglomerates. Notable conglomerates include BYD, CIMC, China Merchants Bank, Huawei, JXD, Meizu, Ping An Insurance, TCL, Tencent, TP-Link, ZTE, Legend Holdings, Dalian Wanda Group, China Poly Group, Beijing Enterprises, and Fosun International. Fosun is currently China's largest civilian-run conglomerate by revenue.
In South Korea, the chaebol is a type of conglomerate owned and operated by a family. A chaebol is also inheritable, as most of the current presidents of chaebols succeeded their fathers or grandfathers. Some of the largest and most well-known Korean chaebols are Samsung, LG, Hyundai Kia and SK.
In India, family-owned enterprises became some of Asia's largest conglomerates, such as the Aditya Birla Group, Tata Group, Emami, Kirloskar Group, Larsen & Toubro, Mahindra Group, Bajaj Group, ITC Limited, Essar Group, Reliance Industries, Adani Group and the Bharti Enterprises.
In Brazil the largest conglomerates are J&F Investimentos, Odebrecht, Itaúsa, Camargo Corrêa, Votorantim Group, Andrade Gutierrez, and Queiroz Galvão.
In Turkey the largest conglomerates are Koç Holding, Sabancı Holding, Yıldız Holding, Çukurova Holding, Doğuş Holding, Doğan Holding.
In New Zealand, Fletcher Challenge was formed in 1981 from the merger of Fletcher Holdings, Challenge Corporation, and Tasman Pulp & Paper, in an attempt to create a New Zealand-based multi-national company. At the time, the newly merged company dealt in construction, building supplies, pulp and paper mills, forestry, and oil & gas. Following a series of bungled investments, the company demerged in the early 2000s to concentrate on building and construction.
In Pakistan, some of the examples are Adamjee Group, Dawood Hercules, House of Habib, Lakson Group and Nishat Group.
In the Philippines, the largest conglomerate of the country is the Ayala Corporation which focuses on malls, bank, real estate development, and telecommunications. The other big conglomerates in the Philippines included JG Summit Holdings, Lopez Holdings Corporation, ABS-CBN Corporation, GMA Network, Inc., MediaQuest Holdings, TV5 Network, Inc.,
SM Investments Corporation, Metro Pacific Investments Corporation, and San Miguel Corporation.
In the United States, some of the examples are The Walt Disney Company, Warner Bros. Discovery and The Trump Organization (see below).
In Canada, one of the examples is Hudson's Bay Company. Another such conglomerate is J.D. Irving, Limited, which controls a large portion of the economic activities as well as media in the Province of New Brunswick.
== Advantages and disadvantages of conglomerates ==
=== Advantages ===
Diversification results in a reduction of investment risk. A downturn suffered by one subsidiary, for instance, can be counterbalanced by stability, or even expansion, in another division. For example, if Berkshire Hathaway's construction materials business has a good year, the profit might be offset by a bad year in its insurance business. This advantage is enhanced by the fact that the business cycle affects industries in different ways.
A conglomerate creates an internal capital market if the external one is not developed enough. Through the internal market, different parts of the conglomerate allocate capital more effectively.
A conglomerate can show earnings growth, by acquiring companies whose shares are more discounted than its own. In fact, Teledyne, GE, and Berkshire Hathaway have delivered high earnings growth for a time.
=== Disadvantages ===
The extra layers of management increase costs.
Accounting disclosure is less useful information, many numbers are disclosed grouped, rather than separately for each business. The complexity of a conglomerate's accounts makes it harder for managers, investors, and regulators to analyze and makes it easier for management to hide issues.
Conglomerates can trade at a discount to the overall individual value of their businesses because investors can achieve diversification on their own simply by purchasing multiple stocks. The whole is often worth less than the sum of its parts.
Culture clashes can destroy value.
Inertia prevents the development of innovation.
Lack of focus, and inability to manage unrelated businesses equally well.
Brand dilution where the brand loses its brand associations with a market segment, product area, or quality, price, or cachet.
Conglomerates more easily run the risk of being too big to fail.
Some cite the decreased cost of conglomerate stock (a phenomenon known as conglomerate discount) as evidential of these disadvantages, while other traders believe this tendency to be a market inefficiency, which undervalues the true strength of these stocks.
== Media conglomerates ==
In her 1999 book No Logo, Naomi Klein provides several examples of mergers and acquisitions between media companies designed to create conglomerates to create synergy between them:
WarnerMedia included several tenuously linked businesses during the 1990s and 2000s, including Internet access, content, film, cable systems, and television. Their diverse portfolio of assets allowed for cross-promotion and economies of scale. However, the company has sold or spun off many of these businesses – including Warner Music Group, Warner Books, AOL, Time Warner Cable, and Time Inc. – since 2004.
Clear Channel Communications, a public company, at one point owned a variety of TV and radio stations and billboard operations, together with many concert venues across the US and a diverse portfolio of assets in the UK and other countries around the world. The concentration of bargaining power in this one entity allowed it to gain better deals for all of its business units. For example, the promise of playlisting (allegedly, sometimes, coupled with the threat of blacklisting) on its radio stations was used to secure better deals from artists performing in events organized by the entertainment division. These policies have been attacked as unfair and even monopolistic, but are a clear advantage of the conglomerate strategy. On December 21, 2005, Clear Channel completed the divestiture of Live Nation, and in 2007 the company divested their television stations to other firms, some of which Clear Channel holds a small interest in. Live Nation owns the events and concert venues previously owned by Clear Channel Communications.
Impact of conglomerates on the media: The four major media conglomerates in the United States are The Walt Disney Company, Comcast, Warner Bros. Discovery and Paramount Global. The Walt Disney Company is linked with the American Broadcasting Company (ABC), creating the largest media corporation, with revenue equal to roughly thirty six billion dollars. Since Walt Disney owns ABC, it controls its news and programming. Walt Disney also acquired most of Fox, for over $70 billion. When General Electric owned NBC, it did not allow negative reporting against General Electric on air (NBCUniversal is now owned by Comcast). Viacom merged with CBS in 2019 as ViacomCBS (now Paramount Global) after originally merged in 2000 with Viacom as the surviving company while also Viacom divested CBS in 2006 due to FCC regulations as the time.
=== Internet conglomerates ===
A relatively new development, Internet conglomerates, such as Alphabet, Google's parent company belong to the modern media conglomerate group and play a major role within various industries, such as brand management. In most cases, Internet conglomerates consist of corporations that own several medium-sized online or hybrid online-offline projects. In many cases, newly joined corporations get higher returns on investment, access to business contacts, and better rates on loans from various banks.
== Food conglomerates ==
Similar to other industries, many food companies can be termed as conglomerates.
The Philip Morris group, which once was the parent company of Altria group, Philip Morris International, and Kraft Foods, had an annual combined turnover of $80 bn. Phillip Morris International and Kraft Foods later spun off into independent companies.
Nestlé
== See also ==
== References ==
== Bibliography ==
Holland, Max (1989), When the Machine Stopped: A Cautionary Tale from Industrial America, Boston: Harvard Business School Press, ISBN 978-0-87584-208-0, OCLC 246343673.
McDonald, Paul and Wasko, Janet (2010), The Contemporary Hollywood Film Industry, Blackwell Publishing Ltd. ISBN 978-1-4051-3388-3
== External links ==
"Conglomerate". Encyclopædia Britannica. 2007. Encyclopædia Britannica Online. November 17, 2007.
Conglomerate Monkeyshines – an example of how conglomerates were used in the 1960s to manufacture earnings growth | Wikipedia/Business_conglomerate |
Business is the practice of making one's living or making money by producing or buying and selling products (such as goods and services). It is also "any activity or enterprise entered into for profit."
A business entity is not necessarily separate from the owner and the creditors can hold the owner liable for debts the business has acquired except for limited liability company. The taxation system for businesses is different from that of the corporates. A business structure does not allow for corporate tax rates. The proprietor is personally taxed on all income from the business.
A distinction is made in law and public offices between the term business and a company (such as a corporation or cooperative). Colloquially, the terms are used interchangeably.
Corporations are distinct from sole proprietors and partnerships. Corporations are separate and unique legal entities from their shareholders; as such they provide limited liability for their owners and members. Corporations are subject to corporate tax rates. Corporations are also more complicated, expensive to set up, along with the mandatory reporting of quarterly or annual financial information to the national (or state) securities commissions or company registers, but offer more protection and benefits for the owners and shareholders.
Individuals who are not working for a government agency (public sector) or for a mission-driven charity (nonprofit sector), are almost always working in the private sector, meaning they are employed by a business (formal or informal), whose primary goal is to generate profit, through the creation and capture of economic value above cost. In almost all countries, most individuals are employed by businesses (based on the minority percentage of public sector employees, relative to the total workforce).
== Forms ==
Forms of business ownership vary by jurisdiction, but several common entities exist:
A sole proprietorship, also known as a sole trader, is owned by one person and operates for their benefit. The owner operates the business alone and may hire employees. A sole proprietor has unlimited liability for all obligations incurred by the business, whether from operating costs or judgments against the business. All assets of the business belong to a sole proprietor, including, for example, a computer infrastructure, any inventory, manufacturing equipment, or retail fixtures, as well as any real property owned by the sole proprietor.
A partnership is a business owned by two or more people. In most forms of partnerships, each partner has unlimited liability for the debts incurred by the business. The three most prevalent types of for-profit partnerships are general partnerships, limited partnerships, and limited liability partnerships.
Corporations' owners have limited liability, and the business has a legal personality separate from its owners. Corporations can be either government-owned or privately owned, and they can organize either for profit or as nonprofit organizations. A privately owned, for-profit corporation is owned by its shareholders, who elect a board of directors to direct the corporation and hire its managerial staff. A privately owned, for-profit corporation can be either privately held by a small group of individuals, or publicly held, with publicly traded shares listed on a stock exchange.
A cooperative or co-op is a limited-liability business that can organize as for-profit or not-for-profit. A cooperative differs from a corporation in that it has members, not shareholders, and they share decision-making authority. Cooperatives are typically classified as either consumer cooperatives or worker cooperatives. Cooperatives are fundamental to the ideology of economic democracy.
Limited liability companies (LLC) and other specific types of business organization protect their owners or shareholders from business failure by doing business under a separate legal entity with certain legal protections. In contrast, a general partnership or persons working on their own are usually not as protected.
A franchise is a system in which entrepreneurs purchase the rights to open and run a business from a larger corporation. Franchising in the United States is widespread and is a major economic powerhouse. One out of twelve retail businesses in the United States are franchised and 8 million people are employed in a franchised business.
Company limited by guarantee is commonly used where companies are formed for non-commercial purposes, such as clubs or charities. The members guarantee the payment of certain (usually nominal) amounts if the company goes into insolvent liquidation, but otherwise, they have no economic rights in relation to the company. This type of company is common in England. A company limited by guarantee may be with or without having share capital.
A company limited by shares is the most common form of the company used for business ventures. Specifically, a limited company is a "company in which the liability of each shareholder is limited to the amount individually invested" with corporations being "the most common example of a limited company." This type of company is common in England and many English-speaking countries. A company limited by shares may be a
publicly traded company or a
privately held company.
A company limited by guarantee with a share capital is a hybrid entity, usually used where the company is formed for non-commercial purposes, but the activities of the company are partly funded by investors who expect a return. This type of company may no longer be formed in the UK, although provisions still exist in law for them to exist.
An unlimited company with or without a share capital is a hybrid entity, a company where the liability of members or shareholders for the debts (if any) of the company are not limited. In this case, the doctrine of a veil of incorporation does not apply.
Less common types of companies are:
Most corporations by letters patent are corporations sole and not companies as the term is commonly understood today.
Charter corporations were the only types of companies before the passing of modern companies legislation. Now they are relatively rare, except for very old companies that still survive (of which there are still many, particularly many British banks), or modern societies that fulfill a quasi-regulatory function (for example, the Bank of England is a corporation formed by a modern charter).
Statutory companies are certain companies that have been formed by a private statute passed in the relevant jurisdiction, and are relatively rare today.
"Ltd after the company's name signifies limited company, and PLC (public limited company) indicates that its shares are widely held."
In legal parlance, the owners of a company are normally referred to as the "members". In a company limited or unlimited by shares (formed or incorporated with a share capital), this will be the shareholders. In a company limited by guarantee, this will be the guarantors. Some offshore jurisdictions have created special forms of offshore company in a bid to attract business for their jurisdictions. Examples include "segregated portfolio companies" and restricted purpose companies.
There are, however, many, many sub-categories of types of company that can be formed in various jurisdictions in the world.
Companies are also sometimes distinguished into public companies and private companies for legal and regulatory purposes. Public companies are companies whose shares can be publicly traded, often (although not always) on a stock exchange which imposes listing requirements/Listing Rules as to the issued shares, the trading of shares and a future issue of shares to help bolster the reputation of the exchange or particular market of exchange. Private companies do not have publicly traded shares, and often contain restrictions on transfers of shares. In some jurisdictions, private companies have maximum numbers of shareholders.
A parent company is a company that owns enough voting stock in another firm to control management and operations by influencing or electing its board of directors; the second company being deemed as a subsidiary of the parent company. The subsidiary company can be allowed to maintain its own board of directors. The definition of a parent company differs by jurisdiction, with the definition normally being defined by way of laws dealing with companies in that jurisdiction.
== Classifications ==
Agriculture, such as the domestication of fish, animals, and livestock, as well as lumber, oil, vegetables, fruits, etc.
Mining businesses that extract natural resources and raw materials, such as wood, petroleum, natural gas, ores, metals or minerals.
Service businesses offer intangible goods or services and typically charge for labor or other services provided to government, to consumers, or to other businesses. Interior decorators, beauticians, hair stylists, make-up artists, tanning salons, laundromats, dry cleaners, and pest controllers are service businesses.
Financial services businesses include banks, brokerage firms, credit unions, credit cards, insurance companies, asset and investment companies such as private-equity firms, private-equity funds, real estate investment trusts, sovereign wealth funds, pension funds, mutual funds, index funds, hedge funds, stock exchanges, and other companies that generate profits through investment and management of capital.
Transportation businesses such as railways, airlines, and shipping companies deliver goods and individuals to their destinations for a fee.
Utilities produce public services such as water, electricity, waste management or sewage treatment. These industries are usually operated under the charge of a public government.
Entertainment companies and mass media agencies generate profits primarily from the sale of intellectual property. They include film studios and production houses, mass media companies such as cable television networks, online digital media agencies, talent agencies, mobile media outlets, newspapers, book and magazine publishing houses.
Sports organizations are involved in producing, facilitating, promoting, or organizing any activity, experience, or business enterprise focused on sports. They make their profits by selling goods and services that are sports related.
Industrial manufacturers produce products, either from raw materials or from component parts, then export the finished products at a profit. They include tangible goods such as cars, buses, medical devices, glass, or aircraft.
Real estate businesses sell, invest, construct and develop properties, including land, residential homes, and other buildings.
Retailers, wholesalers, and distributors act as middlemen and get goods produced by manufacturers to the intended consumers; they make their profits by marking up their prices. Most stores and catalog companies are distributors or retailers.
== Activities ==
=== Accounting ===
Accounting is the measurement, processing, and communication of financial information about economic entities such as businesses and corporations. The modern field was established by the Italian mathematician Luca Pacioli in 1494. Accounting, which has been called the "language of business", measures the results of an organization's economic activities and conveys this information to a variety of users, including investors, creditors, management, and regulators. Practitioners of accounting are known as accountants. The terms "accounting" and "financial reporting" are often used as synonyms.
=== Commerce ===
Commerce is the process of exchanging goods and services.
It is not just a single activity, but a set of activities that includes trade (buying and selling goods and services) and auxiliary services or aids to trade, that includes communication and marketing, logistics, finance, banking, insurance, and legal services related to trade. Business is also defined as engaging in commerce, as these are done in all businesses.
=== Finance ===
Finance is a field that deals with the study of money and investments. It includes the dynamics of assets and liabilities over time under conditions of different degrees of uncertainty and risk.
In the context of business and management, finance deals with the problems of ensuring that the firm can safely and profitably carry out its operational and financial objectives; i.e. that it: (1) has sufficient cash flow for ongoing and upcoming operational expenses, and (2) can service both maturing short-term debt repayments, and scheduled long-term debt payments.
Finance also deals with the long term objective of maximizing the value of the business, while also balancing risk and profitability; this includes the interrelated questions of (1) capital investment, which businesses and projects to invest in; (2) capital structure, deciding on the mix of funding to be used; and (3) dividend policy, what to do with "excess" capital.
=== Human resources ===
Human resources can be defined as division of business that involves finding, screening, recruiting, and training job applicants. Human resources, or HR, is crucial for all businesses to succeed as it helps companies adjust to a fast-moving business environment and the increasing demand for jobs.
The term "Human Resource" was first coined by John R. Commons in his novel 'The Distribution of Wealth'. HR departments are relatively new as they began developing in the late 20th century. HR departments' main goal is to maximize employee productivity and protecting the company from any issues that may arise in the future. Some of the most common activities conducted by those working in HR include increasing innovation and creativity within a company, applying new approaches to work projects, and efficient training and communication with employees.
Two of the most popular subdivisions of HR are Human Resource Management, HRM, and Human Resource Information Systems, or HRIS. The HRM route is for those who prefer an administrative role as it involves oversight of the entirety of the company. HRIS involves the storage and organization of employee data including full names, addresses, means of contact, and anything else required by that certain company.
Some careers of those involved in the Human Resource field include enrollment specialists, HR analyst, recruiter, employment relations manager, etc.
=== Information technology ===
Many businesses have an Information technology (IT) department, which supports the use of information technology and computer systems in support of enterprise goals. The role of a chief information officer is to lead this department. For example, Ford Motor Company in the United States employs "more than 3,000 team members with advanced computing, analytical and technical skills".
=== Manufacturing ===
Manufacturing is the production of merchandise for use or sale using labour and machines, tools, chemical and biological processing, or formulation. The term may refer to a range of human activity, from handicraft to high tech, but is most commonly applied to industrial production, in which raw materials are transformed into finished goods on a large scale.
=== Marketing ===
Marketing is defined by the American Marketing Association as "the activity, set of institutions, and processes for creating, communicating, delivering, and exchanging offerings that have value for customers, clients, partners, and society at large." The term developed from the original meaning which referred literally to going to a market to buy or sell goods or services. Marketing tactics include advertising as well as determining product pricing.
With the rise in technology, marketing is further divided into a class called digital marketing. It is marketing products and services using digital technologies.
=== Research and development ===
Research and development refer to activities in connection with corporate or government innovation. Research and development constitute the first stage of development of a potential new service or product. Research and development are very difficult to manage since the defining feature of the research is that the researchers do not know in advance exactly how to accomplish the desired result.
=== Safety ===
Injuries cost businesses billions of dollars annually. Studies have shown how company acceptance and implementation of comprehensive safety and health management systems reduce incidents, insurance costs, and workers' compensation claims. New technologies, like wearable safety devices and available online safety training, continue to be developed to encourage employers to invest in protection beyond the "canary in the coal mine" and reduce the cost to businesses of protecting their employees.
=== Sales ===
Sales are activity related to selling or the number of goods or services sold in a given time period. Sales are often integrated with all lines of business and are key to a companies' success.
== Management ==
The efficient and effective operation of a business, and study of this subject, is called management. The major branches of management are financial management, marketing management, human resource management, strategic management, production management, operations management, service management, and information technology management.
Owners may manage their businesses themselves, or employ managers to do so for them. Whether they are owners or employees, managers administer three primary components of the business's value: financial resources, capital (tangible resources), and human resources.
=== Restructuring state enterprises ===
In recent decades, states modeled some of their assets and enterprises after business enterprises. In 2003, for example, China modeled 80% of its state-owned enterprises on a company-type management system. Many state institutions and enterprises in China and Russia have transformed into joint-stock companies, with part of their shares being listed on public stock markets.
=== Business process management ===
Business process management (BPM) is a holistic management approach focused on aligning all aspects of an organization with the wants and needs of clients. BPM attempts to improve processes continuously. It can, therefore, be described as a "process optimization process". It is argued that BPM enables organizations to be more efficient, effective and capable of change than a functionally focused, traditional hierarchical management approach.
== Organization and regulation ==
Most legal jurisdictions specify the forms of ownership that a business can take, creating a body of commercial law applicable to business.
The major factors affecting how a business is organized are usually:
The size and scope of the business firm and its structure, management, and ownership, broadly analyzed in the theory of the firm. Generally, a smaller business is more flexible, while larger businesses, or those with wider ownership or more formal structures, will usually tend to be organized as corporations or (less often) partnerships. In addition, a business that wishes to raise money on a stock market or to be owned by a wide range of people will often be required to adopt a specific legal form to do so.
The sector and country. Private profit-making businesses are different from government-owned bodies. In some countries, certain businesses are legally obliged to be organized in certain ways.
Tax advantages. Different structures are treated differently in tax law and may have advantages for this reason.
Disclosure and compliance requirements. Different business structures may be required to make less or more information public (or report it to relevant authorities) and may be bound to comply with different rules and regulations.
Control and coordination requirements. In function of the risk and complexity of the tasks to organize, a business is organized through a set of formal and informal mechanisms. In particular, contractual and relational governance can help mitigate opportunism as well as support communication and information sharing.
Many businesses are operated through a separate entity such as a corporation or a partnership (either formed with or without limited liability). Most legal jurisdictions allow people to organize such an entity by filing certain charter documents with the relevant Secretary of State or equivalent and complying with certain other ongoing obligations. The relationships and legal rights of shareholders, limited partners, or members are governed partly by the charter documents and partly by the law of the jurisdiction where the entity is organized. Generally speaking, shareholders in a corporation, limited partners in a limited partnership, and members in a limited liability company are shielded from personal liability for the debts and obligations of the entity, which is legally treated as a separate "person". This means that unless there is misconduct, the owner's own possessions are strongly protected in law if the business does not succeed.
Where two or more individuals own a business together but have failed to organize a more specialized form of vehicle, they will be treated as a general partnership. The terms of a partnership are partly governed by a partnership agreement if one is created, and partly by the law of the jurisdiction where the partnership is located. No paperwork or filing is necessary to create a partnership, and without an agreement, the relationships and legal rights of the partners will be entirely governed by the law of the jurisdiction where the partnership is located. A single person who owns and runs a business is commonly known as a sole proprietor, whether that person owns it directly or through a formally organized entity. Depending on the business needs, an adviser can decide what kind is proprietorship will be most suitable.
General partners in a partnership (other than a limited liability partnership), plus anyone who personally owns and operates a business without creating a separate legal entity, are personally liable for the debts and obligations of the business.
Generally, corporations are required to pay tax just like "real" people. In some tax systems, this can give rise to so-called double taxation, because first the corporation pays tax on the profit, and then when the corporation distributes its profits to its owners, individuals have to include dividends in their income when they complete their personal tax returns, at which point a second layer of income tax is imposed.
In most countries, there are laws that treat small corporations differently from large ones. They may be exempt from certain legal filing requirements or labor laws, have simplified procedures in specialized areas, and have simplified, advantageous, or slightly different tax treatment.
"Going public" through a process known as an initial public offering (IPO) means that part of the business will be owned by members of the public. This requires the organization as a distinct entity, to disclose information to the public, and adhering to a tighter set of laws and procedures. Most public entities are corporations that have sold shares, but increasingly there are also public LLC's that sell units (sometimes also called shares), and other more exotic entities as well, such as, for example, real estate investment trusts in the US, and unit trusts in the UK. A general partnership cannot "go public".
=== Commercial law ===
A very detailed and well-established body of rules that evolved over a very long period of time applies to commercial transactions. The need to regulate trade and commerce and resolve business disputes helped shape the creation of law and courts. The Code of Hammurabi dates back to about 1772 BC for example and contains provisions that relate, among other matters, to shipping costs and dealings between merchants and brokers. The word "corporation" derives from the Latin corpus, meaning body, and the Maurya Empire in Iron-Age India accorded legal rights to business entities.
In many countries, it is difficult to compile all the laws that can affect a business into a single reference source. Laws can govern the treatment of labour and employee relations, worker protection and safety, discrimination on the basis of age, gender, disability, race, and in some jurisdictions, sexual orientation, and the minimum wage, as well as unions, worker compensation, and working hours and leave.
Some specialized businesses may also require licenses, either due to laws governing entry into certain trades, occupations or professions, that require special education or to raise revenue for local governments. Professions that require special licenses include law, medicine, piloting aircraft, selling liquor, radio broadcasting, selling investment securities, selling used cars, and roofing. Local jurisdictions may also require special licenses and taxes just to operate a business.
Some businesses are subject to ongoing special regulation, for example, public utilities, investment securities, banking, insurance, broadcasting, aviation, and health care providers. Environmental regulations are also very complex and can affect many businesses.
=== Capital ===
When businesses need to raise money (called capital), they sometimes offer securities for sale.
Capital may be raised through private means, by an initial public offering or IPO on a stock exchange, or in multiple other ways.
Major stock exchanges include the Shanghai Stock Exchange, Singapore Exchange, Hong Kong Stock Exchange, New York Stock Exchange and NASDAQ (the US), the London Stock Exchange (UK), the Tokyo Stock Exchange (Japan), and Bombay Stock Exchange (India). Most countries with capital markets have at least one.
Businesses that have gone public are subject to regulations concerning their internal governance, such as how executive officers' compensation is determined, and when and how information is disclosed to shareholders and to the public. In the United States, these regulations are primarily implemented and enforced by the United States Securities and Exchange Commission (SEC). Other western nations have comparable regulatory bodies. The regulations are implemented and enforced by the China Securities Regulation Commission (CSRC) in China. In Singapore, the regulatory authority is the Monetary Authority of Singapore (MAS), and in Hong Kong, it is the Securities and Futures Commission (SFC).
The proliferation and increasing complexity of the laws governing business have forced increasing specialization in corporate law. It is not unheard of for certain kinds of corporate transactions to require a team of five to ten attorneys due to sprawling regulation. Commercial law spans general corporate law, employment and labor law, health-care law, securities law, mergers and acquisitions, tax law, employee benefit plans, food and drug regulation, intellectual property law on copyrights, patents, trademarks, telecommunications law, and financing.
Other types of capital sourcing include crowdsourcing on the Internet, venture capital, bank loans, and debentures.
=== Intellectual property ===
Businesses often have important "intellectual property" that needs protection from competitors for the company to stay profitable. This could require patents, copyrights, trademarks, or preservation of trade secrets. Most businesses have names, logos, and similar branding techniques that could benefit from trademarking. Patents and copyrights in the United States are largely governed by federal law, while trade secrets and trademarking are mostly a matter of state law. Because of the nature of intellectual property, a business needs protection in every jurisdiction in which they are concerned about competitors. Many countries are signatories to international treaties concerning intellectual property, and thus companies registered in these countries are subject to national laws bound by these treaties. In order to protect trade secrets, companies may require employees to sign noncompete clauses which will impose limitations on an employee's interactions with stakeholders, and competitors.
=== Trade unions ===
A trade union (or labor union) is an organization of workers who have come together to achieve common goals such as protecting the integrity of its trade, improving safety standards, achieving higher pay and benefits such as health care and retirement, increasing the number of employees an employer assigns to complete the work, and better working conditions. The trade union, through its leadership, bargains with the employer on behalf of union members (rank and file members) and negotiates labor contracts (collective bargaining) with employers. The most common purpose of these associations or unions is "maintaining or improving the conditions of their employment". This may include the negotiation of wages, work rules, complaint procedures, rules governing hiring, firing, and promotion of workers, benefits, workplace safety and policies.
== See also ==
== References ==
== External links == | Wikipedia/Business_systems |
Joint application design is a term originally used to describe a software development process pioneered and deployed during the mid-1970s by the New York Telephone Company's Systems Development Center under the direction of Dan Gielan. Following a series of implementations of this methodology, Gielan lectured extensively in various forums on the methodology and its practices. Arnie Lind, then a Senior Systems Engineer at IBM Canada in Regina, Saskatchewan created and named joint application design in 1974. Existing methods, however, entailed application developers spending months learning the specifics of a particular department or job function, and then developing an application for the function or department. In addition to development backlog delays, this process resulted in applications taking years to develop, and often not being fully accepted by the application users.
Arnie Lind's idea was that rather than have application developers learn about people's jobs, people doing the work could be taught how to write an application. Arnie pitched the concept to IBM Canada's Vice President Carl Corcoran (later President of IBM Canada), and Carl approved a pilot project. Arnie and Carl together named the methodology JAD, an acronym for joint application design, after Carl Corcoran rejected the acronym JAL, or joint application logistics, upon realizing that Arnie Lind's initials were JAL (John Arnold Lind).
The pilot project was an emergency room project for the Saskatchewan Government. Arnie developed the JAD methodology, and put together a one-week seminar, involving primarily nurses and administrators from the emergency room, but also including some application development personnel. The one-week seminar produced an application framework, which was then coded and implemented in less than one month, versus an average of 18 months for traditional application development. And because the users themselves designed the system, they immediately adopted and liked the application. After the pilot project, IBM was very supportive of the JAD methodology, as they saw it as a way to more quickly implement computing applications, running on IBM hardware.
Arnie Lind spent the next 13 years at IBM Canada continuing to develop the JAD methodology, and traveling around the world performing JAD seminars, and training IBM employees in the methods and techniques of JAD. JADs were performed extensively throughout IBM Canada, and the technique also spread to IBM in the United States. Arnie Lind trained several people at IBM Canada to perform JADs, including Tony Crawford and Chuck Morris. Arnie Lind retired from IBM in 1987, and continued to teach and perform JADs on a consulting basis, throughout Canada, the United States, and Asia.
The JAD process was formalized by Tony Crawford and Chuck Morris of IBM in the late 1970s. It was then deployed at Canadian International Paper. JAD was used in IBM Canada for a while before being brought back to the US. Initially, IBM used JAD to help sell and implement a software program they sold, called COPICS. It was widely adapted to many uses (system requirements, grain elevator design, problem-solving, etc.). Tony Crawford later developed JAD-Plan and then JAR (joint application requirements). In 1985, Gary Rush wrote about JAD and its derivations – Facilitated Application Specification Techniques (FAST) – in Computerworld.
Originally, JAD was designed to bring system developers and users of varying backgrounds and opinions together in a productive as well as creative environment. The meetings were a way of obtaining quality requirements and specifications. The structured approach provides a good alternative to traditional serial interviews by system analysts. JAD has since expanded to cover broader IT work as well as non-IT work (read about Facilitated Application Specification Techniques – FAST – created by Gary Rush in 1985 to expand JAD applicability.
== Key participants ==
Executive Sponsor
The executive who charters the project, the system owner. They must be high enough in the organization to be able to make decisions and provide the necessary strategy, planning, and direction.
Subject Matter Experts
These are the business users, the IS professionals, and the outside experts that will be needed for a successful workshop. This group is the backbone of the meeting; they will drive the changes.
Facilitator/Session Leader
meeting and directs traffic by keeping the group on the meeting agenda. The facilitator is responsible for identifying those issues that can be solved as part of the meeting and those which need to be assigned at the end of the meeting for follow-up investigation and resolution. The facilitator serves the participants and does not contribute information to the meeting.
Scribe/Modeller/Recorder/Documentation Expert
Records and publish the proceedings of the meeting and does not contribute information to the meeting.
Observers
Generally members of the application development team assigned to the project. They are to sit behind the participants and are to silently observe the proceedings.
== 9 key steps ==
Identify project objectives and limitations: It is vital to have clear objectives for the workshop and for the project as a whole. The pre-workshop activities, the planning and scoping, set the expectations of the workshop sponsors and participants. Scoping identifies the business functions that are within the scope of the project. It also tries to assess both the project design and implementation complexity. The political sensitivity of the project should be assessed. Has this been tried in the past? How many false starts were there? How many implementation failures were there? Sizing is important. For best results, systems projects should be sized so that a complete design – right down to screens and menus – can be designed in 8 to 10 workshop days.
Identify critical success factors: It is important to identify the critical success factors for both the development project and the business function being studied. How will we know that the planned changes have been effective? How will success be measured? Planning for outcomes assessment helps to judge the effectiveness and the quality of the implemented system over its entire operational life.
Define project deliverables: In general, the deliverables from a workshop are documentation and a design. It is important to define the form and level of detail of the workshop documentation. What types of diagrams will be provided? What type or form of narrative will be supplied? It is a good idea to start using a CASE tool for diagramming support right from the start. Most of the available tools have good to great diagramming capabilities but their narrative support is generally weak. The narrative is best produced with your standard word processing software.
Define the schedule of workshop activities: Workshops vary in length from one to five days. The initial workshop for a project should not be less than three days. It takes the participants most of the first day to get comfortable with their roles, with each other, and with the environment. The second day is spent learning to understand each other and developing a common language with which to communicate issues and concerns. By the third day, everyone is working together on the problem and real productivity is achieved. After the initial workshop, the team-building has been done. Shorter workshops can be scheduled for subsequent phases of the project, for instance, to verify a prototype. However, it will take the participants from one to three hours to re-establish the team psychology of the initial workshop.
Select the participants: These are the business users, the IT professionals, and the outside experts that will be needed for a successful workshop. These are the true "back bones" of the meeting who will drive the changes.
Prepare the workshop material: Before the workshop, the project manager and the facilitator perform an analysis and build a preliminary design or straw man to focus the workshop. The workshop material consists of documentation, worksheets, diagrams, and even props that will help the participants understand the business function under investigation.
Organize workshop activities and exercises: The facilitator must design workshop exercises and activities to provide interim deliverables that build towards the final output of the workshop. The pre-workshop activities help design those workshop exercises. For example, for a Business Area Analysis, what's in it? A decomposition diagram? A high-level entity-relationship diagram? A normalized data model? A state transition diagram? A dependency diagram? All of the above? None of the above? It is important to define the level of technical diagramming that is appropriate to the environment. The most important thing about a diagram is that it must be understood by the users. Once the diagram choice is made, the facilitator designs exercises into the workshop agenda to get the group to develop those diagrams. A workshop combines exercises that are serially oriented to build on one another, and parallel exercises, with each sub-team working on a piece of the problem or working on the same thing for a different functional area. High-intensity exercises led by the facilitator energize the group and direct it towards a specific goal. Low-intensity exercises allow for detailed discussions before decisions. The discussions can involve the total group or teams can work out the issues and present a limited number of suggestions for the whole group to consider. To integrate the participants, the facilitator can match people with similar expertise from different departments. To help participants learn from each other, the facilitator can mix the expertise. It's up to the facilitator to mix and match the sub-team members to accomplish the organizational, cultural, and political objectives of the workshop. A workshop operates on both the technical level and the political level. It is the facilitator's job to build consensus and communications, to force issues out early in the process. There is no need to worry about the technical implementation of a system if the underlying business issues cannot be resolved.
Prepare, inform, educate the workshop participants: All of the participants in the workshop must be made aware of the objectives and limitations of the project and the expected deliverables of the workshop. Briefing of participants should take place 1 to 5 days before the workshop. This briefing may be teleconferenced if participants are widely dispersed. The briefing document might be called the Familiarization Guide, Briefing Guide, Project Scope Definition, or the Management Definition Guide – or anything else that seems appropriate. It is a document of eight to twelve pages, and it provides a clear definition of the scope of the project for the participants. The briefing itself lasts two to four hours. It provides the psychological preparation everyone needs to move forward into the workshop.
Coordinate workshop logistics: Workshops should be held off-site to avoid interruptions. Projectors, screens, PCs, tables, markers, masking tape, Post-It notes, and many other props should be prepared. What specific facilities and props are needed is up to the facilitator. They can vary from simple flip charts to electronic white boards. In any case, the layout of the room must promote the communication and interaction of the participants.
== Advantages ==
JAD decreases time and costs associated with requirements elicitation process. During 2-4 weeks information not only is collected, but requirements, agreed upon by various system users, are identified. Experience with JAD allows companies to customize their systems analysis process into even more dynamic ones like Double Helix, a methodology for mission-critical work.
JAD sessions help bring experts together giving them a chance to share their views, understand views of others, and develop the sense of project ownership.
The methods of JAD implementation are well-known, as it is "the first accelerated design technique available on the market and probably best known", and can easily be applied by any organization.
Easy integration of CASE tools into JAD workshops improves session productivity and provides systems analysts with discussed and ready to use models.
== Challenges ==
Without multifaceted preparation for a JAD session, professionals' valuable time can be easily wasted. If JAD session organizers do not study the elements of the system being evaluated, an incorrect problem could be addressed, incorrect people could be invited to participate, and inadequate problem-solving resources could be used.
JAD workshop participants should include employees able to provide input on most, if not all, of the pertinent areas of the problem. This is why particular attention should be paid during participant selection. The group should consist not only of employees from various departments who will interact with the new system, but from different hierarchies of the organizational ladder. The participants may have conflicting points of view, but meeting will allow participants to see issues from different viewpoints. JAD brings to light a better model outline with better understanding of underlying processes.
The facilitator has an obligation to ensure all participants – not only the most vocal ones – have a chance to offer their opinions, ideas, and thoughts.
== References ==
== Bibliography ==
Yatco, Mei C. (1999). "Joint Application Design/Development". University of Missouri-St. Louis. Retrieved 2009-02-06.
Soltys, Roman; Anthony Crawford (1999). "JAD for business plans and designs". Archived from the original on 2009-03-13. Retrieved 2009-02-06.
Dennis, Alan R.; Hayes, Glenda S.; Daniels, Robert M. Jr. (Spring 1999). "Business Process Modeling with Group Support Systems". Journal of Management Information Systems. 15 (4): 115–142. doi:10.1080/07421222.1999.11518224. Retrieved 2015-05-14.
Botkin, John C. "Customer Involved Participation as Part of the Application Development Process". Archived from the original on 1998-12-01.
Moeller, Walter E. "Facilitated Information Gathering Sessions: An Information Engineering Technique". Retrieved 2010-03-22.
Bill Jennerich "Joint Application Design -- Business Requirements Analysis for Successful Re-engineering." 18:50, 26 June 2006 (UTC)[2] Last update time unknown. Accessed on Nov. 14, 1999.
Gary Rush "JAD - Its History and Evolution -- MGR Consulting Newsletter." July 2006 [3]
Gary Rush, "JAD Project Aids Design", Computerworld, Volume 18 Number 52, pages 31 and 38, December 24, 1984. [4]
Davidson, E.J (1999). "Joint application design (JAD) in practice". Journal of Systems and Software. 45 (3). Elsevier BV: 215–223. doi:10.1016/s0164-1212(98)10080-8. ISSN 0164-1212.
Gottesdiener, Ellen; Requirements by Collaboration: Workshops for Defining Needs, Addison-Wesley, 2002, ISBN 0-201-78606-0.
Wood, Jane and Silver, Denise; Joint Application Development, John Wiley & Sons Inc, ISBN 0-471-04299-4 | Wikipedia/Joint_applications_development |
Auction theory is a branch of applied economics that deals with how bidders act in auctions and researches how the features of auctions incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-world auctions. Sellers use auction theory to raise higher revenues while allowing buyers to procure at a lower cost. The confluence of the price between the buyer and seller is an economic equilibrium. Auction theorists design rules for auctions to address issues that can lead to market failure. The design of these rulesets encourages optimal bidding strategies in a variety of informational settings. The 2020 Nobel Prize for Economics was awarded to Paul R. Milgrom and Robert B. Wilson "for improvements to auction theory and inventions of new auction formats."
== Introduction ==
Auctions facilitate transactions by enforcing a specific set of rules regarding the resource allocations of a group of bidders. Theorists consider auctions to be economic games that have two aspects: format and information. The format defines the rules for the announcement of prices, the placement of bids, the updating of prices, when the auction closes, and the way a winner is picked. The way auctions differ with respect to information regards the asymmetries of information that exist between bidders. In most auctions, bidders have some private information that they choose to withhold from their competitors. For example, bidders usually know their personal valuation of the item, which is unknown to the other bidders and the seller; however, the behaviour of bidders can influence valuations by other bidders.
== History ==
A purportedly historical event related to auctions is a custom in Babylonia, namely when men make an offers to women in order to marry them. The more familiar the auction system is, the more situations where auctions are conducted. There are auctions for various things, such as livestock, rare and unusual items, and financial assets.
Non-cooperative games have a long history, beginning with Cournot's duopoly model. A 1994 Nobel Laureate for Economic Sciences, John Nash, proved a general-existence theorem for non-cooperative games, which moves beyond simple zero-sum games. This theory was generalized by Vickrey (1961) to deal with the unobservable value of each buyer. By the early 1970s, auction theorists had begun defining equilibrium bidding conditions for single-object auctions under most realistic auction formats and information settings. Recent developments in auction theory consider how multiple-object auctions can be performed efficiently.
== Auction types ==
There are traditionally four types of auctions that are used for the sale of a single item:
First-price sealed-bid auction in which bidders place their bids in sealed envelopes and simultaneously hand them to the auctioneer. The envelopes are opened and the individual with the highest bid wins, paying the amount bid. This form of auction requires strategic considerations since bidders must not only consider their own valuations but other bidders' possible valuations. The first formal analysis of such an auction was by Vickrey (1961). For the case of two buyers and uniformly distributed values, he showed that the symmetric-equilibrium strategy was to submit a bid equal to half of the buyer's valuation.
Second-price sealed-bid auctions (Vickrey auctions) which are the same as first-price sealed-bid auctions except that the winner pays a price equal to the second-highest bid. The logic of this auction type is that the dominant strategy for all bidders is to bid their true valuation. William Vickrey was the first scholar to study second-price valuation auctions, but their use goes back in history, with some evidence suggesting that Goethe sold his manuscripts to a publisher using the second-price auction format. Online auctions often use an equivalent version of Vickrey's second-price auction wherein bidders provide proxy bids for items. A proxy bid is an amount an individual values some item at. The online auction house will bid up the price of the item until the proxy bid for the winner is at the top. However, the individual only has to pay one increment higher than the second-highest price, despite their own proxy valuation.
Open ascending-bid auctions (English auctions) are the oldest, and possibly most common, type of auction in which participants make increasingly higher bids, each stopping bidding when they are not prepared to pay more than the current highest bid. This continues until no participant is prepared to make a higher bid; the highest bidder wins the auction at the final amount bid. Sometimes the lot is sold only if the bidding reaches a reserve price set by the seller.
Open descending-bid auctions (Dutch auctions) are those in which the price is set by the auctioneer at a level sufficiently high to deter all bidders, and is progressively lowered until a bidder is prepared to buy at the current price, winning the auction.
Most auction theory revolves around these four "basic" auction types. However, other types have also received some academic study (see Auction § Types). Developments in the world and in technology have also influenced the current auction system. With the existence of the internet, online auctions have become an option.
Online auctions are efficient platforms for establishing precise prices based on supply and demand. Furthermore, they can overcome geographic boundaries. Online auction sites are used for a variety of purposes, such as online "garage sales" by companies liquidating unwanted inventory. A significant difference between online auctions and traditional auctions is that bidders on the internet are unable to inspect the actual item, leading to differences between initial perception and reality.
== Auction process ==
There are six basic activities that complement the auction-based trading process:
Initial buyer and seller registration: authentication of trading parties, exchange of cryptography keys when the auction is online, and profile creation.
Setting up a particular auction event: describing items sold or acquired and establishing auction rules. Auction rules define the type of auction, starting date, closing rules, and other parameters.
Scheduling and advertising, as well as grouping of items of the same category to be auctioned together, is done to attract potential buyers. Popular auctions can be combined with less-popular auctions to persuade people to attend the less popular ones.
Bidding step: bids are collected and bid control rules of the auction are implemented.
Evaluation of bids and closing the auction: winners and losers are declared.
Trade settlement: payment to seller, transfer of goods, fees to agents.
== Auction envelope theorem ==
The auction envelope theorem defines certain probabilities expected to arise in an auction.
=== Benchmark model ===
The benchmark model for auctions, as defined by McAfee and McMillan (1987), is as follows:
All of the bidders are risk-neutral.
Each bidder has a private valuation for the item, which is almost always independently drawn from some probability distribution.
The bidders possess symmetric information.
The payment is represented only as a function of the bids.
=== Win probability ===
In an auction a buyer bidding
B
(
v
)
{\displaystyle B(v)}
wins if the opposing bidders make lower bids.
The mapping from valuations to bids is strictly increasing; the high-valuation bidder therefore wins.
In statistics the probability of having the "first" valuation is written as:
W
=
F
(
1
)
(
v
)
{\textstyle W=F_{({\scriptstyle {\text{1}}})}(v)}
With independent valuations and N other bidders
W
=
F
(
v
)
N
{\displaystyle W=F(v)^{N}}
=== The auction ===
A buyer's payoff is
u
(
v
,
b
)
=
w
(
b
)
(
v
−
b
)
{\displaystyle u(v,b)=w(b)(v-b)}
Let
B
{\displaystyle B}
be the bid that maximizes the buyer's payoff.
Therefore
u
(
v
,
B
)
>
u
(
v
,
b
)
=
W
(
b
)
(
v
−
b
)
{\displaystyle u(v,B)>u(v,b)=W(b)(v-b)}
The equilibrium payoff is therefore
U
(
v
)
=
W
(
B
)
(
v
−
B
)
)
{\displaystyle U(v)=W(B)(v-B))}
Necessary condition for the maximum:
∂
u
/
∂
b
=
0
{\displaystyle \partial u/\partial b=0}
when
b
=
B
{\displaystyle b=B}
The final step is to take the total derivative of the equilibrium payoff
U
′
(
v
)
=
W
(
B
)
+
∂
u
/
∂
b
{\displaystyle U'(v)=W(B)+\partial u/\partial b}
The second term is zero. Therefore
U
′
(
v
)
=
W
{\displaystyle U'(v)=W}
Then
U
′
(
v
)
=
W
{\displaystyle U'(v)=W}
=
F
(
1
)
(
v
)
{\displaystyle =F_{({\scriptstyle {\text{1}}})}(v)}
Example uniform distribution with two buyers. For the uniform distribution the probability if having a higher value that one other buyer is
F
(
v
)
=
v
{\displaystyle F(v)=v}
.
Then
U
′
(
v
)
=
v
{\displaystyle U'(v)=v}
The equilibrium payoff is therefore
U
(
v
)
=
∫
0
v
x
d
x
=
(
1
/
2
)
v
2
{\displaystyle U(v)=\textstyle \int _{0}^{v}\displaystyle xdx=(1/2)v^{2}}
.
The win probability is
W
=
F
(
v
)
=
v
{\displaystyle W=F(v)=v}
.
U
(
v
)
=
W
(
B
)
(
v
−
B
)
)
{\displaystyle U(v)=W(B)(v-B))}
Then
(
1
/
2
)
v
2
=
v
(
v
−
B
(
v
)
)
{\displaystyle (1/2)v^{2}=v(v-B(v))}
.
Rearranging this expression,
B
(
v
)
=
(
1
/
2
)
v
{\displaystyle B(v)=(1/2)v}
With three buyers,
U
′
(
v
)
=
W
{\displaystyle U'(v)=W}
=
F
(
1
)
(
v
)
=
F
(
v
)
2
=
v
2
{\displaystyle =F_{({\scriptstyle {\text{1}}})}(v)=F(v)^{2}=v^{2}}
, then
B
(
v
)
=
(
2
/
3
)
v
{\displaystyle B(v)=(2/3)v}
With
N
+
1
{\displaystyle N+1}
buyers
B
(
v
)
=
(
N
/
(
N
+
1
)
)
v
{\displaystyle B(v)=(N/(N+1))v}
Lebrun (1996) provides a general proof that there are no asymmetric equilibriums.
== Optimal auctions ==
=== Auctions from a buyer's perspective ===
The revelation principle is a simple but powerful insight.
In 1979 Riley & Samuelson (1981) proved a general revenue equivalence theorem that applies to all buyers and hence to the seller. Their primary interest was finding out which auction rule would be better for the buyers. For example, there might be a rule that all buyers pay a nonrefundable bid (such auctions are conducted on-line). The equivalence theorem shows that any allocation mechanism or auction that satisfies the four main assumptions of the benchmark model will lead to the same expected revenue for the seller. (Buyer i with value v has the same "payoff" or "buyer surplus" across all auctions.)
=== Symmetric auctions with correlated valuation distributions ===
The first model for a broad class of models was Milgrom and Weber's (1983) paper on auctions with affiliated valuations.
In a recent working paper on general asymmetric auctions, Riley (2022) characterized equilibrium bids for all valuation distributions. Each buyer's valuation can be positively or negatively correlated.
The revelation principle as applied to auctions is that the marginal buyer payoff or "buyer surplus" is P(v), the probability of being the winner.
In every participant-efficient auction, the probability of winning is 1 for a high-valuation buyer. The marginal payoff to a buyer is therefore the same in every such auction. The payoff must therefore be the same as well.
=== Auctions from the seller's perspective (revenue maximization) ===
Quite independently and soon after, Myerson (1981) used the revelation principle to characterize revenue-maximizing sealed high-bid auctions. In the "regular" case this is a participation-efficient auction. Setting a reserve price is therefore optimal for the seller. In the "irregular" case it has since been shown that the outcome can be implemented by prohibiting bids in certain sub-intervals.
Relaxing each of the four main assumptions of the benchmark model yields auction formats with unique characteristics.
Risk-averse bidders incur some kind of cost from participating in risky behaviours, which affects their valuation of a product. In sealed-bid first-price auctions, risk-averse bidders are more willing to bid more to increase their probability of winning, which, in turn, increases the bid's utility. This allows sealed-bid first-price auctions to produce higher expected revenue than English and sealed-bid second-price auctions.
In formats with correlated values—where the bidders' valuations of the item are not independent—one of the bidders, perceiving their valuation of the item to be high, makes it more likely that the other bidders will perceive their own valuations to be high. A notable example of this instance is the winner’s curse, where the results of the auction convey to the winner that everyone else estimated the value of the item to be less than they did. Additionally, the linkage principle allows revenue comparisons amongst a fairly general class of auctions with interdependence between bidders' values.
The asymmetric model assumes that bidders are separated into two classes that draw valuations from different distributions (e.g., dealers and collectors in an antique auction).
In formats with royalties or incentive payments, the seller incorporates additional factors, especially those that affect the true value of the item (e.g., supply, production costs, and royalty payments), into the price function.
The theory of efficient trading processes developed in a static framework relies heavily on the premise of non-repetition. For example, an auction-seller-optimal design (as derived in Myerson) involves the best lowest price that exceeds both the seller's valuation and the lowest possible buyer's valuation.
== Game-theoretic models ==
A game-theoretic auction model is a mathematical game represented by a set of players, a set of actions (strategies) available to each player, and a payoff vector corresponding to each combination of strategies. Generally, the players are the buyer(s) and the seller(s). The action set of each player is a set of bid functions or reservation prices (reserves). Each bid function maps the player's value (in the case of a buyer) or cost (in the case of a seller) to a bid price. The payoff of each player under a combination of strategies is the expected utility (or expected profit) of that player under that combination of strategies.
Game-theoretic models of auctions and strategic bidding generally fall into either of the following two categories. In a private values model, each participant (bidder) assumes that each of the competing bidders obtains a random private value from a probability distribution. In a common value model, the participants have equal valuations of the item, but they do not have perfectly accurate information to arrive at this valuation. In lieu of knowing the exact value of the item, each participant can assume that any other participant obtains a random signal, which can be used to estimate the true value, from a probability distribution common to all bidders. Usually, but not always, the private-values model assumes that the valuations are independent across bidders, whereas a common-value model usually assumes that the valueations are independent up to the common parameters of the probability distribution.
A more general category for strategic bidding is the affiliated values model, in which the bidder's total utility depends on both their individual private signal and some unknown common value. Both the private value and common value models can be perceived as extensions of the general affiliated values model.
When it is necessary to make explicit assumptions about bidders' value distributions, most of the published research assumes symmetric bidders. This means that the probability distribution from which the bidders obtain their values (or signals) is identical across bidders. In a private values model which assumes independence, symmetry implies that the bidders' values are "i.i.d." – independently and identically distributed.
An important example (which does not assume independence) is Milgrom and Weber's general symmetric model (1982).
== Asymmetric auctions ==
The earliest paper on asymmetric value distributions is by Vickrey (1961). One buyer's valuation is uniformly distributed over the closed interval [0,1]. The other buyer has a known value of 1/2. Both the equilibrium and uniform bid distributions will support [0,1/2].
Jump-bidding;
Suppose that the buyers' valuations are uniformly distributed on [0,1] and [0,2] and buyer 1 has the wider support. Then both continue to bid half their valuations except at v=1.
The jump bid: buyer 2 jumps from bidding 1/2 to bidding 3/4. If buyer 1 follows suit she halves her profit margin and less than doubles her win probability (because of the tie breaking rule, a coin toss).
So buyer 2 does not jump. This makes buyer 1 much better off. He wins for use if his valuation is above 1/2.
The next paper, by Maskin and Riley (2000), provides a qualitative characterization of equilibrium bids when the "strong buyer" S has a value distribution that dominates that of the "weak buyer" under the assumption of conditional stochastic dominance (first-order stochastic dominance for every right-truncated value distribution). Another early contribution is Keith Waehrer's 1999 article. Later published research includes Susan Athey's 2001 Econometrica article, as well as that by Reny and Zamir (2004).
== Revenue equivalence ==
One of the major findings of auction theory is the revenue equivalence theorem. Early equivalence results focused on a comparison of revenues in the most common auctions. The first such proof, for the case of two buyers and uniformly distributed values, was by Vickrey (1961). In 1979 Riley & Samuelson (1981) proved a much more general result. (Quite independently and soon after, this was also derived by Myerson (1981)).The revenue equivalence theorem states that any allocation mechanism, or auction that satisfies the four main assumptions of the benchmark model, will lead to the same expected revenue for the seller (and player i of type v can expect the same surplus across auction types). The basic version of the theorem asserts that, as long as the Symmetric Independent Private Value (SIPV) environment assumption holds, all standard auctions give the same expected profit to the auctioneer and the same expected surplus to the bidder.
== Winner's curse ==
The winner's curse is a phenomenon which can occur in common value settings—when the actual values to the different bidders are unknown but correlated, and the bidders make bidding decisions based on estimated values. In such cases, the winner will tend to be the bidder with the highest estimate, but the results of the auction will show that the remaining bidders' estimates of the item's value are less than that of the winner, giving the winner the impression that they "bid too much".
In an equilibrium of such a game, the winner's curse does not occur because the bidders account for the bias in their bidding strategies. Behaviorally and empirically, however, winner's curse is a common phenomenon, described in detail by Richard Thaler.
== Optimal auctions ==
With identically and independently distributed private valuations, Riley and Samuelson (1981) showed that in any auction or auction-like action (such as the "War of Attrition") the allocation is "participant efficient", i.e. the item is allocated to the buyer submitting the highest bid, with a probability of 1. They then showed that allocation equivalence implied payoff equivalence for all reserve prices. They then showed that discriminating against low-value buyers by setting a minimum, or reserve, price would increase expected revenue. Along with Myerson, they showed that the most profitable reserve price is independent of the number of bidders. The reserve price only comes into play if there is a single bid. Thus it is equivalent to ask what reserve price would maximize the revenue from a single buyer. If values are uniformly distributed over the interval [0, 100], then the probability p(r) that this buyer's value is less than r is p(r) = (100-r)/100. Therefore the expected revenue is
p(r)*r = (100 - r)*r/100 =(r-50)*(r-50) + 25
Thus, the expected revenue-maximizing reserve price is 50. Also examined is the question of whether it might ever be more profitable to design a mechanism that awards the item to a bidder other than one with the highest value. Surprisingly, this is the case. As Maskin and Riley then showed, this is equivalent to excluding bids over certain intervals above the optimal reserve price.
Bulow and Klemperer (1996) have shown that an auction with n bidders and an optimally chosen reserve price generates a smaller profit for the seller than a standard auction with n+1 bidders and no reserve price.
== JEL classification ==
In the Journal of Economic Literature Classification System, game theory is classified as C7, under Mathematical and Quantitative Methods, and auctions are classified as D44, under Microeconomics.
== Applications to business strategy ==
Scholars of managerial economics have noted some applications of auction theory in business strategy. Namely, auction theory can be applied to preemption games and attrition games.
Preemption games are games where entrepreneurs preempt other firms by entering a market with new technology before it's ready for commercial deployment. The value generated from waiting for the technology to become commercially viable also increases the risk that a competitor will enter the market preemptively. Preemptive games can be modeled as a first-priced sealed auction. Both companies would prefer to enter the market when the technology is ready for commercial deployment; this can be considered the valuation by both companies. However, one firm might hold information stating that technology is viable earlier than the other firm believes. The company with better information would then "bid" to enter the market earlier, even as the risk of failure is higher.
Games of attrition are games of preempting other firms to leave the market. This often occurs in the airline industry as these markets are considered highly contestable. As a new airline enters the market, they will decrease prices to gain market share. This forces established airlines to also decrease prices to avoid losing market share. This creates an auction game. Usually, market entrants will use a strategy of attempting to bankrupt established firms. Thus, the auction is measured in how much each firm is willing to lose as they stay in the game of attrition. The firm that lasts the longest in the game wins the market share. This strategy has been used more recently by entertainment streaming services such as Netflix, Hulu, Disney+, and HBO Max which are all loss-making firms attempting to gain market share by bidding to expand entertainment content.
== Nobel Memorial Prize in Economic Sciences ==
Two Stanford University professors, Paul Milgrom and Robert Wilson, won the 2020 Nobel Memorial Prize in Economic Sciences for advancing auction theory by inventing several new auction formats, including the simultaneous multiple-round auction (SMRA), which combines the benefit of both the English (open-outcry), and sealed-bid, auctions. SMRAs are deemed to solve a problem facing the Federal Communications Commission (FCC). If the FCC were to sell all of its telecommunication frequency slots by using a traditional auction method, it would eventually either give away licenses for free or end up with a telecom monopoly in the United States.
The process of simultaneous multiple-round auctions is that there are three- to four-round auctions. Every bidder seals their bid, and the auctioneer announces the highest bid to all bidders at the end of each round. All the bidders can adjust and change their auction price and strategy after they listen to the highest bid in a particular round. The auction will continue until the highest bid of the current round is lower than the previous round's highest bid.
SMRA's first distinguishing feature is that the auction is taking place simultaneously for different items; therefore, it seriously increases the cost for speculators. For the same reason, sealed bidding can ensure that all bidding reflects the bidder’s valuation of the product. The second difference is that the bidding takes place in numerous rounds and the highest price of bidding is announced each round, allowing bidders to learn more about their competitors' preferences and information and to adjust their strategy accordingly, thus decreasing the effect of asymmetric information inside the auction. In addition, multiple-round bidding can maintain the bidder's activity in the auction. It has substantially increased the information the bidder has about the highest bid, because at the end of every round, the host will announce the highest bid after the bidding.
== Footnotes ==
== Further reading ==
Cassady, R. (1967). Auctions and auctioneering. University of California Press. An influential early survey.
Klemperer, P. (Ed.). (1999b). The economic theory of auctions. Edward Elgar. A collection of seminal papers in auction theory.
Klemperer, P. (1999a). Auction theory: A guide to the literature. Journal of Economic Surveys, 13(3), 227–286. A good modern survey; the first chapter of the preceding book.
Klemperer, Paul (2004). Auctions: Theory and Practice. Princeton University Press. ISBN 0-691-11925-2. Draft edition available online
Krishna, Vijay (2002). Auction theory. New York: Elsevier. ISBN 978-0-12-426297-3. A very good modern textbook on auction theory.
McAfee, R. P. and J. McMillan (1987). "Auctions and Bidding". Journal of Economic Literature. 25: 708–47. A survey.
Myerson, Roger B. (1981). "Optimal Auction Design". Mathematics of Operations Research. 6 (1): 58–73. doi:10.1287/moor.6.1.58. ISSN 0364-765X. S2CID 12282691. A seminal paper, introduced revenue equivalence and optimal auctions.
Riley, J., and Samuelson, W. (1981). Optimal auctions. The American Economic Review, 71(3), 381–392. A seminal paper; published concurrently with Myerson's paper cited above.
Parsons, S., Rodriguez-Aguilar, J. A., and Klein, M. (2011). Auctions and bidding: A guide for computer scientists.
Shoham, Yoav; Leyton-Brown, Kevin (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. New York: Cambridge University Press. ISBN 978-0-521-89943-7. A recent textbook; see Chapter 11, which presents auction theory from a computational perspective. Downloadable free online.
Vickrey, William (1961). "Counterspeculation, Auctions, and Competitive Sealed Tenders". The Journal of Finance. 16 (1): 8–37. doi:10.1111/j.1540-6261.1961.tb02789.x.
Wilson, R. (1987a). Auction theory. In J. Eatwell, M. Milgate, P. Newman (Eds.), The New Palgrave Dictionary of Economics, vol. I. London: Macmillan.
== External links ==
Auctions on GameTheory.net, also available on the Wayback Machine | Wikipedia/Auction_Theory |
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time. The field of approximation algorithms, therefore, tries to understand how closely it is possible to approximate optimal solutions to such problems in polynomial time. In an overwhelming majority of the cases, the guarantee of such algorithms is a multiplicative one expressed as an approximation ratio or approximation factor i.e., the optimal solution is always guaranteed to be within a (predetermined) multiplicative factor of the returned solution. However, there are also many approximation algorithms that provide an additive guarantee on the quality of the returned solution. A notable example of an approximation algorithm that provides both is the classic approximation algorithm of Lenstra, Shmoys and Tardos for scheduling on unrelated parallel machines.
The design and analysis of approximation algorithms crucially involves a mathematical proof certifying the quality of the returned solutions in the worst case. This distinguishes them from heuristics such as annealing or genetic algorithms, which find reasonably good solutions on some inputs, but provide no clear indication at the outset on when they may succeed or fail.
There is widespread interest in theoretical computer science to better understand the limits to which we can approximate certain famous optimization problems. For example, one of the long-standing open questions in computer science is to determine whether there is an algorithm that outperforms the 2-approximation for the Steiner Forest problem by Agrawal et al. The desire to understand hard optimization problems from the perspective of approximability is motivated by the discovery of surprising mathematical connections and broadly applicable techniques to design algorithms for hard optimization problems. One well-known example of the former is the Goemans–Williamson algorithm for maximum cut, which solves a graph theoretic problem using high dimensional geometry.
== Introduction ==
A simple example of an approximation algorithm is one for the minimum vertex cover problem, where the goal is to choose the smallest set of vertices such that every edge in the input graph contains at least one chosen vertex. One way to find a vertex cover is to repeat the following process: find an uncovered edge, add both its endpoints to the cover, and remove all edges incident to either vertex from the graph. As any vertex cover of the input graph must use a distinct vertex to cover each edge that was considered in the process (since it forms a matching), the vertex cover produced, therefore, is at most twice as large as the optimal one. In other words, this is a constant-factor approximation algorithm with an approximation factor of 2. Under the recent unique games conjecture, this factor is even the best possible one.
NP-hard problems vary greatly in their approximability; some, such as the knapsack problem, can be approximated within a multiplicative factor
1
+
ϵ
{\displaystyle 1+\epsilon }
, for any fixed
ϵ
>
0
{\displaystyle \epsilon >0}
, and therefore produce solutions arbitrarily close to the optimum (such a family of approximation algorithms is called a polynomial-time approximation scheme or PTAS). Others are impossible to approximate within any constant, or even polynomial, factor unless P = NP, as in the case of the maximum clique problem. Therefore, an important benefit of studying approximation algorithms is a fine-grained classification of the difficulty of various NP-hard problems beyond the one afforded by the theory of NP-completeness. In other words, although NP-complete problems may be equivalent (under polynomial-time reductions) to each other from the perspective of exact solutions, the corresponding optimization problems behave very differently from the perspective of approximate solutions.
== Algorithm design techniques ==
By now there are several established techniques to design approximation algorithms. These include the following ones.
Greedy algorithm
Local search
Enumeration and dynamic programming (which is also often used for parameterized approximations)
Solving a convex programming relaxation to get a fractional solution. Then converting this fractional solution into a feasible solution by some appropriate rounding. The popular relaxations include the following.
Linear programming relaxations
Semidefinite programming relaxations
Primal-dual methods
Dual fitting
Embedding the problem in some metric and then solving the problem on the metric. This is also known as metric embedding.
Random sampling and the use of randomness in general in conjunction with the methods above.
== A posteriori guarantees ==
While approximation algorithms always provide an a priori worst case guarantee (be it additive or multiplicative), in some cases they also provide an a posteriori guarantee that is often much better. This is often the case for algorithms that work by solving a convex relaxation of the optimization problem on the given input. For example, there is a different approximation algorithm for minimum vertex cover that solves a linear programming relaxation to find a vertex cover that is at most twice the value of the relaxation. Since the value of the relaxation is never larger than the size of the optimal vertex cover, this yields another 2-approximation algorithm. While this is similar to the a priori guarantee of the previous approximation algorithm, the guarantee of the latter can be much better (indeed when the value of the LP relaxation is far from the size of the optimal vertex cover).
== Hardness of approximation ==
Approximation algorithms as a research area is closely related to and informed by inapproximability theory where the non-existence of efficient algorithms with certain approximation ratios is proved (conditioned on widely believed hypotheses such as the P ≠ NP conjecture) by means of reductions. In the case of the metric traveling salesman problem, the best known inapproximability result rules out algorithms with an approximation ratio less than 123/122 ≈ 1.008196 unless P = NP, Karpinski, Lampis, Schmied. Coupled with the knowledge of the existence of Christofides' 1.5 approximation algorithm, this tells us that the threshold of approximability for metric traveling salesman (if it exists) is somewhere between 123/122 and 1.5.
While inapproximability results have been proved since the 1970s, such results were obtained by ad hoc means and no systematic understanding was available at the time. It is only since the 1990 result of Feige, Goldwasser, Lovász, Safra and Szegedy on the inapproximability of Independent Set and the famous PCP theorem, that modern tools for proving inapproximability results were uncovered. The PCP theorem, for example, shows that Johnson's 1974 approximation algorithms for Max SAT, set cover, independent set and coloring all achieve the optimal approximation ratio, assuming P ≠ NP.
== Practicality ==
Not all approximation algorithms are suitable for direct practical applications. Some involve solving non-trivial linear programming/semidefinite relaxations (which may themselves invoke the ellipsoid algorithm), complex data structures, or sophisticated algorithmic techniques, leading to difficult implementation issues or improved running time performance (over exact algorithms) only on impractically large inputs. Implementation and running time issues aside, the guarantees provided by approximation algorithms may themselves not be strong enough to justify their consideration in practice. Despite their inability to be used "out of the box" in practical applications, the ideas and insights behind the design of such algorithms can often be incorporated in other ways in practical algorithms. In this way, the study of even very expensive algorithms is not a completely theoretical pursuit as they can yield valuable insights.
In other cases, even if the initial results are of purely theoretical interest, over time, with an improved understanding, the algorithms may be refined to become more practical. One such example is the initial PTAS for Euclidean TSP by Sanjeev Arora (and independently by Joseph Mitchell) which had a prohibitive running time of
n
O
(
1
/
ϵ
)
{\displaystyle n^{O(1/\epsilon )}}
for a
1
+
ϵ
{\displaystyle 1+\epsilon }
approximation. Yet, within a year these ideas were incorporated into a near-linear time
O
(
n
log
n
)
{\displaystyle O(n\log n)}
algorithm for any constant
ϵ
>
0
{\displaystyle \epsilon >0}
.
== Structure of approximation algorithms ==
Given an optimization problem:
Π
:
I
×
S
{\displaystyle \Pi :I\times S}
where
Π
{\displaystyle \Pi }
is an approximation problem,
I
{\displaystyle I}
the set of inputs and
S
{\displaystyle S}
the set of solutions, we can define the cost function:
c
:
S
→
R
+
{\displaystyle c:S\rightarrow \mathbb {R} ^{+}}
and the set of feasible solutions:
∀
i
∈
I
,
S
(
i
)
=
s
∈
S
:
i
Π
s
{\displaystyle \forall i\in I,S(i)={s\in S:i\Pi _{s}}}
finding the best solution
s
∗
{\displaystyle s^{*}}
for a maximization or a minimization problem:
s
∗
∈
S
(
i
)
{\displaystyle s^{*}\in S(i)}
,
c
(
s
∗
)
=
m
i
n
/
m
a
x
c
(
S
(
i
)
)
{\displaystyle c(s^{*})=min/max\ c(S(i))}
Given a feasible solution
s
∈
S
(
i
)
{\displaystyle s\in S(i)}
, with
s
≠
s
∗
{\displaystyle s\neq s^{*}}
, we would want a guarantee of the quality of the solution, which is a performance to be guaranteed (approximation factor).
Specifically, having
A
Π
(
i
)
∈
S
i
{\displaystyle A_{\Pi }(i)\in S_{i}}
, the algorithm has an approximation factor (or approximation ratio) of
ρ
(
n
)
{\displaystyle \rho (n)}
if
∀
i
∈
I
s
.
t
.
|
i
|
=
n
{\displaystyle \forall i\in I\ s.t.|i|=n}
, we have:
for a minimization problem:
c
(
A
Π
(
i
)
)
c
(
s
∗
(
i
)
)
≤
ρ
(
n
)
{\displaystyle {\frac {c(A_{\Pi }(i))}{c(s^{*}(i))}}\leq \rho (n)}
, which in turn means the solution taken by the algorithm divided by the optimal solution achieves a ratio of
ρ
(
n
)
{\displaystyle \rho (n)}
;
for a maximization problem:
c
(
s
∗
(
i
)
)
c
(
A
Π
(
i
)
)
≤
ρ
(
n
)
{\displaystyle {\frac {c(s^{*}(i))}{c(A_{\Pi }(i))}}\leq \rho (n)}
, which in turn means the optimal solution divided by the solution taken by the algorithm achieves a ratio of
ρ
(
n
)
{\displaystyle \rho (n)}
;
The approximation can be proven tight (tight approximation) by demonstrating that there exist instances where the algorithm performs at the approximation limit, indicating the tightness of the bound. In this case, it's enough to construct an input instance designed to force the algorithm into a worst-case scenario.
== Performance guarantees ==
For some approximation algorithms it is possible to prove certain properties about the approximation of the optimum result. For example, a ρ-approximation algorithm A is defined to be an algorithm for which it has been proven that the value/cost, f(x), of the approximate solution A(x) to an instance x will not be more (or less, depending on the situation) than a factor ρ times the value, OPT, of an optimum solution.
{
O
P
T
≤
f
(
x
)
≤
ρ
O
P
T
,
if
ρ
>
1
;
ρ
O
P
T
≤
f
(
x
)
≤
O
P
T
,
if
ρ
<
1.
{\displaystyle {\begin{cases}\mathrm {OPT} \leq f(x)\leq \rho \mathrm {OPT} ,\qquad {\mbox{if }}\rho >1;\\\rho \mathrm {OPT} \leq f(x)\leq \mathrm {OPT} ,\qquad {\mbox{if }}\rho <1.\end{cases}}}
The factor ρ is called the relative performance guarantee. An approximation algorithm has an absolute performance guarantee or bounded error c, if it has been proven for every instance x that
(
O
P
T
−
c
)
≤
f
(
x
)
≤
(
O
P
T
+
c
)
.
{\displaystyle (\mathrm {OPT} -c)\leq f(x)\leq (\mathrm {OPT} +c).}
Similarly, the performance guarantee, R(x,y), of a solution y to an instance x is defined as
R
(
x
,
y
)
=
max
(
O
P
T
f
(
y
)
,
f
(
y
)
O
P
T
)
,
{\displaystyle R(x,y)=\max \left({\frac {OPT}{f(y)}},{\frac {f(y)}{OPT}}\right),}
where f(y) is the value/cost of the solution y for the instance x. Clearly, the performance guarantee is greater than or equal to 1 and equal to 1 if and only if y is an optimal solution. If an algorithm A guarantees to return solutions with a performance guarantee of at most r(n), then A is said to be an r(n)-approximation algorithm and has an approximation ratio of r(n). Likewise, a problem with an r(n)-approximation algorithm is said to be r(n)-approximable or have an approximation ratio of r(n).
For minimization problems, the two different guarantees provide the same result and that for maximization problems, a relative performance guarantee of ρ is equivalent to a performance guarantee of
r
=
ρ
−
1
{\displaystyle r=\rho ^{-1}}
. In the literature, both definitions are common but it is clear which definition is used since, for maximization problems, as ρ ≤ 1 while r ≥ 1.
The absolute performance guarantee
P
A
{\displaystyle \mathrm {P} _{A}}
of some approximation algorithm A, where x refers to an instance of a problem, and where
R
A
(
x
)
{\displaystyle R_{A}(x)}
is the performance guarantee of A on x (i.e. ρ for problem instance x) is:
P
A
=
inf
{
r
≥
1
∣
R
A
(
x
)
≤
r
,
∀
x
}
.
{\displaystyle \mathrm {P} _{A}=\inf\{r\geq 1\mid R_{A}(x)\leq r,\forall x\}.}
That is to say that
P
A
{\displaystyle \mathrm {P} _{A}}
is the largest bound on the approximation ratio, r, that one sees over all possible instances of the problem. Likewise, the asymptotic performance ratio
R
A
∞
{\displaystyle R_{A}^{\infty }}
is:
R
A
∞
=
inf
{
r
≥
1
∣
∃
n
∈
Z
+
,
R
A
(
x
)
≤
r
,
∀
x
,
|
x
|
≥
n
}
.
{\displaystyle R_{A}^{\infty }=\inf\{r\geq 1\mid \exists n\in \mathbb {Z} ^{+},R_{A}(x)\leq r,\forall x,|x|\geq n\}.}
That is to say that it is the same as the absolute performance ratio, with a lower bound n on the size of problem instances. These two types of ratios are used because there exist algorithms where the difference between these two is significant.
== Epsilon terms ==
In the literature, an approximation ratio for a maximization (minimization) problem of c - ϵ (min: c + ϵ) means that the algorithm has an approximation ratio of c ∓ ϵ for arbitrary ϵ > 0 but that the ratio has not (or cannot) be shown for ϵ = 0. An example of this is the optimal inapproximability — inexistence of approximation — ratio of 7 / 8 + ϵ for satisfiable MAX-3SAT instances due to Johan Håstad. As mentioned previously, when c = 1, the problem is said to have a polynomial-time approximation scheme.
An ϵ-term may appear when an approximation algorithm introduces a multiplicative error and a constant error while the minimum optimum of instances of size n goes to infinity as n does. In this case, the approximation ratio is c ∓ k / OPT = c ∓ o(1) for some constants c and k. Given arbitrary ϵ > 0, one can choose a large enough N such that the term k / OPT < ϵ for every n ≥ N. For every fixed ϵ, instances of size n < N can be solved by brute force, thereby showing an approximation ratio — existence of approximation algorithms with a guarantee — of c ∓ ϵ for every ϵ > 0.
== See also ==
Domination analysis considers guarantees in terms of the rank of the computed solution.
PTAS - a type of approximation algorithm that takes the approximation ratio as a parameter
Parameterized approximation algorithm - a type of approximation algorithm that runs in FPT time
APX is the class of problems with some constant-factor approximation algorithm
Approximation-preserving reduction
Exact algorithm
== Citations ==
== References ==
Vazirani, Vijay V. (2003). Approximation Algorithms. Berlin: Springer. ISBN 978-3-540-65367-7.
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, Second Edition. MIT Press and McGraw-Hill, 2001. ISBN 0-262-03293-7. Chapter 35: Approximation Algorithms, pp. 1022–1056.
Dorit S. Hochbaum, ed. Approximation Algorithms for NP-Hard problems, PWS Publishing Company, 1997. ISBN 0-534-94968-1. Chapter 9: Various Notions of Approximations: Good, Better, Best, and More
Williamson, David P.; Shmoys, David B. (April 26, 2011), The Design of Approximation Algorithms, Cambridge University Press, ISBN 978-0521195270
== External links ==
Pierluigi Crescenzi, Viggo Kann, Magnús Halldórsson, Marek Karpinski and Gerhard Woeginger, A compendium of NP optimization problems. | Wikipedia/Approximation_ratio |
A reputation system is a program or algorithm that allow users of an online community to rate each other in order to build trust through reputation. Some common uses of these systems can be found on E-commerce websites such as eBay, Amazon.com, and Etsy as well as online advice communities such as Stack Exchange. These reputation systems represent a significant trend in "decision support for Internet mediated service provisions". With the popularity of online communities for shopping, advice, and exchange of other important information, reputation systems are becoming vitally important to the online experience. The idea of reputation systems is that even if the consumer can't physically try a product or service, or see the person providing information, that they can be confident in the outcome of the exchange through trust built by recommender systems.
Collaborative filtering, used most commonly in recommender systems, are related to reputation systems in that they both collect ratings from members of a community. The core difference between reputation systems and collaborative filtering is the ways in which they use user feedback. In collaborative filtering, the goal is to find similarities between users in order to recommend products to customers. The role of reputation systems, in contrast, is to gather a collective opinion in order to build trust between users of an online community.
== Types ==
=== Online ===
Howard Rheingold states that online reputation systems are "computer-based technologies that make it possible to manipulate in new and powerful ways an old and essential human trait". Rheingold says that these systems arose as a result of the need for Internet users to gain trust in the individuals they transact with online. The trait he notes in human groups is that social functions such as gossip "keeps us up to date on who to trust, who other people trust, who is important, and who decides who is important". Internet sites such as eBay and Amazon, he argues, seek to make use of this social trait and are "built around the contributions of millions of customers, enhanced by reputation systems that police the quality of the content and transactions exchanged through the site".
=== Reputation banks ===
The emerging sharing economy increases the importance of trust in peer-to-peer marketplaces and services. Users can build up reputation and trust in individual systems but usually don't have the ability to carry those reputations to other systems. Rachel Botsman and Roo Rogers argue in their book What's Mine is Yours (2010), that "it is only a matter of time before there is some form of network that aggregates reputation capital across multiple forms of Collaborative Consumption". These systems, often referred to as reputation banks, try to give users a platform to manage their reputation capital across multiple systems.
== Maintaining effective reputation systems ==
The main function of reputation systems is to build a sense of trust among users of online communities. As with brick and mortar stores, trust and reputation can be built through customer feedback. Paul Resnick from the Association for Computing Machinery describes three properties that are necessary for reputation systems to operate effectively.
Entities must have a long lifetime and create accurate expectations of future interactions.
They must capture and distribute feedback about prior interactions.
They must use feedback to guide trust.
These three properties are critically important in building reliable reputations, and all revolve around one important element: user feedback. User feedback in reputation systems, whether it be in the form of comments, ratings, or recommendations, is a valuable piece of information. Without user feedback, reputation systems cannot sustain an environment of trust.
Eliciting user feedback can have three related problems.
The first of these problems is the willingness of users to provide feedback when the option to do so is not required. If an online community has a large stream of interactions happening, but no feedback is gathered, the environment of trust and reputation cannot be formed.
The second of these problems is gaining negative feedback from users. Many factors contribute to users not wanting to give negative feedback, the most prominent being a fear of retaliation. When feedback is not anonymous, many users fear retaliation if negative feedback is given.
The final problem related to user feedback is eliciting honest feedback from users. Although there is no concrete method for ensuring the truthfulness of feedback, if a community of honest feedback is established, new users will be more likely to give honest feedback as well.
Other pitfalls to effective reputation systems described by A. Josang et al. include change of identities and discrimination. Again these ideas tie back to the idea of regulating user actions in order to gain accurate and consistent user feedback. When analyzing different types of reputation systems it is important to look at these specific features in order to determine the effectiveness of each system.
=== Standardization attempt ===
The IETF proposed a protocol to exchange reputation data. It was originally aimed at email applications, but it was subsequently developed as a general architecture for a reputation-based service, followed by an email-specific part. However, the workhorse of email reputation remains with DNSxL's, which do not follow that protocol. Those specification don't say how to collect feedback —in fact, the granularity of email sending entities makes it impractical to collect feedback directly from recipients— but are only concerned with reputation query/response methods.
== Notable examples of practical applications ==
Search: web (see PageRank)
eCommerce: eBay, Epinions, Bizrate, Trustpilot
Social news: Reddit, Digg, Imgur
Programming communities: Advogato, freelance marketplaces, Stack Overflow
Wikis: Increase contribution quantity and quality
Internet Security: TrustedSource
Question-and-Answer sites: Quora, Yahoo! Answers, Gutefrage.net, Stack Exchange
Email: DNSBL and DNSWL provide global reputation about email senders
Personal Reputation: CouchSurfing (for travelers),
Non Governmental organizations (NGOs): GreatNonProfits.org, GlobalGiving
Professional reputation of translators and translation outsourcers: BlueBoard at ProZ.com
All purpose reputation system: Yelp, Inc.
Academia: general bibliometric measures, e.g. the h-index of a researcher.
== Reputation as a resource ==
High reputation capital often confers benefits upon the holder. For example, a wide range of studies have found a positive correlation between seller rating and selling price on eBay, indicating that high reputation can help users obtain more money for their items. High product reviews on online marketplaces can also help drive higher sales volumes.
Abstract reputation can be used as a kind of resource, to be traded away for short-term gains or built up by investing effort. For example, a company with a good reputation may sell lower-quality products for higher profit until their reputation falls, or they may sell higher-quality products to increase their reputation. Some reputation systems go further, making it explicitly possible to spend reputation within the system to derive a benefit. For example, on the Stack Overflow community, reputation points can be spent on question "bounties" to incentivize other users to answer the question.
Even without an explicit spending mechanism in place, reputation systems often make it easier for users to spend their reputation without harming it excessively. For example, a ridesharing company driver with a high ride acceptance score (a metric often used for driver reputation) may opt to be more selective about his or her clientele, decreasing the driver's acceptance score but improving his or her driving experience. With the explicit feedback provided by the service, drivers can carefully manage their selectivity to avoid being penalized too heavily.
== Attacks and defense ==
Reputation systems are in general vulnerable to attacks, and many types of attacks are possible. As the reputation system tries to generate an accurate assessment based on various factors including but not limited to unpredictable user size and potential adversarial environments, the attacks and defense mechanisms play an important role in the reputation systems.
Attack classification of reputation system is based on identifying which system components and design choices are the targets of attacks. While the defense mechanisms are concluded based on existing reputation systems.
=== Attacker model ===
The capability of the attacker is determined by several characteristics, e.g., the location of the attacker related to the system (insider attacker vs. outsider attacker). An insider is an entity who has legitimate access to the system and can participate according to the system specifications, while an outsider is any unauthorized entity in the system who may or may not be identifiable.
As the outsider attack is much more similar to other attacks in a computer system environment, the insider attack gets more focus in the reputation system. Usually, there are some common assumptions: the attackers are motivated either by selfish or malicious intent and the attackers can either work alone or in coalitions.
=== Attack classification ===
Attacks against reputation systems are classified based on the goals and methods of the attacker.
Self-promoting Attack. The attacker falsely increases their own reputation. A typical example is the so-called Sybil attack where an attacker subverts the reputation system by creating a large number of pseudonymous entities, and using them to gain a disproportionately large influence. A reputation system's vulnerability to a Sybil attack depends on how cheaply Sybils can be generated, the degree to which the reputation system accepts input from entities that do not have a chain of trust linking them to a trusted entity, and whether the reputation system treats all entities identically.
Whitewashing Attack. The attacker uses some system vulnerability to update their reputation. This attack usually targets the reputation system's formulation that is used to calculate the reputation result. The whitewashing attack can be combined with other types of attacks to make each one more effective.
Slandering Attack. The attacker reports false data to lower the reputation of the victim nodes. It can be achieved by a single attacker or a coalition of attackers.
Orchestrated Attack. The attacker orchestrates their efforts and employs several of the above strategies. One famous example of an orchestrated attack is known as an oscillation attack.
Denial of Service Attack. The attacker prevents the calculation and dissemination of reputation values in reputation systems by using Denial of Service method.
=== Defense strategies ===
Here are some strategies to prevent the above attacks.
Preventing Multiple Identities
Mitigating Generation of False Rumors
Mitigating Spreading of False Rumors
Preventing Short-Term Abuse of the System
Mitigating Denial of Service Attacks
== See also ==
== References ==
Dellarocas, C. (2003). "The Digitization of Word-of-Mouth: Promise and Challenges of Online Reputation Mechanisms" (PDF). Management Science. 49 (10): 1407–1424. doi:10.1287/mnsc.49.10.1407.17308. hdl:1721.1/1851.
Vavilis, S.; Petković, M.; Zannone, N. (2014). "A reference model for reputation systems" (PDF). Decision Support Systems. 61: 147–154. doi:10.1016/j.dss.2014.02.002. Archived from the original (PDF) on 2017-07-13. Retrieved 2014-06-03.
D. Quercia, S. Hailes, L. Capra. Lightweight Distributed Trust Propagation. ICDM 2007.
R. Guha, R. Kumar, P. Raghavan, A. Tomkins. Propagation of Trust and Distrust WWW2004.
A. Cheng, E. Friedman. Sybilproof reputation mechanisms SIGCOMM workshop on Economics of peer-to-peer systems, 2005.
Hamed Alhoori, Omar Alvarez, Richard Furuta, Miguel Muñiz, Eduardo Urbina: Supporting the Creation of Scholarly Bibliographies by Communities through Online Reputation Based Social Collaboration. ECDL 2009: 180-191
Sybil Attacks Against Mobile Users: Friends and Foes to the Rescue by Daniele Quercia and Stephen Hailes. IEEE INFOCOM 2010.
J.R. Douceur. The Sybil Attack . IPTPS02 2002.
Hoffman, K.; Zage, D.; Nita-Rotaru, C. (2009). "A survey of attack and defense techniques for reputation systems". ACM Computing Surveys. 42 (1): 1. CiteSeerX 10.1.1.172.8253. doi:10.1145/1592451.1592452. S2CID 2294541.
Rheingold, Howard (2002). Smart Mobs: The Next Social Revolution. Perseus, Cambridge, Massachusetts.
Cattalibys, K. (2010). "I could be someone else - social networks, pseudonyms and sockpuppets". Schizoaffective Disorders. 49 (3).
Zhang, Jie; Cohen, Robin (2006). Trusting Advice from Other Buyers in E-Marketplaces: The Problem of Unfair Ratings (PDF). Proceedings of the Eighth International Conference on Electronic Commerce (ICEC). New Brunswick, Canada.
== External links ==
Reputation Systems - 2008 tutorial by Yury Lifshits
Contracts in Cyberspace - 2008 essay (book chapter) by David D. Friedman. | Wikipedia/Reputation_systems |
A multi-agent system (MAS or "self-organized system") is a computerized system composed of multiple interacting intelligent agents. Multi-agent systems can solve problems that are difficult or impossible for an individual agent or a monolithic system to solve. Intelligence may include methodic, functional, procedural approaches, algorithmic search or reinforcement learning. With advancements in large language models (LLMs), LLM-based multi-agent systems have emerged as a new area of research, enabling more sophisticated interactions and coordination among agents.
Despite considerable overlap, a multi-agent system is not always the same as an agent-based model (ABM). The goal of an ABM is to search for explanatory insight into the collective behavior of agents (which do not necessarily need to be "intelligent") obeying simple rules, typically in natural systems, rather than in solving specific practical or engineering problems. The terminology of ABM tends to be used more often in the science, and MAS in engineering and technology. Applications where multi-agent systems research may deliver an appropriate approach include online trading, disaster response, target surveillance and social structure modelling.
== Concept ==
Multi-agent systems consist of agents and their environment. Typically multi-agent systems research refers to software agents. However, the agents in a multi-agent system could equally well be robots, humans or human teams. A multi-agent system may contain combined human-agent teams.
Agents can be divided into types spanning simple to complex. Categories include:
Passive agents or "agent without goals" (such as obstacle, apple or key in any simple simulation)
Active agents with simple goals (like birds in flocking, or wolf–sheep in prey-predator model)
Cognitive agents (complex calculations)
Agent environments can be divided into:
Virtual
Discrete
Continuous
Agent environments can also be organized according to properties such as accessibility (whether it is possible to gather complete information about the environment), determinism (whether an action causes a definite effect), dynamics (how many entities influence the environment in the moment), discreteness (whether the number of possible actions in the environment is finite), episodicity (whether agent actions in certain time periods influence other periods), and dimensionality (whether spatial characteristics are important factors of the environment and the agent considers space in its decision making). Agent actions are typically mediated via an appropriate middleware. This middleware offers a first-class design abstraction for multi-agent systems, providing means to govern resource access and agent coordination.
=== Characteristics ===
The agents in a multi-agent system have several important characteristics:
Autonomy: agents at least partially independent, self-aware, autonomous
Local views: no agent has a full global view, or the system is too complex for an agent to exploit such knowledge
Decentralization: no agent is designated as controlling (or the system is effectively reduced to a monolithic system)
=== Self-organisation and self-direction ===
Multi-agent systems can manifest self-organisation as well as self-direction and other control paradigms and related complex behaviors even when the individual strategies of all their agents are simple. When agents can share knowledge using any agreed language, within the constraints of the system's communication protocol, the approach may lead to a common improvement. Example languages are Knowledge Query Manipulation Language (KQML) or Agent Communication Language (ACL).
=== System paradigms ===
Many MAS are implemented in computer simulations, stepping the system through discrete "time steps". The MAS components communicate typically using a weighted request matrix, e.g.
Speed-VERY_IMPORTANT: min=45 mph,
Path length-MEDIUM_IMPORTANCE: max=60 expectedMax=40,
Max-Weight-UNIMPORTANT
Contract Priority-REGULAR
and a weighted response matrix, e.g.
Speed-min:50 but only if weather sunny,
Path length:25 for sunny / 46 for rainy
Contract Priority-REGULAR
note – ambulance will override this priority and you'll have to wait
A challenge-response-contract scheme is common in MAS systems, where
First a "Who can?" question is distributed.
Only the relevant components respond: "I can, at this price".
Finally, a contract is set up, usually in several short communication steps between sides,
also considering other components, evolving "contracts" and the restriction sets of the component algorithms.
Another paradigm commonly used with MAS is the "pheromone", where components leave information for other nearby components. These pheromones may evaporate/concentrate with time, that is their values may decrease (or increase).
=== Properties ===
MAS tend to find the best solution for their problems without intervention. There is high similarity here to physical phenomena, such as energy minimizing, where physical objects tend to reach the lowest energy possible within the physically constrained world. For example: many of the cars entering a metropolis in the morning will be available for leaving that same metropolis in the evening.
The systems also tend to prevent propagation of faults, self-recover and be fault tolerant, mainly due to the redundancy of components.
== Research ==
The study of multi-agent systems is "concerned with the development and analysis of sophisticated AI problem-solving and control architectures for both single-agent and multiple-agent systems." Research topics include:
agent-oriented software engineering
beliefs, desires, and intentions (BDI)
cooperation and coordination
distributed constraint optimization (DCOPs)
organization
communication
negotiation
distributed problem solving
multi-agent learning
agent mining
scientific communities (e.g., on biological flocking, language evolution, and economics)
dependability and fault-tolerance
robotics, multi-robot systems (MRS), robotic clusters
multi-agent systems also present possible applications in microrobotics, where the physical interaction between the agents are exploited to perform complex tasks such as manipulation and assembly of passive components.
language model-based multi-agent systems
== Frameworks ==
Frameworks have emerged that implement common standards (such as the FIPA and OMG MASIF standards). These frameworks e.g. JADE, save time and aid in the standardization of MAS development.
Currently though, no standard is actively maintained from FIPA or OMG. Efforts for further development of software agents in industrial context are carried out in IEEE IES technical committee on Industrial Agents.
With advancements in large language models (LLMs) such as ChatGPT, LLM-based multi-agent frameworks, such as CAMEL, have emerged as a new paradigm for developing multi-agent applications.
== Applications ==
MAS have not only been applied in academic research, but also in industry. MAS are applied in the real world to graphical applications such as computer games. Agent systems have been used in films. It is widely advocated for use in networking and mobile technologies, to achieve automatic and dynamic load balancing, high scalability and self-healing networks. They are being used for coordinated defence systems.
Other applications include transportation, logistics, graphics, manufacturing, power system, smartgrids, and the GIS.
Also, Multi-agent Systems Artificial Intelligence (MAAI) are used for simulating societies, the purpose thereof being helpful in the fields of climate, energy, epidemiology, conflict management, child abuse, ....
Some organisations working on using multi-agent system models include Center for Modelling Social Systems, Centre for Research in Social Simulation, Centre for Policy Modelling, Society for Modelling and Simulation International.
Vehicular traffic with controlled autonomous vehicles can be modelling as a multi-agent system involving crowd dynamics.
Hallerbach et al. discussed the application of agent-based approaches for the development and validation of automated driving systems via a digital twin of the vehicle-under-test and microscopic traffic simulation based on independent agents. Waymo has created a multi-agent simulation environment Carcraft to test algorithms for self-driving cars. It simulates traffic interactions between human drivers, pedestrians and automated vehicles. People's behavior is imitated by artificial agents based on data of real human behavior.
== See also ==
== References ==
== Further reading ==
Wooldridge, Michael (2002). An Introduction to MultiAgent Systems. John Wiley & Sons. p. 366. ISBN 978-0-471-49691-5.
Shoham, Yoav; Leyton-Brown, Kevin (2008). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press. p. 496. ISBN 978-0-521-89943-7.
Mamadou, Tadiou Koné; Shimazu, A.; Nakajima, T. (August 2000). "The State of the Art in Agent Communication Languages (ACL)". Knowledge and Information Systems. 2 (2): 1–26.
Hewitt, Carl; Inman, Jeff (November–December 1991). "DAI Betwixt and Between: From "Intelligent Agents" to Open Systems Science" (PDF). IEEE Transactions on Systems, Man, and Cybernetics. 21 (6): 1409–1419. doi:10.1109/21.135685. S2CID 39080989. Archived from the original (PDF) on August 31, 2017.
The Journal of Autonomous Agents and Multi-Agent Systems (JAAMAS)
Weiss, Gerhard, ed. (1999). Multiagent Systems, A Modern Approach to Distributed Artificial Intelligence. MIT Press. ISBN 978-0-262-23203-6.
Ferber, Jacques (1999). Multi-Agent Systems: An Introduction to Artificial Intelligence. Addison-Wesley. ISBN 978-0-201-36048-6.
Weyns, Danny (2010). Architecture-Based Design of Multi-Agent Systems. Springer. ISBN 978-3-642-01063-7.
Sun, Ron (2006). Cognition and Multi-Agent Interaction. Cambridge University Press. ISBN 978-0-521-83964-8.
Keil, David; Goldin, Dina (2006). Weyns, Danny; Parunak, Van; Michel, Fabien (eds.). Indirect Interaction in Environments for Multiagent Systems. LNCS 3830. Vol. 3830. Springer. pp. 68–87. doi:10.1007/11678809_5. ISBN 978-3-540-32614-4. {{cite book}}: |journal= ignored (help)
Whitestein Series in Software Agent Technologies and Autonomic Computing, published by Springer Science+Business Media Group
Salamon, Tomas (2011). Design of Agent-Based Models : Developing Computer Simulations for a Better Understanding of Social Processes. Bruckner Publishing. ISBN 978-80-904661-1-1.
Russell, Stuart J.; Norvig, Peter (2003), Artificial Intelligence: A Modern Approach (2nd ed.), Upper Saddle River, New Jersey: Prentice Hall, ISBN 0-13-790395-2
Fasli, Maria (2007). Agent-technology for E-commerce. John Wiley & Sons. p. 480. ISBN 978-0-470-03030-1.
Cao, Longbing, Gorodetsky, Vladimir, Mitkas, Pericles A. (2009). Agent Mining: The Synergy of Agents and Data Mining, IEEE Intelligent Systems, vol. 24, no. 3, 64-72. | Wikipedia/Multi-agent_systems |
Vapnik–Chervonenkis theory (also known as VC theory) was developed during 1960–1990 by Vladimir Vapnik and Alexey Chervonenkis. The theory is a form of computational learning theory, which attempts to explain the learning process from a statistical point of view.
== Introduction ==
VC theory covers at least four parts (as explained in The Nature of Statistical Learning Theory):
Theory of consistency of learning processes
What are (necessary and sufficient) conditions for consistency of a learning process based on the empirical risk minimization principle?
Nonasymptotic theory of the rate of convergence of learning processes
How fast is the rate of convergence of the learning process?
Theory of controlling the generalization ability of learning processes
How can one control the rate of convergence (the generalization ability) of the learning process?
Theory of constructing learning machines
How can one construct algorithms that can control the generalization ability?
VC Theory is a major subbranch of statistical learning theory. One of its main applications in statistical learning theory is to provide generalization conditions for learning algorithms. From this point of view, VC theory is related to stability, which is an alternative approach for characterizing generalization.
In addition, VC theory and VC dimension are instrumental in the theory of empirical processes, in the case of processes indexed by VC classes. Arguably these are the most important applications of the VC theory, and are employed in proving generalization. Several techniques will be introduced that are widely used in the empirical process and VC theory. The discussion is mainly based on the book Weak Convergence and Empirical Processes: With Applications to Statistics.
== Overview of VC theory in empirical processes ==
=== Background on empirical processes ===
Let
(
X
,
A
)
{\displaystyle ({\mathcal {X}},{\mathcal {A}})}
be a measurable space. For any measure
Q
{\displaystyle Q}
on
(
X
,
A
)
{\displaystyle ({\mathcal {X}},{\mathcal {A}})}
, and any measurable functions
f
:
X
→
R
{\displaystyle f:{\mathcal {X}}\to \mathbf {R} }
, define
Q
f
=
∫
f
d
Q
{\displaystyle Qf=\int fdQ}
Measurability issues will be ignored here, for more technical detail see. Let
F
{\displaystyle {\mathcal {F}}}
be a class of measurable functions
f
:
X
→
R
{\displaystyle f:{\mathcal {X}}\to \mathbf {R} }
and define:
‖
Q
‖
F
=
sup
{
|
Q
f
|
:
f
∈
F
}
.
{\displaystyle \|Q\|_{\mathcal {F}}=\sup\{\vert Qf\vert \ :\ f\in {\mathcal {F}}\}.}
Let
X
1
,
…
,
X
n
{\displaystyle X_{1},\ldots ,X_{n}}
be independent, identically distributed random elements of
(
X
,
A
)
{\displaystyle ({\mathcal {X}},{\mathcal {A}})}
. Then define the empirical measure
P
n
=
n
−
1
∑
i
=
1
n
δ
X
i
,
{\displaystyle \mathbb {P} _{n}=n^{-1}\sum _{i=1}^{n}\delta _{X_{i}},}
where δ here stands for the Dirac measure. The empirical measure induces a map
F
→
R
{\displaystyle {\mathcal {F}}\to \mathbf {R} }
given by:
f
↦
P
n
f
=
1
n
(
f
(
X
1
)
+
.
.
.
+
f
(
X
n
)
)
{\displaystyle f\mapsto \mathbb {P} _{n}f={\frac {1}{n}}(f(X_{1})+...+f(X_{n}))}
Now suppose P is the underlying true distribution of the data, which is unknown. Empirical Processes theory aims at identifying classes
F
{\displaystyle {\mathcal {F}}}
for which statements such as the following hold:
uniform law of large numbers:
‖
P
n
−
P
‖
F
→
n
0
,
{\displaystyle \|\mathbb {P} _{n}-P\|_{\mathcal {F}}{\underset {n}{\to }}0,}
That is, as
n
→
∞
{\displaystyle n\to \infty }
,
|
1
n
(
f
(
X
1
)
+
.
.
.
+
f
(
X
n
)
)
−
∫
f
d
P
|
→
0
{\displaystyle \left|{\frac {1}{n}}(f(X_{1})+...+f(X_{n}))-\int fdP\right|\to 0}
uniformly for all
f
∈
F
{\displaystyle f\in {\mathcal {F}}}
.
uniform central limit theorem:
G
n
=
n
(
P
n
−
P
)
⇝
G
,
in
ℓ
∞
(
F
)
{\displaystyle \mathbb {G} _{n}={\sqrt {n}}(\mathbb {P} _{n}-P)\rightsquigarrow \mathbb {G} ,\quad {\text{in }}\ell ^{\infty }({\mathcal {F}})}
In the former case
F
{\displaystyle {\mathcal {F}}}
is called Glivenko–Cantelli class, and in the latter case (under the assumption
∀
x
,
sup
f
∈
F
|
f
(
x
)
−
P
f
|
<
∞
{\displaystyle \forall x,\sup \nolimits _{f\in {\mathcal {F}}}\vert f(x)-Pf\vert <\infty }
) the class
F
{\displaystyle {\mathcal {F}}}
is called Donsker or P-Donsker. A Donsker class is Glivenko–Cantelli in probability by an application of Slutsky's theorem .
These statements are true for a single
f
{\displaystyle f}
, by standard LLN, CLT arguments under regularity conditions, and the difficulty in the Empirical Processes comes in because joint statements are being made for all
f
∈
F
{\displaystyle f\in {\mathcal {F}}}
. Intuitively then, the set
F
{\displaystyle {\mathcal {F}}}
cannot be too large, and as it turns out that the geometry of
F
{\displaystyle {\mathcal {F}}}
plays a very important role.
One way of measuring how big the function set
F
{\displaystyle {\mathcal {F}}}
is to use the so-called covering numbers. The covering number
N
(
ε
,
F
,
‖
⋅
‖
)
{\displaystyle N(\varepsilon ,{\mathcal {F}},\|\cdot \|)}
is the minimal number of balls
{
g
:
‖
g
−
f
‖
<
ε
}
{\displaystyle \{g:\|g-f\|<\varepsilon \}}
needed to cover the set
F
{\displaystyle {\mathcal {F}}}
(here it is obviously assumed that there is an underlying norm on
F
{\displaystyle {\mathcal {F}}}
). The entropy is the logarithm of the covering number.
Two sufficient conditions are provided below, under which it can be proved that the set
F
{\displaystyle {\mathcal {F}}}
is Glivenko–Cantelli or Donsker.
A class
F
{\displaystyle {\mathcal {F}}}
is P-Glivenko–Cantelli if it is P-measurable with envelope F such that
P
∗
F
<
∞
{\displaystyle P^{\ast }F<\infty }
and satisfies:
∀
ε
>
0
sup
Q
N
(
ε
‖
F
‖
Q
,
F
,
L
1
(
Q
)
)
<
∞
.
{\displaystyle \forall \varepsilon >0\quad \sup \nolimits _{Q}N(\varepsilon \|F\|_{Q},{\mathcal {F}},L_{1}(Q))<\infty .}
The next condition is a version of the celebrated Dudley's theorem. If
F
{\displaystyle {\mathcal {F}}}
is a class of functions such that
∫
0
∞
sup
Q
log
N
(
ε
‖
F
‖
Q
,
2
,
F
,
L
2
(
Q
)
)
d
ε
<
∞
{\displaystyle \int _{0}^{\infty }\sup \nolimits _{Q}{\sqrt {\log N\left(\varepsilon \|F\|_{Q,2},{\mathcal {F}},L_{2}(Q)\right)}}d\varepsilon <\infty }
then
F
{\displaystyle {\mathcal {F}}}
is P-Donsker for every probability measure P such that
P
∗
F
2
<
∞
{\displaystyle P^{\ast }F^{2}<\infty }
. In the last integral, the notation means
‖
f
‖
Q
,
2
=
(
∫
|
f
|
2
d
Q
)
1
2
{\displaystyle \|f\|_{Q,2}=\left(\int |f|^{2}dQ\right)^{\frac {1}{2}}}
.
=== Symmetrization ===
The majority of the arguments of how to bound the empirical process rely on symmetrization, maximal and concentration inequalities, and chaining. Symmetrization is usually the first step of the proofs, and since it is used in many machine learning proofs on bounding empirical loss functions (including the proof of the VC inequality which is discussed in the next section) it is presented here.
Consider the empirical process:
f
↦
(
P
n
−
P
)
f
=
1
n
∑
i
=
1
n
(
f
(
X
i
)
−
P
f
)
{\displaystyle f\mapsto (\mathbb {P} _{n}-P)f={\dfrac {1}{n}}\sum _{i=1}^{n}(f(X_{i})-Pf)}
Turns out that there is a connection between the empirical and the following symmetrized process:
f
↦
P
n
0
f
=
1
n
∑
i
=
1
n
ε
i
f
(
X
i
)
{\displaystyle f\mapsto \mathbb {P} _{n}^{0}f={\dfrac {1}{n}}\sum _{i=1}^{n}\varepsilon _{i}f(X_{i})}
The symmetrized process is a Rademacher process, conditionally on the data
X
i
{\displaystyle X_{i}}
. Therefore, it is a sub-Gaussian process by Hoeffding's inequality.
Lemma (Symmetrization). For every nondecreasing, convex Φ: R → R and class of measurable functions
F
{\displaystyle {\mathcal {F}}}
,
E
Φ
(
‖
P
n
−
P
‖
F
)
≤
E
Φ
(
2
‖
P
n
0
‖
F
)
{\displaystyle \mathbb {E} \Phi (\|\mathbb {P} _{n}-P\|_{\mathcal {F}})\leq \mathbb {E} \Phi \left(2\left\|\mathbb {P} _{n}^{0}\right\|_{\mathcal {F}}\right)}
The proof of the Symmetrization lemma relies on introducing independent copies of the original variables
X
i
{\displaystyle X_{i}}
(sometimes referred to as a ghost sample) and replacing the inner expectation of the LHS by these copies. After an application of Jensen's inequality different signs could be introduced (hence the name symmetrization) without changing the expectation. The proof can be found below because of its instructive nature. The same proof method can be used to prove the Glivenko–Cantelli theorem.
A typical way of proving empirical CLTs, first uses symmetrization to pass the empirical process to
P
n
0
{\displaystyle \mathbb {P} _{n}^{0}}
and then argue conditionally on the data, using the fact that Rademacher processes are simple processes with nice properties.
=== VC Connection ===
It turns out that there is a fascinating connection between certain combinatorial properties of the set
F
{\displaystyle {\mathcal {F}}}
and the entropy numbers. Uniform covering numbers can be controlled by the notion of Vapnik–Chervonenkis classes of sets – or shortly VC sets.
Consider a collection
C
{\displaystyle {\mathcal {C}}}
of subsets of the sample space
X
{\displaystyle {\mathcal {X}}}
.
C
{\displaystyle {\mathcal {C}}}
is said to pick out a certain subset
W
{\displaystyle W}
of the finite set
S
=
{
x
1
,
…
,
x
n
}
⊂
X
{\displaystyle S=\{x_{1},\ldots ,x_{n}\}\subset {\mathcal {X}}}
if
W
=
S
∩
C
{\displaystyle W=S\cap C}
for some
C
∈
C
{\displaystyle C\in {\mathcal {C}}}
.
C
{\displaystyle {\mathcal {C}}}
is said to shatter S if it picks out each of its 2n subsets. The VC-index (similar to VC dimension + 1 for an appropriately chosen classifier set)
V
(
C
)
{\displaystyle V({\mathcal {C}})}
of
C
{\displaystyle {\mathcal {C}}}
is the smallest n for which no set of size n is shattered by
C
{\displaystyle {\mathcal {C}}}
.
Sauer's lemma then states that the number
Δ
n
(
C
,
x
1
,
…
,
x
n
)
{\displaystyle \Delta _{n}({\mathcal {C}},x_{1},\ldots ,x_{n})}
of subsets picked out by a VC-class
C
{\displaystyle {\mathcal {C}}}
satisfies:
max
x
1
,
…
,
x
n
Δ
n
(
C
,
x
1
,
…
,
x
n
)
≤
∑
j
=
0
V
(
C
)
−
1
(
n
j
)
≤
(
n
e
V
(
C
)
−
1
)
V
(
C
)
−
1
{\displaystyle \max _{x_{1},\ldots ,x_{n}}\Delta _{n}({\mathcal {C}},x_{1},\ldots ,x_{n})\leq \sum _{j=0}^{V({\mathcal {C}})-1}{n \choose j}\leq \left({\frac {ne}{V({\mathcal {C}})-1}}\right)^{V({\mathcal {C}})-1}}
Which is a polynomial number
O
(
n
V
(
C
)
−
1
)
{\displaystyle O(n^{V({\mathcal {C}})-1})}
of subsets rather than an exponential number. Intuitively this means that a finite VC-index implies that
C
{\displaystyle {\mathcal {C}}}
has an apparent simplistic structure.
A similar bound can be shown (with a different constant, same rate) for the so-called VC subgraph classes. For a function
f
:
X
→
R
{\displaystyle f:{\mathcal {X}}\to \mathbf {R} }
the subgraph is a subset of
X
×
R
{\displaystyle {\mathcal {X}}\times \mathbf {R} }
such that:
{
(
x
,
t
)
:
t
<
f
(
x
)
}
{\displaystyle \{(x,t):t<f(x)\}}
. A collection of
F
{\displaystyle {\mathcal {F}}}
is called a VC subgraph class if all subgraphs form a VC-class.
Consider a set of indicator functions
I
C
=
{
1
C
:
C
∈
C
}
{\displaystyle {\mathcal {I}}_{\mathcal {C}}=\{1_{C}:C\in {\mathcal {C}}\}}
in
L
1
(
Q
)
{\displaystyle L_{1}(Q)}
for discrete empirical type of measure Q (or equivalently for any probability measure Q). It can then be shown that quite remarkably, for
r
≥
1
{\displaystyle r\geq 1}
:
N
(
ε
,
I
C
,
L
r
(
Q
)
)
≤
K
V
(
C
)
(
4
e
)
V
(
C
)
ε
−
r
(
V
(
C
)
−
1
)
{\displaystyle N(\varepsilon ,{\mathcal {I}}_{\mathcal {C}},L_{r}(Q))\leq KV({\mathcal {C}})(4e)^{V({\mathcal {C}})}\varepsilon ^{-r(V({\mathcal {C}})-1)}}
Further consider the symmetric convex hull of a set
F
{\displaystyle {\mathcal {F}}}
:
sconv
F
{\displaystyle \operatorname {sconv} {\mathcal {F}}}
being the collection of functions of the form
∑
i
=
1
m
α
i
f
i
{\displaystyle \sum _{i=1}^{m}\alpha _{i}f_{i}}
with
∑
i
=
1
m
|
α
i
|
≤
1
{\displaystyle \sum _{i=1}^{m}|\alpha _{i}|\leq 1}
. Then if
N
(
ε
‖
F
‖
Q
,
2
,
F
,
L
2
(
Q
)
)
≤
C
ε
−
V
{\displaystyle N\left(\varepsilon \|F\|_{Q,2},{\mathcal {F}},L_{2}(Q)\right)\leq C\varepsilon ^{-V}}
the following is valid for the convex hull of
F
{\displaystyle {\mathcal {F}}}
:
log
N
(
ε
‖
F
‖
Q
,
2
,
sconv
F
,
L
2
(
Q
)
)
≤
K
ε
−
2
V
V
+
2
{\displaystyle \log N\left(\varepsilon \|F\|_{Q,2},\operatorname {sconv} {\mathcal {F}},L_{2}(Q)\right)\leq K\varepsilon ^{-{\frac {2V}{V+2}}}}
The important consequence of this fact is that
2
V
V
+
2
<
2
,
{\displaystyle {\frac {2V}{V+2}}<2,}
which is just enough so that the entropy integral is going to converge, and therefore the class
sconv
F
{\displaystyle \operatorname {sconv} {\mathcal {F}}}
is going to be P-Donsker.
Finally an example of a VC-subgraph class is considered. Any finite-dimensional vector space
F
{\displaystyle {\mathcal {F}}}
of measurable functions
f
:
X
→
R
{\displaystyle f:{\mathcal {X}}\to \mathbf {R} }
is VC-subgraph of index smaller than or equal to
dim
(
F
)
+
2
{\displaystyle \dim({\mathcal {F}})+2}
.
Proof: Take
n
=
dim
(
F
)
+
2
{\displaystyle n=\dim({\mathcal {F}})+2}
points
(
x
1
,
t
1
)
,
…
,
(
x
n
,
t
n
)
{\displaystyle (x_{1},t_{1}),\ldots ,(x_{n},t_{n})}
. The vectors:
(
f
(
x
1
)
,
…
,
f
(
x
n
)
)
−
(
t
1
,
…
,
t
n
)
{\displaystyle (f(x_{1}),\ldots ,f(x_{n}))-(t_{1},\ldots ,t_{n})}
are in a n − 1 dimensional subspace of Rn. Take a ≠ 0, a vector that is orthogonal to this subspace. Therefore:
∑
a
i
>
0
a
i
(
f
(
x
i
)
−
t
i
)
=
∑
a
i
<
0
(
−
a
i
)
(
f
(
x
i
)
−
t
i
)
,
∀
f
∈
F
{\displaystyle \sum _{a_{i}>0}a_{i}(f(x_{i})-t_{i})=\sum _{a_{i}<0}(-a_{i})(f(x_{i})-t_{i}),\quad \forall f\in {\mathcal {F}}}
Consider the set
S
=
{
(
x
i
,
t
i
)
:
a
i
>
0
}
{\displaystyle S=\{(x_{i},t_{i}):a_{i}>0\}}
. This set cannot be picked out since if there is some
f
{\displaystyle f}
such that
S
=
{
(
x
i
,
t
i
)
:
f
(
x
i
)
>
t
i
}
{\displaystyle S=\{(x_{i},t_{i}):f(x_{i})>t_{i}\}}
that would imply that the LHS is strictly positive but the RHS is non-positive.
There are generalizations of the notion VC subgraph class, e.g. there is the notion of pseudo-dimension.
== VC inequality ==
A similar setting is considered, which is more common to machine learning. Let
X
{\displaystyle {\mathcal {X}}}
is a feature space and
Y
=
{
0
,
1
}
{\displaystyle {\mathcal {Y}}=\{0,1\}}
. A function
f
:
X
→
Y
{\displaystyle f:{\mathcal {X}}\to {\mathcal {Y}}}
is called a classifier. Let
F
{\displaystyle {\mathcal {F}}}
be a set of classifiers. Similarly to the previous section, define the shattering coefficient (also known as growth function):
S
(
F
,
n
)
=
max
x
1
,
…
,
x
n
|
{
(
f
(
x
1
)
,
…
,
f
(
x
n
)
)
,
f
∈
F
}
|
{\displaystyle S({\mathcal {F}},n)=\max _{x_{1},\ldots ,x_{n}}|\{(f(x_{1}),\ldots ,f(x_{n})),f\in {\mathcal {F}}\}|}
Note here that there is a 1:1 go between each of the functions in
F
{\displaystyle {\mathcal {F}}}
and the set on which the function is 1. We can thus define
C
{\displaystyle {\mathcal {C}}}
to be the collection of subsets obtained from the above mapping for every
f
∈
F
{\displaystyle f\in {\mathcal {F}}}
. Therefore, in terms of the previous section the shattering coefficient is precisely
max
x
1
,
…
,
x
n
Δ
n
(
C
,
x
1
,
…
,
x
n
)
{\displaystyle \max _{x_{1},\ldots ,x_{n}}\Delta _{n}({\mathcal {C}},x_{1},\ldots ,x_{n})}
.
This equivalence together with Sauer's Lemma implies that
S
(
F
,
n
)
{\displaystyle S({\mathcal {F}},n)}
is going to be polynomial in n, for sufficiently large n provided that the collection
C
{\displaystyle {\mathcal {C}}}
has a finite VC-index.
Let
D
n
=
{
(
X
1
,
Y
1
)
,
…
,
(
X
n
,
Y
m
)
}
{\displaystyle D_{n}=\{(X_{1},Y_{1}),\ldots ,(X_{n},Y_{m})\}}
is an observed dataset. Assume that the data is generated by an unknown probability distribution
P
X
Y
{\displaystyle P_{XY}}
. Define
R
(
f
)
=
P
(
f
(
X
)
≠
Y
)
{\displaystyle R(f)=P(f(X)\neq Y)}
to be the expected 0/1 loss. Of course since
P
X
Y
{\displaystyle P_{XY}}
is unknown in general, one has no access to
R
(
f
)
{\displaystyle R(f)}
. However the empirical risk, given by:
R
^
n
(
f
)
=
1
n
∑
i
=
1
n
I
(
f
(
X
i
)
≠
Y
i
)
{\displaystyle {\hat {R}}_{n}(f)={\dfrac {1}{n}}\sum _{i=1}^{n}\mathbb {I} (f(X_{i})\neq Y_{i})}
can certainly be evaluated. Then one has the following Theorem:
=== Theorem (VC Inequality) ===
For binary classification and the 0/1 loss function we have the following generalization bounds:
P
(
sup
f
∈
F
|
R
^
n
(
f
)
−
R
(
f
)
|
>
ε
)
≤
8
S
(
F
,
n
)
e
−
n
ε
2
/
32
E
[
sup
f
∈
F
|
R
^
n
(
f
)
−
R
(
f
)
|
]
≤
2
log
S
(
F
,
n
)
+
log
2
n
{\displaystyle {\begin{aligned}P\left(\sup _{f\in {\mathcal {F}}}\left|{\hat {R}}_{n}(f)-R(f)\right|>\varepsilon \right)&\leq 8S({\mathcal {F}},n)e^{-n\varepsilon ^{2}/32}\\\mathbb {E} \left[\sup _{f\in {\mathcal {F}}}\left|{\hat {R}}_{n}(f)-R(f)\right|\right]&\leq 2{\sqrt {\dfrac {\log S({\mathcal {F}},n)+\log 2}{n}}}\end{aligned}}}
In words the VC inequality is saying that as the sample increases, provided that
F
{\displaystyle {\mathcal {F}}}
has a finite VC dimension, the empirical 0/1 risk becomes a good proxy for the expected 0/1 risk. Note that both RHS of the two inequalities will converge to 0, provided that
S
(
F
,
n
)
{\displaystyle S({\mathcal {F}},n)}
grows polynomially in n.
The connection between this framework and the Empirical Process framework is evident. Here one is dealing with a modified empirical process
|
R
^
n
−
R
|
F
{\displaystyle \left|{\hat {R}}_{n}-R\right|_{\mathcal {F}}}
but not surprisingly the ideas are the same. The proof of the (first part of) VC inequality, relies on symmetrization, and then argue conditionally on the data using concentration inequalities (in particular Hoeffding's inequality). The interested reader can check the book Theorems 12.4 and 12.5.
== References ==
See references in articles: Richard M. Dudley, empirical processes, Shattered set.
Vapnik, V. N.; Chervonenkis, A. Ya. (1968). "On the uniform convergence of relative frequencies of events to their probabilities". Soviet Mathematics. 9: 915–918. This is a translation by B. Seckler, of the 1968 note.
Reprinted in Vapnik, V. N.; Chervonenkis, A. Ya. (2015), Vovk, Vladimir; Papadopoulos, Harris; Gammerman, Alexander (eds.), "On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities", Measures of Complexity, Cham: Springer International Publishing, pp. 11–30, doi:10.1007/978-3-319-21852-6_3, ISBN 978-3-319-21851-9
They obtained results in a draft form in July 1966 and announced in 1968 in their note Vapnik, V.N.; Chervonenkis, A.Ya. (1968). "On the uniform convergence of relative frequencies of events to their probabilities". Doklady Akademii Nauk SSSR SSSR (in Russian). 181 (4): 781–783.
The paper was first published properly in Russian as Vapnik, V.N.; Chervonenkis, A.Ya. (1971). "О равномерноЙ сходимости частот появления событиЙ к их вероятностям" [On the uniform convergence of frequencies of occurrence of events to their probabilities]. Теория вероятностеЙ и ее применения [Theory of Probability and Its Applications] (in Russian). 16 (2): 264–279.
Bousquet, Olivier; Elisseeff, Andr´e (1 March 2002). "Stability and Generalization". The Journal of Machine Learning Research. 2: 499–526. doi:10.1162/153244302760200704. S2CID 1157797. Retrieved 10 December 2022.
Vapnik, V.; Chervonenkis, A. (2004). "On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities". Theory Probab. Appl. 16 (2): 264–280. doi:10.1137/1116025. | Wikipedia/VC_theory |
Stability, also known as algorithmic stability, is a notion in computational learning theory of how a machine learning algorithm output is changed with small perturbations to its inputs. A stable learning algorithm is one for which the prediction does not change much when the training data is modified slightly. For instance, consider a machine learning algorithm that is being trained to recognize handwritten letters of the alphabet, using 1000 examples of handwritten letters and their labels ("A" to "Z") as a training set. One way to modify this training set is to leave out an example, so that only 999 examples of handwritten letters and their labels are available. A stable learning algorithm would produce a similar classifier with both the 1000-element and 999-element training sets.
Stability can be studied for many types of learning problems, from language learning to inverse problems in physics and engineering, as it is a property of the learning process rather than the type of information being learned. The study of stability gained importance in computational learning theory in the 2000s when it was shown to have a connection with generalization. It was shown that for large classes of learning algorithms, notably empirical risk minimization algorithms, certain types of stability ensure good generalization.
== History ==
A central goal in designing a machine learning system is to guarantee that the learning algorithm will generalize, or perform accurately on new examples after being trained on a finite number of them. In the 1990s, milestones were reached in obtaining generalization bounds for supervised learning algorithms. The technique historically used to prove generalization was to show that an algorithm was consistent, using the uniform convergence properties of empirical quantities to their means. This technique was used to obtain generalization bounds for the large class of empirical risk minimization (ERM) algorithms. An ERM algorithm is one that selects a solution from a hypothesis space
H
{\displaystyle H}
in such a way to minimize the empirical error on a training set
S
{\displaystyle S}
.
A general result, proved by Vladimir Vapnik for an ERM binary classification algorithms, is that for any target function and input distribution, any hypothesis space
H
{\displaystyle H}
with VC-dimension
d
{\displaystyle d}
, and
n
{\displaystyle n}
training examples, the algorithm is consistent and will produce a training error that is at most
O
(
d
n
)
{\displaystyle O\left({\sqrt {\frac {d}{n}}}\right)}
(plus logarithmic factors) from the true error. The result was later extended to almost-ERM algorithms with function classes that do not have unique minimizers.
Vapnik's work, using what became known as VC theory, established a relationship between generalization of a learning algorithm and properties of the hypothesis space
H
{\displaystyle H}
of functions being learned. However, these results could not be applied to algorithms with hypothesis spaces of unbounded VC-dimension. Put another way, these results could not be applied when the information being learned had a complexity that was too large to measure. Some of the simplest machine learning algorithms—for instance, for regression—have hypothesis spaces with unbounded VC-dimension. Another example is language learning algorithms that can produce sentences of arbitrary length.
Stability analysis was developed in the 2000s for computational learning theory and is an alternative method for obtaining generalization bounds. The stability of an algorithm is a property of the learning process, rather than a direct property of the hypothesis space
H
{\displaystyle H}
, and it can be assessed in algorithms that have hypothesis spaces with unbounded or undefined VC-dimension such as nearest neighbor. A stable learning algorithm is one for which the learned function does not change much when the training set is slightly modified, for instance by leaving out an example. A measure of Leave one out error is used in a Cross Validation Leave One Out (CVloo) algorithm to evaluate a learning algorithm's stability with respect to the loss function. As such, stability analysis is the application of sensitivity analysis to machine learning.
== Summary of classic results ==
Early 1900s - Stability in learning theory was earliest described in terms of continuity of the learning map
L
{\displaystyle L}
, traced to Andrey Nikolayevich Tikhonov.
1979 - Devroye and Wagner observed that the leave-one-out behavior of an algorithm is related to its sensitivity to small changes in the sample.
1999 - Kearns and Ron discovered a connection between finite VC-dimension and stability.
2002 - In a landmark paper, Bousquet and Elisseeff proposed the notion of uniform hypothesis stability of a learning algorithm and showed that it implies low generalization error. Uniform hypothesis stability, however, is a strong condition that does not apply to large classes of algorithms, including ERM algorithms with a hypothesis space of only two functions.
2002 - Kutin and Niyogi extended Bousquet and Elisseeff's results by providing generalization bounds for several weaker forms of stability which they called almost-everywhere stability. Furthermore, they took an initial step in establishing the relationship between stability and consistency in ERM algorithms in the Probably Approximately Correct (PAC) setting.
2004 - Poggio et al. proved a general relationship between stability and ERM consistency. They proposed a statistical form of leave-one-out-stability which they called CVEEEloo stability, and showed that it is a) sufficient for generalization in bounded loss classes, and b) necessary and sufficient for consistency (and thus generalization) of ERM algorithms for certain loss functions such as the square loss, the absolute value and the binary classification loss.
2010 - Shalev Shwartz et al. noticed problems with the original results of Vapnik due to the complex relations between hypothesis space and loss class. They discuss stability notions that capture different loss classes and different types of learning, supervised and unsupervised.
2016 - Moritz Hardt et al. proved stability of gradient descent given certain assumption on the hypothesis and number of times each instance is used to update the model.
== Preliminary definitions ==
We define several terms related to learning algorithms training sets, so that we can then define stability in multiple ways and present theorems from the field.
A machine learning algorithm, also known as a learning map
L
{\displaystyle L}
, maps a training data set, which is a set of labeled examples
(
x
,
y
)
{\displaystyle (x,y)}
, onto a function
f
{\displaystyle f}
from
X
{\displaystyle X}
to
Y
{\displaystyle Y}
, where
X
{\displaystyle X}
and
Y
{\displaystyle Y}
are in the same space of the training examples. The functions
f
{\displaystyle f}
are selected from a hypothesis space of functions called
H
{\displaystyle H}
.
The training set from which an algorithm learns is defined as
S
=
{
z
1
=
(
x
1
,
y
1
)
,
.
.
,
z
m
=
(
x
m
,
y
m
)
}
{\displaystyle S=\{z_{1}=(x_{1},\ y_{1})\ ,..,\ z_{m}=(x_{m},\ y_{m})\}}
and is of size
m
{\displaystyle m}
in
Z
=
X
×
Y
{\displaystyle Z=X\times Y}
drawn i.i.d. from an unknown distribution D.
Thus, the learning map
L
{\displaystyle L}
is defined as a mapping from
Z
m
{\displaystyle Z_{m}}
into
H
{\displaystyle H}
, mapping a training set
S
{\displaystyle S}
onto a function
f
S
{\displaystyle f_{S}}
from
X
{\displaystyle X}
to
Y
{\displaystyle Y}
. Here, we consider only deterministic algorithms where
L
{\displaystyle L}
is symmetric with respect to
S
{\displaystyle S}
, i.e. it does not depend on the order of the elements in the training set. Furthermore, we assume that all functions are measurable and all sets are countable.
The loss
V
{\displaystyle V}
of a hypothesis
f
{\displaystyle f}
with respect to an example
z
=
(
x
,
y
)
{\displaystyle z=(x,y)}
is then defined as
V
(
f
,
z
)
=
V
(
f
(
x
)
,
y
)
{\displaystyle V(f,z)=V(f(x),y)}
.
The empirical error of
f
{\displaystyle f}
is
I
S
[
f
]
=
1
n
∑
V
(
f
,
z
i
)
{\displaystyle I_{S}[f]={\frac {1}{n}}\sum V(f,z_{i})}
.
The true error of
f
{\displaystyle f}
is
I
[
f
]
=
E
z
V
(
f
,
z
)
{\displaystyle I[f]=\mathbb {E} _{z}V(f,z)}
Given a training set S of size m, we will build, for all i = 1....,m, modified training sets as follows:
By removing the i-th element
S
|
i
=
{
z
1
,
.
.
.
,
z
i
−
1
,
z
i
+
1
,
.
.
.
,
z
m
}
{\displaystyle S^{|i}=\{z_{1},...,\ z_{i-1},\ z_{i+1},...,\ z_{m}\}}
By replacing the i-th element
S
i
=
{
z
1
,
.
.
.
,
z
i
−
1
,
z
i
′
,
z
i
+
1
,
.
.
.
,
z
m
}
{\displaystyle S^{i}=\{z_{1},...,\ z_{i-1},\ z_{i}',\ z_{i+1},...,\ z_{m}\}}
== Definitions of stability ==
=== Hypothesis Stability ===
An algorithm
L
{\displaystyle L}
has hypothesis stability β with respect to the loss function V if the following holds:
∀
i
∈
{
1
,
.
.
.
,
m
}
,
E
S
,
z
[
|
V
(
f
S
,
z
)
−
V
(
f
S
|
i
,
z
)
|
]
≤
β
.
{\displaystyle \forall i\in \{1,...,m\},\mathbb {E} _{S,z}[|V(f_{S},z)-V(f_{S^{|i}},z)|]\leq \beta .}
=== Point-wise Hypothesis Stability ===
An algorithm
L
{\displaystyle L}
has point-wise hypothesis stability β with respect to the loss function V if the following holds:
∀
i
∈
{
1
,
.
.
.
,
m
}
,
E
S
[
|
V
(
f
S
,
z
i
)
−
V
(
f
S
|
i
,
z
i
)
|
]
≤
β
.
{\displaystyle \forall i\in \ \{1,...,m\},\mathbb {E} _{S}[|V(f_{S},z_{i})-V(f_{S^{|i}},z_{i})|]\leq \beta .}
=== Error Stability ===
An algorithm
L
{\displaystyle L}
has error stability β with respect to the loss function V if the following holds:
∀
S
∈
Z
m
,
∀
i
∈
{
1
,
.
.
.
,
m
}
,
|
E
z
[
V
(
f
S
,
z
)
]
−
E
z
[
V
(
f
S
|
i
,
z
)
]
|
≤
β
{\displaystyle \forall S\in Z^{m},\forall i\in \{1,...,m\},|\mathbb {E} _{z}[V(f_{S},z)]-\mathbb {E} _{z}[V(f_{S^{|i}},z)]|\leq \beta }
=== Uniform Stability ===
An algorithm
L
{\displaystyle L}
has uniform stability β with respect to the loss function V if the following holds:
∀
S
∈
Z
m
,
∀
i
∈
{
1
,
.
.
.
,
m
}
,
sup
z
∈
Z
|
V
(
f
S
,
z
)
−
V
(
f
S
|
i
,
z
)
|
≤
β
{\displaystyle \forall S\in Z^{m},\forall i\in \{1,...,m\},\sup _{z\in Z}|V(f_{S},z)-V(f_{S^{|i}},z)|\leq \beta }
A probabilistic version of uniform stability β is:
∀
S
∈
Z
m
,
∀
i
∈
{
1
,
.
.
.
,
m
}
,
P
S
{
sup
z
∈
Z
|
V
(
f
S
,
z
)
−
V
(
f
S
|
i
,
z
)
|
≤
β
}
≥
1
−
δ
{\displaystyle \forall S\in Z^{m},\forall i\in \{1,...,m\},\mathbb {P} _{S}\{\sup _{z\in Z}|V(f_{S},z)-V(f_{S^{|i}},z)|\leq \beta \}\geq 1-\delta }
An algorithm is said to be stable, when the value of
β
{\displaystyle \beta }
decreases as
O
(
1
m
)
{\displaystyle O({\frac {1}{m}})}
.
=== Leave-one-out cross-validation (CVloo) Stability ===
An algorithm
L
{\displaystyle L}
has CVloo stability β with respect to the loss function V if the following holds:
∀
i
∈
{
1
,
.
.
.
,
m
}
,
P
S
{
|
V
(
f
S
,
z
i
)
−
V
(
f
S
|
i
,
z
i
)
|
≤
β
C
V
}
≥
1
−
δ
C
V
{\displaystyle \forall i\in \{1,...,m\},\mathbb {P} _{S}\{|V(f_{S},z_{i})-V(f_{S^{|i}},z_{i})|\leq \beta _{CV}\}\geq 1-\delta _{CV}}
The definition of (CVloo) Stability is equivalent to Pointwise-hypothesis stability seen earlier.
=== Expected-leave-one-out error ( ===
E
l
o
o
e
r
r
{\displaystyle Eloo_{err}}
) Stability
An algorithm
L
{\displaystyle L}
has
E
l
o
o
e
r
r
{\displaystyle Eloo_{err}}
stability if for each n there exists a
β
E
L
m
{\displaystyle \beta _{EL}^{m}}
and a
δ
E
L
m
{\displaystyle \delta _{EL}^{m}}
such that:
∀
i
∈
{
1
,
.
.
.
,
m
}
,
P
S
{
|
I
[
f
S
]
−
1
m
∑
i
=
1
m
V
(
f
S
|
i
,
z
i
)
|
≤
β
E
L
m
}
≥
1
−
δ
E
L
m
{\displaystyle \forall i\in \{1,...,m\},\mathbb {P} _{S}\{|I[f_{S}]-{\frac {1}{m}}\sum _{i=1}^{m}V(f_{S^{|i}},z_{i})|\leq \beta _{EL}^{m}\}\geq 1-\delta _{EL}^{m}}
, with
β
E
L
m
{\displaystyle \beta _{EL}^{m}}
and
δ
E
L
m
{\displaystyle \delta _{EL}^{m}}
going to zero for
m
,
→
∞
{\displaystyle m,\rightarrow \infty }
== Classic theorems ==
From Bousquet and Elisseeff (02):
For symmetric learning algorithms with bounded loss, if the algorithm has Uniform Stability with the probabilistic definition above, then the algorithm generalizes.
Uniform Stability is a strong condition which is not met by all algorithms but is, surprisingly, met by the large and important class of Regularization algorithms.
The generalization bound is given in the article.
From Mukherjee et al. (06):
For symmetric learning algorithms with bounded loss, if the algorithm has both Leave-one-out cross-validation (CVloo) Stability and Expected-leave-one-out error (
E
l
o
o
e
r
r
{\displaystyle Eloo_{err}}
) Stability as defined above, then the algorithm generalizes.
Neither condition alone is sufficient for generalization. However, both together ensure generalization (while the converse is not true).
For ERM algorithms specifically (say for the square loss), Leave-one-out cross-validation (CVloo) Stability is both necessary and sufficient for consistency and generalization.
This is an important result for the foundations of learning theory, because it shows that two previously unrelated properties of an algorithm, stability and consistency, are equivalent for ERM (and certain loss functions).
The generalization bound is given in the article.
== Algorithms that are stable ==
This is a list of algorithms that have been shown to be stable, and the article where the associated generalization bounds are provided.
Linear regression
k-NN classifier with a {0-1} loss function.
Support Vector Machine (SVM) classification with a bounded kernel and where the regularizer is a norm in a Reproducing Kernel Hilbert Space. A large regularization constant
C
{\displaystyle C}
leads to good stability.
Soft margin SVM classification.
Regularized Least Squares regression.
The minimum relative entropy algorithm for classification.
A version of bagging regularizers with the number
k
{\displaystyle k}
of regressors increasing with
n
{\displaystyle n}
.
Multi-class SVM classification.
All learning algorithms with Tikhonov regularization satisfies Uniform Stability criteria and are, thus, generalizable.
== References ==
== Further reading == | Wikipedia/Stability_(learning_theory) |
In machine learning (ML), boosting is an ensemble metaheuristic for primarily reducing bias (as opposed to variance). It can also improve the stability and accuracy of ML classification and regression algorithms. Hence, it is prevalent in supervised learning for converting weak learners to strong learners.
The concept of boosting is based on the question posed by Kearns and Valiant (1988, 1989): "Can a set of weak learners create a single strong learner?" A weak learner is defined as a classifier that is only slightly correlated with the true classification. A strong learner is a classifier that is arbitrarily well-correlated with the true classification. Robert Schapire answered the question in the affirmative in a paper published in 1990. This has had significant ramifications in machine learning and statistics, most notably leading to the development of boosting.
Initially, the hypothesis boosting problem simply referred to the process of turning a weak learner into a strong learner. Algorithms that achieve this quickly became known as "boosting". Freund and Schapire's arcing (Adapt[at]ive Resampling and Combining), as a general technique, is more or less synonymous with boosting.
== Algorithms ==
While boosting is not algorithmically constrained, most boosting algorithms consist of iteratively learning weak classifiers with respect to a distribution and adding them to a final strong classifier. When they are added, they are weighted in a way that is related to the weak learners' accuracy. After a weak learner is added, the data weights are readjusted, known as "re-weighting". Misclassified input data gain a higher weight and examples that are classified correctly lose weight. Thus, future weak learners focus more on the examples that previous weak learners misclassified.
There are many boosting algorithms. The original ones, proposed by Robert Schapire (a recursive majority gate formulation), and Yoav Freund (boost by majority), were not adaptive and could not take full advantage of the weak learners. Schapire and Freund then developed AdaBoost, an adaptive boosting algorithm that won the prestigious Gödel Prize.
Only algorithms that are provable boosting algorithms in the probably approximately correct learning formulation can accurately be called boosting algorithms. Other algorithms that are similar in spirit to boosting algorithms are sometimes called "leveraging algorithms", although they are also sometimes incorrectly called boosting algorithms.
The main variation between many boosting algorithms is their method of weighting training data points and hypotheses. AdaBoost is very popular and the most significant historically as it was the first algorithm that could adapt to the weak learners. It is often the basis of introductory coverage of boosting in university machine learning courses. There are many more recent algorithms such as LPBoost, TotalBoost, BrownBoost, xgboost, MadaBoost, LogitBoost, and others. Many boosting algorithms fit into the AnyBoost framework, which shows that boosting performs gradient descent in a function space using a convex cost function.
== Object categorization in computer vision ==
Given images containing various known objects in the world, a classifier can be learned from them to automatically classify the objects in future images. Simple classifiers built based on some image feature of the object tend to be weak in categorization performance. Using boosting methods for object categorization is a way to unify the weak classifiers in a special way to boost the overall ability of categorization.
=== Problem of object categorization ===
Object categorization is a typical task of computer vision that involves determining whether or not an image contains some specific category of object. The idea is closely related with recognition, identification, and detection. Appearance based object categorization typically contains feature extraction, learning a classifier, and applying the classifier to new examples. There are many ways to represent a category of objects, e.g. from shape analysis, bag of words models, or local descriptors such as SIFT, etc. Examples of supervised classifiers are Naive Bayes classifiers, support vector machines, mixtures of Gaussians, and neural networks. However, research has shown that object categories and their locations in images can be discovered in an unsupervised manner as well.
=== Status quo for object categorization ===
The recognition of object categories in images is a challenging problem in computer vision, especially when the number of categories is large. This is due to high intra class variability and the need for generalization across variations of objects within the same category. Objects within one category may look quite different. Even the same object may appear unalike under different viewpoint, scale, and illumination. Background clutter and partial occlusion add difficulties to recognition as well. Humans are able to recognize thousands of object types, whereas most of the existing object recognition systems are trained to recognize only a few, e.g. human faces, cars, simple objects, etc. Research has been very active on dealing with more categories and enabling incremental additions of new categories, and although the general problem remains unsolved, several multi-category objects detectors (for up to hundreds or thousands of categories) have been developed. One means is by feature sharing and boosting.
=== Boosting for binary categorization ===
AdaBoost can be used for face detection as an example of binary categorization. The two categories are faces versus background. The general algorithm is as follows:
Form a large set of simple features
Initialize weights for training images
For T rounds
Normalize the weights
For available features from the set, train a classifier using a single feature and evaluate the training error
Choose the classifier with the lowest error
Update the weights of the training images: increase if classified wrongly by this classifier, decrease if correctly
Form the final strong classifier as the linear combination of the T classifiers (coefficient larger if training error is small)
After boosting, a classifier constructed from 200 features could yield a 95% detection rate under a
10
−
5
{\displaystyle 10^{-5}}
false positive rate.
Another application of boosting for binary categorization is a system that detects pedestrians using patterns of motion and appearance. This work is the first to combine both motion information and appearance information as features to detect a walking person. It takes a similar approach to the Viola-Jones object detection framework.
=== Boosting for multi-class categorization ===
Compared with binary categorization, multi-class categorization looks for common features that can be shared across the categories at the same time. They turn to be more generic edge like features. During learning, the detectors for each category can be trained jointly. Compared with training separately, it generalizes better, needs less training data, and requires fewer features to achieve the same performance.
The main flow of the algorithm is similar to the binary case. What is different is that a measure of the joint training error shall be defined in advance. During each iteration the algorithm chooses a classifier of a single feature (features that can be shared by more categories shall be encouraged). This can be done via converting multi-class classification into a binary one (a set of categories versus the rest), or by introducing a penalty error from the categories that do not have the feature of the classifier.
In the paper "Sharing visual features for multiclass and multiview object detection", A. Torralba et al. used GentleBoost for boosting and showed that when training data is limited, learning via sharing features does a much better job than no sharing, given same boosting rounds. Also, for a given performance level, the total number of features required (and therefore the run time cost of the classifier) for the feature sharing detectors, is observed to scale approximately logarithmically with the number of class, i.e., slower than linear growth in the non-sharing case. Similar results are shown in the paper "Incremental learning of object detectors using a visual shape alphabet", yet the authors used AdaBoost for boosting.
== Convex vs. non-convex boosting algorithms ==
Boosting algorithms can be based on convex or non-convex optimization algorithms. Convex algorithms, such as AdaBoost and LogitBoost, can be "defeated" by random noise such that they can't learn basic and learnable combinations of weak hypotheses. This limitation was pointed out by Long & Servedio in 2008. However, by 2009, multiple authors demonstrated that boosting algorithms based on non-convex optimization, such as BrownBoost, can learn from noisy datasets and can specifically learn the underlying classifier of the Long–Servedio dataset.
== See also ==
== Implementations ==
scikit-learn, an open source machine learning library for Python
Orange, a free data mining software suite, module Orange.ensemble
Weka is a machine learning set of tools that offers variate implementations of boosting algorithms like AdaBoost and LogitBoost
R package GBM (Generalized Boosted Regression Models) implements extensions to Freund and Schapire's AdaBoost algorithm and Friedman's gradient boosting machine.
jboost; AdaBoost, LogitBoost, RobustBoost, Boostexter and alternating decision trees
R package adabag: Applies Multiclass AdaBoost.M1, AdaBoost-SAMME and Bagging
R package xgboost: An implementation of gradient boosting for linear and tree-based models.
== Notes ==
== References ==
== Further reading ==
Freund, Yoav; Schapire, Robert E. (1997). "A Decision-Theoretic Generalization of On-line Learning and an Application to Boosting" (PDF). Journal of Computer and System Sciences. 55 (1): 119–139. doi:10.1006/jcss.1997.1504.
Schapire, Robert E. (1990). "The strength of weak learnability". Machine Learning. 5 (2): 197–227. doi:10.1007/BF00116037. S2CID 6207294.
Schapire, Robert E.; Singer, Yoram (1999). "Improved Boosting Algorithms Using Confidence-Rated Predictors". Machine Learning. 37 (3): 297–336. doi:10.1023/A:1007614523901. S2CID 2329907.
Zhou, Zhihua (2008). "On the margin explanation of boosting algorithm" (PDF). In: Proceedings of the 21st Annual Conference on Learning Theory (COLT'08): 479–490.
Zhou, Zhihua (2013). "On the doubt about margin explanation of boosting" (PDF). Artificial Intelligence. 203: 1–18. arXiv:1009.3613. doi:10.1016/j.artint.2013.07.002. S2CID 2828847.
== External links ==
Robert E. Schapire (2003); The Boosting Approach to Machine Learning: An Overview, MSRI (Mathematical Sciences Research Institute) Workshop on Nonlinear Estimation and Classification
Boosting: Foundations and Algorithms by Robert E. Schapire and Yoav Freund | Wikipedia/Boosting_(meta-algorithm) |
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