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natural language processing | Complexity of natural language processing problems | https://cs.stackexchange.com/questions/32276/complexity-of-natural-language-processing-problems | <p>Which natural language processing problems are NP-Complete or NP-Hard?</p>
<p>I've searched the <a href="/questions/tagged/natural-lang-processing" class="post-tag" title="show questions tagged 'natural-lang-processing'" rel="tag">natural-lang-processing</a> and <a href="/questions/tagged/complexity-theory"... | <p>LFG (Lexical-Functional Grammar) <a href="http://ato.ms/MITECS/Entry/dalrymple" rel="nofollow noreferrer">recognition is NP-Complete</a>.</p>
<p>Edit per request: Lexical-Functional Grammar (LFG) [1] is a theory of natural language syntax, developed as an alternative to Chomsky's theories of transformational syntax... | 0 |
natural language processing | Advantages of knowing foreign languages for natural language processing | https://cs.stackexchange.com/questions/13833/advantages-of-knowing-foreign-languages-for-natural-language-processing | <p>I wonder about cases in which knowing several languages can lead a researcher to interesting results in natural language processing.</p>
<p>For example, knowledge of foreign languages can without doubt contribute to better machine translation, it's the most obvious example.</p>
<p>In what other fields of NLP can ... | 1 | |
natural language processing | What aspects of linguistics are necessary or good for natural language processing? | https://cs.stackexchange.com/questions/21334/what-aspects-of-linguistics-are-necessary-or-good-for-natural-language-processin | <p>What aspects of linguistics are necessary or good to know for natural language processing? What references do you recommend for studying those aspects? Thanks!</p>
| <p>NLP is a big place, you might want to be more specific.</p>
<p>Within information retrieval, <a href="https://en.wikipedia.org/wiki/Stemming" rel="nofollow">stemming</a> is a linguistic idea that has become useful as a heuristic means of reducing vocabulary size. As a practitioner I learned about it from <a href="... | 2 |
natural language processing | Natural language query processing | https://cs.stackexchange.com/questions/33430/natural-language-query-processing | <p>I am trying to implement a natural language query preprocessing module which would, given a query formulated in natural language, extract the keywords from that query and submit it to an IR (information retrieval system) system.</p>
<p>At first, I thought about using some training set to compute <a href="http://en.... | <p>I don't know the relative sizes and the nature of your problem, these details could completely change the view. But generally, if the only thing you have at your disposal is a small set of test documents, I would not recommend using that for term weighting at all. A small set of documents would give you an illusion ... | 3 |
natural language processing | Semantic natural language processing - from texts to logical expressions? Universal knowledge base? | https://cs.stackexchange.com/questions/68398/semantic-natural-language-processing-from-texts-to-logical-expressions-univer | <p>My question is - <strong>is there a semantic natural language processing that tries to understand the meaning of the texts and that tries to derive the consequences of the understood meaning? Is there a universal knowledge base that can be used for the "grounding" of the texts?</strong></p>
<p>I have heard a lot ab... | <p>There are several implementations of <a href="http://www.cs.utexas.edu/~ml/publications/area/77/learning_for_semantic_parsing" rel="nofollow noreferrer">semantic parsers</a> that convert natural-language texts into formal logical representations of their meanings. <a href="https://en.wikipedia.org/wiki/Natural_langu... | 4 |
natural language processing | Constraint satisfaction problems in Natural language processing | https://cs.stackexchange.com/questions/157042/constraint-satisfaction-problems-in-natural-language-processing | <p>I have just started learning about CSP and NLP, for which I have to write a review paper of some research articles.</p>
<p>The problem is that when a searched for research articles on some trusted digital libraries with the keywords CSP and NLP, there weren't many results that were related to both.</p>
<p>Do you hav... | 5 | |
natural language processing | Does programming language detection need more input than natural language detection? | https://cs.stackexchange.com/questions/28668/does-programming-language-detection-need-more-input-than-natural-language-detect | <p>I wonder which one of the two needs a larger input to achieve a decent accuracy:
<br>
programming language detection or natural language detection?</p>
<hr>
<p>More details:</p>
<p>Definition of <a href="http://en.wikipedia.org/wiki/Language_identification" rel="nofollow">Language detection</a>: </p>
<blockquote... | <p>Answering knowingly this question would require experiments. I am sure
there is some data for natural languages, where it is a common
problem. I recall from memory that one study gave ridiculously small
figures for natural language, which is not too surprising. If you take
5 consecutive word in a sentence (the figur... | 6 |
natural language processing | Question on word probability for hierarchical softmax used in natural language processing | https://cs.stackexchange.com/questions/94228/question-on-word-probability-for-hierarchical-softmax-used-in-natural-language-p | <p>I am reading the following paper: <a href="https://papers.nips.cc/paper/5021-distributed-representations-of-words-and-phrases-and-their-compositionality.pdf" rel="nofollow noreferrer">https://papers.nips.cc/paper/5021-distributed-representations-of-words-and-phrases-and-their-compositionality.pdf</a></p>
<p>On page... | <p>I have figured out my confusion.</p>
<p>The indicator function is $\lbrack x \rbrack$ is set to output a $-1$ or a $1$ based on the argument being false or true, respectively. </p>
<p>When the authors say "let $ch(n)$ be an arbitrary fixed child of node $n$", they mean arbitrary in the sense of left child or right... | 7 |
natural language processing | Where can I find a study on the amount of different word frequencies in a corpus? | https://cs.stackexchange.com/questions/33631/where-can-i-find-a-study-on-the-amount-of-different-word-frequencies-in-a-corpus | <p>I need to know how many different values the frequency of a certain word in a corpus can there be for a natural language processing problem. Is there any study or site that has such estimation?</p>
| <p>What you're asking directly refers to <a href="http://en.wikipedia.org/wiki/Information_retrieval" rel="nofollow">Information Retrieval</a>. Information Retrieval directly creates models for such things as frequency of words in a corpus and so on.</p>
<p>In a corpus, different indicators are estimated in order to c... | 8 |
natural language processing | How are PCFGs used in programming language design? | https://cs.stackexchange.com/questions/167192/how-are-pcfgs-used-in-programming-language-design | <p>I've been reading the <a href="https://en.wikipedia.org/wiki/Probabilistic_context-free_grammar" rel="nofollow noreferrer">wikipedia article</a> about probabilistic context-free grammars (PCFGs), and they state that</p>
<blockquote>
<p>PCFGs have application in areas as diverse as natural language processing to the ... | <p>I am not aware of applications in programming language design, and I am a bit skeptical. However, PCFGs <em>are</em> useful for generating test cases, for program testing.</p>
| 9 |
natural language processing | What is the natural language of computers mathematics or logic? | https://cs.stackexchange.com/questions/48157/what-is-the-natural-language-of-computers-mathematics-or-logic | <p>I was reading about the history of computers where i came by <a href="https://en.wikipedia.org/wiki/Machine_code" rel="nofollow">machine code</a></p>
<blockquote>
<p>A Machine code or machine language is a set of instructions executed directly by a computer's central processing unit (CPU). Each instruction perfor... | <p>There is really no such thing as a <em>natural language</em> for computers. Natural language is a concept from linguistics, and pertains mostly to humans (and perhaps also to some animals).</p>
<p>The corresponding concept for computers is <em>machine language</em> or <em>native code</em>, which is what the computi... | 10 |
natural language processing | How to determine agreement between two sentences? | https://cs.stackexchange.com/questions/56828/how-to-determine-agreement-between-two-sentences | <p>A common Natural Language Processing (NLP) task is to determine semantic similarity between two sentences. Has the question of agreement/disagreement between two sentences been covered in NLP or other literature? I tried searching on Google Scholar but didn't get any relevant results.</p>
| <p>I would propose to do some researching in the field of <strong>Stance Classification</strong>. Given a target claim or argument we can classify whether a number of sentences are in favor, against or neither of that claim. So an idea is to extract the topic of those sentences classify whether they agree or disagree w... | 11 |
natural language processing | How to translate lambda calculus into (first-order, modal) logic, is it possible at all? | https://cs.stackexchange.com/questions/82878/how-to-translate-lambda-calculus-into-first-order-modal-logic-is-it-possible | <p>It is possible (using formal semantics) to translate natural language sentences into lambda expressions. So, is it possible to translate those lambda expressions into some logic, e.g. into first-order logic or into modal logic?</p>
<p>I am aware of the Curry-Howard correspondence, but I have not found actual transl... | 12 | |
natural language processing | Are there any neural NLG systems which don't generate in left-to-right order? | https://cs.stackexchange.com/questions/99987/are-there-any-neural-nlg-systems-which-dont-generate-in-left-to-right-order | <p>For a while, all classification tasks in natural language processing were based on simple RNN's, which operate in a very word-by-word order. Adding gating mechanisms increased ability to "look back", and the newer addition of context vectors which can train attention to different words during the task have made cla... | 13 | |
natural language processing | Relation and difference between information retrieval and information extraction? | https://cs.stackexchange.com/questions/7181/relation-and-difference-between-information-retrieval-and-information-extraction | <p>From <a href="http://en.wikipedia.org/wiki/Information_retrieval" rel="noreferrer">Wikipedia</a> </p>
<blockquote>
<p><strong>Information retrieval</strong> is the activity of obtaining information resources relevant to an information need from a collection of information resources. Searches can be based on metad... | <p><strong>Information retrieval</strong> is <strong><em>based on a query</em></strong> - you specify what information you need and it is returned in human understandable form.</p>
<p><strong>Information extraction</strong> is about structuring unstructured information - given some sources <strong><em>all of the (rele... | 14 |
natural language processing | Language to Construct Finite State Transducer | https://cs.stackexchange.com/questions/28175/language-to-construct-finite-state-transducer | <p>I am attempting to write a Finite State Transducer module in OCaml, because I think it's a good exercise, which is because I have been teaching myself Natural Language Processing.</p>
<p>You typically construct finite automata using regular expressions, for example (a | b).</p>
<p>What language does one typically ... | <p>Yes, such a specification would work. Basically a FST is a finite state automaton, with different labels on the edges. We can go from FST to regex by a standard algorithm. The same method works with transducers, only the labels are now pairs of strings. The concatenation of labels is done component-wise: $(a,x)(b,y)... | 15 |
natural language processing | Difference between LR parsing and Shift-Reduce parsing? | https://cs.stackexchange.com/questions/68278/difference-between-lr-parsing-and-shift-reduce-parsing | <p>I'm learning natural language processing and I can't understand the difference between <a href="https://en.wikipedia.org/wiki/Shift-reduce_parser" rel="nofollow noreferrer">Shift-Reduce parser</a> and <a href="https://en.wikipedia.org/wiki/LR_parser" rel="nofollow noreferrer">LR parser</a>. </p>
<p>As I've understo... | 16 | |
natural language processing | Natural Language Parser that can handle syntactic and lexical errors | https://cs.stackexchange.com/questions/33514/natural-language-parser-that-can-handle-syntactic-and-lexical-errors | <p>I have some background in natural language processing and I know that all parsers (top down or bottom up, or mix), at least when I studied just about a few years ago, cannot handle any error. A small error like a grammatical one or a spelling one will result in unexpected parsed tree.</p>
<p>This is unacceptable in... | <p>I assume you already know about dynamic programming parsing, aka chart
parsing. This is usually defined for Context-Free grammars (CFG), but
can be extended to other grammatical formalisms, where it can make
more or less sense, depending on the structural complexity of these
algorithms. There are various papers desc... | 17 |
natural language processing | What are open problems in computer science? | https://cs.stackexchange.com/questions/112399/what-are-open-problems-in-computer-science | <p>I should prepare some paper for a colloquium (kinda student-task) and it should cover the following points:</p>
<p>(1) at least one notable discovery in theoretical informatics (or computer science)</p>
<p>(2) at least one open problems in theoretical informatics</p>
<p>(3) an example of short notable proof of so... | 18 | |
natural language processing | Resources to learn NLP | https://cs.stackexchange.com/questions/157606/resources-to-learn-nlp | <p>I am an undergraduate student in mathematics. I have a fair bit of experience with deep learning in computer vision research and am willing to dabble into Natural Language Processing (NLP). I hope that things won't be very disjointed and some of the knowledge can be transferred.</p>
<p>I wanted to know if y'all can ... | <p>I like <a href="https://www.youtube.com/playlist?list=PLoROMvodv4rOSH4v6133s9LFPRHjEmbmJ" rel="nofollow noreferrer">The Stanford CS224N 2021 YouTube channel</a>,
which focuses on deep learning models for NLP (but many things changed since 2021, esp. LLMs). For a pre-deep-learning NLP courses, I like:</p>
<ul>
<li><a... | 19 |
natural language processing | Operations on regular languages | https://cs.stackexchange.com/questions/89191/operations-on-regular-languages | <p>I am taking a course on natural language processing that assumes the students have some background on theory of computation. I dont, but have read up till chapter 3 of the book "Speech and Language Processing by Jufrasky".</p>
<p>I therefore understand the following</p>
<ul>
<li>regular expressions and regular lan... | 20 | |
natural language processing | Quantum algorithms for logical inference - reference request? | https://cs.stackexchange.com/questions/81752/quantum-algorithms-for-logical-inference-reference-request | <p>Microsoft is committed to the building of the scalable, industrial size topological quantum computer, Visual Studio integrated programming language and SDK will be released by the end of this year (2017). From the other side, logical/symbolic methods in computer science (natural language processing, inference, knowl... | 21 | |
natural language processing | Difference Between Residual Neural Net and Recurrent Neural Net? | https://cs.stackexchange.com/questions/63541/difference-between-residual-neural-net-and-recurrent-neural-net | <p>What is the difference between a <strong>Residual</strong> Neural Net and a <strong>Recurrent</strong> Neural Net?</p>
<p>As I understand,</p>
<p><a href="https://arxiv.org/pdf/1512.03385v1.pdf" rel="noreferrer">Residual Neural Networks</a> are very deep networks that implement 'shortcut' connections across multip... | <p>The answer is YES, they basically are the same according to this <a href="https://arxiv.org/abs/1604.03640v1" rel="nofollow noreferrer">paper</a> </p>
<p><img src="https://i.sstatic.net/q7JdV.pnghttps://" alt="enter image description here"></p>
<p>The figure above shows how they compared both and how a ResNet can ... | 22 |
natural language processing | Combining Ontology and Relational Databases in Question Answering system | https://cs.stackexchange.com/questions/74514/combining-ontology-and-relational-databases-in-question-answering-system | <p>I'm introducing to the Natural Language Processing field and it's application. I'm planning to build a question answering system for a project, but some approaches are making me a bit confuse about the use of ontologies and it's application on the architecture of the system. I understand that an Ontology in definiti... | 23 | |
natural language processing | Estimate entropy, based upon observed frequency counts | https://cs.stackexchange.com/questions/15010/estimate-entropy-based-upon-observed-frequency-counts | <p>Suppose I have $n$ independent observations $x_1,\dots,x_n$ from some unknown distribution over a known alphabet $\Sigma$, and I want to estimate the entropy of the distribution. I can count the frequency $f_s$ of each symbol $s \in \Sigma$ among the observations; how should I use them to estimate the Shannon entro... | <p>Like most things of this nature the best method is best found by empirical evaluation. One thing worth noting is that most smoothing schemes can be thought of as the incorporation of a prior into your likelihood estimate. For example if you are trying to estimate the parameter $\theta$ of a binary random variable $X... | 24 |
natural language processing | How do IR researchers evaluate the ranks of documents? | https://cs.stackexchange.com/questions/41578/how-do-ir-researchers-evaluate-the-ranks-of-documents | <p>I am developing a new IR system in a specialized context. I understand that a traditional IR system (like a search engine) should rank documents in terms of their relevance for a query. The most relevant documents should come first and the least relevant (perhaps: least relevant above some threshold) should come las... | <p>If I understand what you're trying to achieve correctly, you can use <a href="https://en.wikipedia.org/wiki/Discounted_cumulative_gain" rel="nofollow">this</a> technique <strong>discounted cumulative gain</strong>.</p>
<p>$$DCG_p=\sum_{i=1}^{p}{\frac{2^{rel_i}-1}{\log_2{(i+1)}}}$$</p>
<p>$i$ is the rank, and $p$ i... | 25 |
natural language processing | How to represent symbolic knowledge using real numbers - theory about neural networks and natural/analog computing? | https://cs.stackexchange.com/questions/98067/how-to-represent-symbolic-knowledge-using-real-numbers-theory-about-neural-net | <p>One can define the semantics of one definite word using the references to real world entities, relationships with the other words and other concepts and represent all this knowledge about this one word using logical symbolic expressions. And then one can encode all this set of symbolic expressions into vector of rea... | <p>No, probably not. I think you're expecting too much from the current state of the art in word embeddings. Word embeddings don't magically capture all semantic knowledge. They don't reflect perfect understanding of the language. Instead, they're just useful mappings where similar words often have similar embeddin... | 26 |
natural language processing | Semantic/DRT methods for conversational agents / chatbots / dialogue systems - reference request? | https://cs.stackexchange.com/questions/82575/semantic-drt-methods-for-conversational-agents-chatbots-dialogue-systems-r | <p>The wiki pages about chabots mention that statistical methods, keyword search and precompiled answers are used for the chatbots. But I feel that there should exist different - semantical approach for constructing chatbots. There are formal semantics of natural language (recent results in <a href="http://www.springer... | 27 | |
natural language processing | Solving the part-of-speech tagging problem with HMM | https://cs.stackexchange.com/questions/20185/solving-the-part-of-speech-tagging-problem-with-hmm | <p>There is a famous <a href="http://en.wikipedia.org/wiki/Part-of-speech_tagging" rel="nofollow">part-of-speech tagging problem</a> in Natural Language Processing. The popular solution is to use <a href="http://en.wikipedia.org/wiki/Hidden_Markov_model" rel="nofollow">Hidden Markov Models</a>.</p>
<p>So that, given t... | <p>Isn't this exactly the same question you asked <a href="https://cs.stackexchange.com/questions/16777/hidden-markov-model-in-tagging-problem">previously</a>? I'll make some additional comments and add some links here. Hopefully that will help.</p>
<blockquote>
<p>is there are any particular reason why we prefere t... | 28 |
natural language processing | Which fields of Computer Science are involved in knowledge-based and text-based dialog systems? | https://cs.stackexchange.com/questions/63423/which-fields-of-computer-science-are-involved-in-knowledge-based-and-text-based | <p>One of my future goals is to know in depth about building a text-based dialog system to answer questions about a specific topic (say, Tolkien's legendarium), assume that I have a large body of article-formed facts about that topic (say, Wikipedia). Excluding the "Computer Engineering" part of the problem, I have a q... | 29 | |
natural language processing | Can you suggest a topic for a Bachelor Thesis in Mathematics that is related to Machine Learning? | https://cs.stackexchange.com/questions/133808/can-you-suggest-a-topic-for-a-bachelor-thesis-in-mathematics-that-is-related-to | <h2>Context</h2>
<p>I am a final year Bachelor of Mathematics student and next semester I will write my Bachelor thesis.<br />
My interests are in Machine Learning (ML) and I will do a master in ML next year. More specific sub-fields I like are</p>
<ul>
<li>Deep Learning</li>
<li>Computer Vision</li>
<li>Natural Langua... | <p>I would like to make two points clear as a researcher:</p>
<ol>
<li><p>Mathematics is a very broad discipline. When you're on bachelor level it is still appropriate to call it "Mathematics" but already in Masters, you'll need to specialize! Youll have to choose a branch and then you won't be "a mathem... | 30 |
natural language processing | Context-free grammar for DAGs? | https://cs.stackexchange.com/questions/55109/context-free-grammar-for-dags | <p>I'm looking for a "safe" representation of DAGs. With "safe" representation I mean that it can be described by a context-free grammar. Ideally, this grammar would be suitable for a simple LR parser.</p>
<p>The same problem for trees instead of DAGs is already solved: Just use one of the many well-known tree represe... | 31 | |
natural language processing | How to define a formal language for describing procedural activities | https://cs.stackexchange.com/questions/142868/how-to-define-a-formal-language-for-describing-procedural-activities | <p>I do not have a formal computer science background here so I am looking for pointers.</p>
<p>How would you advice I go about describing a formal way to describe procedures like cooking recipes, manufacturing process, driving to a location etc.</p>
<p>Given the fact that these types of process does feel like algorith... | <p>Your question is very broad and has possibly hundreds of answers depending on the interpretation. The fact you tagged it with "formal-languages" and "formal-grammars" suggests you are actually asking "how the syntax of a language describing this kind of stuff should look like".
Sometime... | 32 |
natural language processing | What is the activation function, label and loss function for Hierachical Softmax | https://cs.stackexchange.com/questions/43912/what-is-the-activation-function-label-and-loss-function-for-hierachical-softmax | <p>Several papers(<a href="http://www.iro.umontreal.ca/%7Elisa/pointeurs/hierarchical-nnlm-aistats05.pdf" rel="nofollow noreferrer">1</a> (originator), <a href="http://arxiv.org/pdf/1310.4546.pdf" rel="nofollow noreferrer">2</a>, <a href="http://dx.doi.org/10.1007/978-3-662-45924-9_16" rel="nofollow noreferrer">3</a>) ... | 33 | |
natural language processing | Automatic learning/discovery of logics | https://cs.stackexchange.com/questions/85749/automatic-learning-discovery-of-logics | <p>Are there efforts to automatically discover new logics? Logics are simple structures - they have formal language, deduction rules, semantics and certain properties that are proved or discarded for every new logic. In fact, each logic can be put into framework of institutions (by Diaconescu et al).</p>
<p>So - is it... | 34 | |
natural language processing | If we spoke in TM-computable English, what would it look like? | https://cs.stackexchange.com/questions/62607/if-we-spoke-in-tm-computable-english-what-would-it-look-like | <p>We know that any "effectively computable" process is computable by a Turing machine (Turing-Church thesis).</p>
<p>Although it seems that "effectively computable" is still open to discussion, the intuitive interpretation is that any process that is "mechanical enough" can be computed by a Turing machine.</p>
<p>Tu... | <p>Under reasonable assumptions, there is a TM which can decide whether something is a valid piece of English legalese. We can safely assume that the length of a law is bounded by some finite number $k$, say the number of characters the fastest human reader can read in less than two hundred years. There is then only a ... | 35 |
natural language processing | Are the definitions of constructs in terms of lambda terms issues in implementation/design or uses of functional languages? | https://cs.stackexchange.com/questions/112384/are-the-definitions-of-constructs-in-terms-of-lambda-terms-issues-in-implementat | <p>In Lambda Calculus, natural numbers, boolean values, list processing functions, recursion, if function are defined in terms of lambda terms. For example, natural numbers are defined as Church numerals, and recursion is defined in terms of a fixed point of a function.</p>
<p>Functional languages are said to be based... | <ol>
<li>Those features are almost never implemented like the lambda calculus in modern programming language implementation. In some cases, using the lambda calculus representation for datatypes has performance improvements (this is associated with so-called tagless representations). Historically, the Haskell compiler ... | 36 |
natural language processing | What are the theoretical and practical contributions of Multiagent Systems to science? | https://cs.stackexchange.com/questions/49957/what-are-the-theoretical-and-practical-contributions-of-multiagent-systems-to-sc | <p>Speaking about multiagent systems (MAS) is about as fuzzy as talking about artificial intelligence systems (AI). They are in essence the distributed counterpart of AI.</p>
<p>While there are no so-called "AI theorem", AI research had given rise to many subfields, algorithms and scores of theorems (e.g. game solving... | 37 | |
natural language processing | string matching algorithm question for matching approximately similar names between two lists | https://cs.stackexchange.com/questions/171466/string-matching-algorithm-question-for-matching-approximately-similar-names-betw | <p>The focus of this question is on natural language processing, specifically matching names between 2 lists. I am looking at employees that work in the same organization, however I obtained data from two different databases. Unfortunately, there is no unique key or ID that matches the users between lists, so I have to... | 38 | |
natural language processing | Are there any examples of programming synthesis in vulnerability research? | https://cs.stackexchange.com/questions/63242/are-there-any-examples-of-programming-synthesis-in-vulnerability-research | <h2>Program Synthesis</h2>
<p>To borrow from Microsoft: </p>
<blockquote>
<p><a href="https://homes.cs.washington.edu/~bornholt/post/synthesis-for-architects.html" rel="nofollow">Program synthesis</a> is the task of automatically discovering an executable piece of code given user intent expressed using various form... | <p>Yes, there's plenty of work on synthesizing exploits using program synthesis. One of the seminal papers was:</p>
<p>Thanassis Avgerinos, Sang Kil Cha, Alexandre Rebert, Edward J. Schwartz, Maverick Woo, and David Brumley. <a href="https://users.ece.cmu.edu/~dbrumley/pdf/Avgerinos%20et%20al._2014_Automatic%20Exploi... | 39 |
natural language processing | Numeral systems other than unary used in nature or in animal and human behaviours | https://cs.stackexchange.com/questions/4906/numeral-systems-other-than-unary-used-in-nature-or-in-animal-and-human-behaviour | <p>Representing numeric values using <a href="http://en.wikipedia.org/wiki/Positional_notation">positional notation</a> is one of the milestones in the history of arithmetic. Babylons used a base 60 system, Maya a base 20 system; base 10 system became "the standard" used by modern civilizations; digital computers use t... | <p>There is at least one example where a string of symbols from an alphabet is also used: proteins.</p>
<p>Proteins consist of chains of 20 different amino acids (usually, in some cases, it's 21 or 22) and the sequence of amino acids determines what given protein does.</p>
<p>This example is closely related to the DN... | 40 |
natural language processing | Language of words that begin and end with same symbol and have equal numbers of a's and b's | https://cs.stackexchange.com/questions/52324/language-of-words-that-begin-and-end-with-same-symbol-and-have-equal-numbers-of | <p>I wish to find the CFG for a language on two symbols (say <em>a</em> and <em>b</em>) whose words begin and terminate with the same symbol, and have equal quantities of <em>a</em>'s and <em>b</em>'s. What is the thought process I should use for finding such a grammar? What is the most natural or simplest grammar fo... | <p>Here is the thought process I would use. I would notice that your language $L$ can be written as $L= L_1 \cap L_2$, where $L_1$ is the set of words that begin and end with the same symbol, and $L_2$ is the set of words that have equal quantities of <em>a</em>'s and <em>b</em>'s.</p>
<p>Then, I would note that $L_1... | 41 |
natural language processing | How to transform lambda function to multi-argument lambda function and how to rewrite or approximate terms? | https://cs.stackexchange.com/questions/96533/how-to-transform-lambda-function-to-multi-argument-lambda-function-and-how-to-re | <p>I am trying to do the formal semantics (Montague grammar, abstract categorial grammar) of natural language and encode the sentence <code>John is boss</code>. The type system has to primitive types - <code>e</code> for entity and <code>t</code> for Boolean type. <code>John</code> has type <code>e</code>, <code>is</co... | <p>You are looking for <a href="https://en.wikipedia.org/wiki/Currying#Lambda_calculi" rel="nofollow noreferrer">currying and uncurrying</a> which transform functions of type $A \times B \to C$ to functions of type $A \to (B \to C)$, and vice versa. Currying takes <code>IS</code> to <code>is</code>, while uncurrying ta... | 42 |
natural language processing | Is a Turing Machine that only takes strings of the form $0^*$ Turing Complete? | https://cs.stackexchange.com/questions/24125/is-a-turing-machine-that-only-takes-strings-of-the-form-0-turing-complete | <p>You have a Turing machine that only processes input on the form $0^*$. If it is given an input without 0's, it will simply halt without accepting or do anything else. Is it Turing Complete?</p>
<p>The set $0^*$ is countably infinite, since you can make the bijective function $f(x) : 0^* → \mathbb{N} $:</p>
<p>$f(x... | <p>It looks like Turing machines remain Turing-complete when the alphabet is restricted to have one symbol, $0$. First, preprocess your input by replacing every $0$ with $0\square$, where $\square$ is the blank symbol. Now, you can simulate a 2-symbol alphabet by using $0\square$ to represent zero and $\square0$ t... | 43 |
natural language processing | Specific Examples with Explanation of Similarities and Differences of how Distance Functions are used Across Different Fields | https://cs.stackexchange.com/questions/80327/specific-examples-with-explanation-of-similarities-and-differences-of-how-distan | <p>I took a tangent from a <a href="https://github.com/davidkitfriedman/segment_fusion/blob/master/cs_stackexchange_question.md" rel="nofollow noreferrer">student
project</a>
I had done a number of years ago and spent some time studying distance
functions.</p>
<p>(please note that the above link contains the full ques... | <p>Okay, so here are some of my thoughts along with some links to some of the things that I found interesting in my independent study. </p>
<p>(please note that a <a href="https://github.com/davidkitfriedman/segment_fusion/blob/master/cs_stackexchange_response.md" rel="nofollow noreferrer">version with additional link... | 44 |
natural language processing | What is the minimum type of logical system that recognizes if a formalized sentence is a well-formed formula thus reducible to the boolean value? | https://cs.stackexchange.com/questions/107244/what-is-the-minimum-type-of-logical-system-that-recognizes-if-a-formalized-sente | <p>The formula, in the old way of using it, can contain symbols in order and a mixture that does not meet the criteria of correctness (i.e. arbitrary symbols do not form a well-formed formula (WFF) and do not conform to the grammar).</p>
<p>Also, a sentence written in a natural language could be in such a form that it... | <p>There is no systematic algorithm that, given any English sentence, can always determine whether it can be translated to a well-formed formula in first-order logic. The English language allows expression of statements that are inherently subjective and imprecise; the meaning of some English sentences is unavoidably ... | 45 |
natural language processing | How does lack of deadlock relate to computability in process calculi? | https://cs.stackexchange.com/questions/64153/how-does-lack-of-deadlock-relate-to-computability-in-process-calculi | <p>I'm interested in knowing things about the computability of concurrent programs. If you had a Turing complete language that also let you branch off new programs but had no means of communication between them there would be programs that you couldn't write. Namely those that required communication between concurrentl... | <p>I think you are asking about expressivity of concurrent programming languages. This is a deep and not well-understood field. For example you say that "the $\pi$-calculus [...] has the power to implement almost any synchronization primitive I've ever heard of". It is well known that the $\pi$-calculus cannot implemen... | 46 |
natural language processing | What roadblocks are there to HSA becoming standard, similar to floating point units becoming standard? | https://cs.stackexchange.com/questions/130289/what-roadblocks-are-there-to-hsa-becoming-standard-similar-to-floating-point-un | <p>I remember when my dad explained to me for the first time how a certain model of computer he had came with a "math coprocessor" which made certain math operations much faster than if they were done on the main CPU without it. That feels a lot like the situation we are in with GPUs today.</p>
<p>If I unders... | <p>A couple issues come to mind:</p>
<h3>Synchronization/Communication overhead</h3>
<p>In order to seamlessly transition from CPU to GPU code you need to communicate with the GPU. The GPU additionally has to be available(aka not rendering the screen), and all instructions on the CPU side of things need to retire/finis... | 47 |
word embeddings | Word embeddings with documents and users | https://cs.stackexchange.com/questions/70136/word-embeddings-with-documents-and-users | <p>I understand how one can generate a latent vector space from a collection of words or documents, using something like Glove, word2vec, doc2vec, etc. I don't understand how this representation can be turned into features for something generating these documents at a "higher level", like a user or a product.</p>
<p>H... | 48 | |
word embeddings | Why word embeddings are compared with cosine distance and not euclidean? | https://cs.stackexchange.com/questions/147713/why-word-embeddings-are-compared-with-cosine-distance-and-not-euclidean | <p>In most articles that compare word embeddings they use cosine distance to determine if words are similar. Why?</p>
<p>I guess that euclidean distance should work too. So, my question is: it doesn't?
And why cosine distance doesn't fail?</p>
| <p>Those are two different measures of similarity. You could in principle use either one.</p>
<p>Both metrics are very closely connected. Let <span class="math-container">$v,w$</span> be two unit-length vectors (i.e., <span class="math-container">$\|v\|=\|w\|=1$</span>), and let <span class="math-container">$d(v,w)=1... | 49 |
word embeddings | Question about word embeddings in a specific language model - GPT-2 | https://cs.stackexchange.com/questions/116184/question-about-word-embeddings-in-a-specific-language-model-gpt-2 | <p>How were the <a href="https://openai.com/blog/better-language-models/" rel="nofollow noreferrer">GPT-2</a> token embeddings constructed? </p>
<p>The authors mention that they used Byte Pair Encoding to construct their vocabulary. But BPE is a compression algorithm that returns a list of subword tokens that would be... | 50 | |
word embeddings | How should I create a word-embedding an NLP model recognizing HTML elements? | https://cs.stackexchange.com/questions/143225/how-should-i-create-a-word-embedding-an-nlp-model-recognizing-html-elements | <p>I'm currently doing a small-time project where I have to deliver a model which can classify specific elements on a web-page using the HTML code.</p>
<p>For this, I have considered using the HTML tags for each specific element (which I can extract using some other code) and then transforming it to a vector to give a ... | 51 | |
word embeddings | How do I find the most similar phrase in "Extending Multi-Sense Word Embedding to Phrases and Sentences for Unsupervised Semantic Applications"? | https://cs.stackexchange.com/questions/144405/how-do-i-find-the-most-similar-phrase-in-extending-multi-sense-word-embedding-t | <p>This question is about de paper <a href="https://arxiv.org/pdf/2103.15330.pdf" rel="nofollow noreferrer">Extending Multi-Sense Word Embedding to Phrases and Sentences for Unsupervised Semantic Applications</a>, depicted in the following picture:</p>
<p><a href="https://i.sstatic.net/1Taan.jpg" rel="nofollow noreferr... | <p>If your goal is simply to find the most similar phrases, you do not need to use the methods in this paper. As the unsupervised phrase experiments show in this paper, multiple embeddings do not improve the similarity measurement.</p>
<p>There are many techniques you can use to find the nearest neighbors efficiently i... | 52 |
word embeddings | How can I modify this detail in the article ""Extending Multi-Sense Word Embedding to Phrases and Sentences for Unsupervised Semantic Applications"?" | https://cs.stackexchange.com/questions/144325/how-can-i-modify-this-detail-in-the-article-extending-multi-sense-word-embeddi | <p>This question is about de paper <a href="https://arxiv.org/pdf/2103.15330.pdf" rel="nofollow noreferrer">Extending Multi-Sense Word Embedding to Phrases and Sentences
for Unsupervised Semantic Applications</a>.</p>
<p>I am interested in the transformer part of the paper and the main structures of the algorithm is re... | <p>Thanks for being interested in our work.</p>
<p>The role of the decoder is to model the dependency between the codebook embeddings. For example, in this case, outputting an embedding close to sings might be correlated to outputting an embedding close to microphone.</p>
<p>There are several reasons that we choose to ... | 53 |
word embeddings | self embedded nonterminal in derivation of a Word | https://cs.stackexchange.com/questions/97252/self-embedded-nonterminal-in-derivation-of-a-word | <p><a href="https://i.sstatic.net/plIou.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/plIou.png" alt="questions from cohen"></a></p>
<p>consider this question of finding words with no self embedded nonterminal in their derivation.
The author(cohen) says that If CFG is in CNF then all the words with le... | 54 | |
word embeddings | How can node2vec help find similar "roles" within a graph (nodes whose connections have similar structure within the graph)? | https://cs.stackexchange.com/questions/95458/how-can-node2vec-help-find-similar-roles-within-a-graph-nodes-whose-connectio | <p>I have a question on the node2vec algorithm described in <a href="https://arxiv.org/pdf/1607.00653.pdf" rel="nofollow noreferrer">this paper</a>.</p>
<p>Node2vec is a deep learning algorithm that word2vec to graphs to learn embeddings. The authors claim that it can help find nodes with similar "roles", or nodes who... | 55 | |
word embeddings | Space efficient data structure to store precomputed All Nearest Neighbors in high dimensions | https://cs.stackexchange.com/questions/160119/space-efficient-data-structure-to-store-precomputed-all-nearest-neighbors-in-hig | <p><strong>Seeking an indexing data structure that is smaller than quadratic in space.</strong></p>
<p>As part of an NLP algorithm using word embeddings of 300-dimensions, I am trying to improve the speed of <a href="http://proceedings.mlr.press/v37/kusnerb15.pdf" rel="nofollow noreferrer">Word Mover's Distance</a> (WM... | <p>After pondering this for days, I have arrived at a possible data structure. It may be some time before I get to testing whether it performs as well as hoped.</p>
<p>The index will be derived from the Hilbert Curve ordering of the points. The index construction time will be O(N-cubed).</p>
<ol>
<li>Normalize and Quan... | 56 |
word embeddings | In what sense do we mean 'distributed' when talking about a distributed representation of words? | https://cs.stackexchange.com/questions/68714/in-what-sense-do-we-mean-distributed-when-talking-about-a-distributed-represen | <p>In machine learning literature, when handling words or text inputs, the strings are often mapped onto a vector space using techniques such as word2vec.</p>
<p>The terminology in this is that the individual word vectors are 'embeddings' and the embeddings together are a distributed representation of the input words ... | 57 | |
word embeddings | How to represent symbolic knowledge using real numbers - theory about neural networks and natural/analog computing? | https://cs.stackexchange.com/questions/98067/how-to-represent-symbolic-knowledge-using-real-numbers-theory-about-neural-net | <p>One can define the semantics of one definite word using the references to real world entities, relationships with the other words and other concepts and represent all this knowledge about this one word using logical symbolic expressions. And then one can encode all this set of symbolic expressions into vector of rea... | <p>No, probably not. I think you're expecting too much from the current state of the art in word embeddings. Word embeddings don't magically capture all semantic knowledge. They don't reflect perfect understanding of the language. Instead, they're just useful mappings where similar words often have similar embeddin... | 58 |
word embeddings | Confusion on the use of the chain-rule for the total derivative of the NLL Loss function | https://cs.stackexchange.com/questions/163325/confusion-on-the-use-of-the-chain-rule-for-the-total-derivative-of-the-nll-loss | <p>So my question is about when we want to find the total derivative of the NLL Loss function <span class="math-container">$L$</span> w.r.t. <span class="math-container">$w_i$</span>.</p>
<p>So the "pipeline" is often expressed as:
<span class="math-container">$$\frac{\partial L}{\partial w_i} = \frac{\partia... | 59 | |
word embeddings | How to represent sentences with their dependency parses as input to an RNN? | https://cs.stackexchange.com/questions/96814/how-to-represent-sentences-with-their-dependency-parses-as-input-to-an-rnn | <p>I am working on a task embedding sentences into a lower-dimensional space according to style, both grammatical and lexical. As such, I want to have as input the linear ordering of tokens in each sentence, together with its dependency parse as provided by spacy. </p>
<p>In particular, I'd like to find a way to tie ... | 60 | |
word embeddings | Why does parallelising slow down this simple problem against looping through all the data? | https://cs.stackexchange.com/questions/95896/why-does-parallelising-slow-down-this-simple-problem-against-looping-through-all | <p>I've been using multiprocessing and parallelisation for the first time this week on a very large data set using 32 CPUs. I decided to explore it for a smaller task just to see if I could learn anything, just on the 4 CPUs of my Mac.</p>
<p>I created a task to add 100 to every element in a 500,000 element list. To m... | <p>Parallelism has costs. The processes have to be scheduled, communicate with each other, manage resources, etc. In return you can do multiple things at the same time.</p>
<p>When you have a lot of slow tasks that can be done independently, parallel processing will speed things up a lot.</p>
<p>But when you try to p... | 61 |
word embeddings | Is copying and pasting a sort of object embedding? | https://cs.stackexchange.com/questions/151679/is-copying-and-pasting-a-sort-of-object-embedding | <p>If I copy a picture and paste it into Microsoft Word, would there be the difference if I embedded the same picture into another Word file ? Are they both object embedding?(As the object is saved in the document?)</p>
| 62 | |
word embeddings | What is the name of the word problem for free groups under straight line program encoding? | https://cs.stackexchange.com/questions/55413/what-is-the-name-of-the-word-problem-for-free-groups-under-straight-line-program | <p>I <a href="http://www.math.vanderbilt.edu/~msapir/ftp/pub/survey/survey.pdf" rel="nofollow">believe</a> that the <a href="https://en.wikipedia.org/wiki/Word_problem_for_groups" rel="nofollow">word problem</a> is the problem to decide whether two different expressions denote the same element of a suitably defined alg... | <p>The blog post you link to already gives a <em>deterministic</em> polynomial-time (in fact, linear-time) algorithm for the word problem over a free group with 2 letters.</p>
<p>In contrast, no deterministic polynomial-time algorithm for identity testing for polynomials is currently known (this is a famous open probl... | 63 |
word embeddings | For regular languages A and B, determine whether B might match early in (A B) | https://cs.stackexchange.com/questions/10852/for-regular-languages-a-and-b-determine-whether-b-might-match-early-in-a-b | <p>I have two regular languages <em>A</em> and <em>B</em>, and I want to determine whether there is any pair of strings, <em>a</em> in <em>A</em> and <em>b</em> in <em>B</em>, such that (<em>a</em> <em>b</em>) is a prefix of a string in (<em>A</em> <em>B</em>) and the left-most match of <em>B</em> in (<em>a</... | <p>If I translate your description properly, here is what you want to ask:</p>
<blockquote>
<p>Given two regular language $A$, $B$, is there a prefix of a word $b$ in $B$ that is a suffix of a word in $A$ so that the rest of $b$ is a prefix of another word in $B$?</p>
</blockquote>
<p>Formally:</p>
<blockquote>
... | 64 |
word embeddings | Numerically validate CRC performance | https://cs.stackexchange.com/questions/69262/numerically-validate-crc-performance | <p><a href="https://users.ece.cmu.edu/~koopman/roses/dsn04/koopman04_crc_poly_embedded.pdf" rel="nofollow noreferrer">Koopman, P., & Chakravarty, T. (2004, June). Cyclic redundancy code (CRC) polynomial selection for embedded networks. In Dependable Systems and Networks, 2004 International Conference on (pp. 145-15... | <p>There are multiple techniques to compute the minimum Hamming distance for a given CRC polynomial. I don't know what technique they used, but here are three techniques that seem suitable.</p>
<p>I will assume the problem is as follows:</p>
<p>Given a CRC polynomial $p(x)$, determine whether there exists a $d$-bit ... | 65 |
word embeddings | Why is Hamming Weight (in the CRC context) independent from the data? | https://cs.stackexchange.com/questions/51758/why-is-hamming-weight-in-the-crc-context-independent-from-the-data | <p>I'm designing a communication protocol for 24 to 52 bits (typically 32 bits) data including the CRC-8 for error detection. I'm trying to select the best polynomial for this kind of application.</p>
<p>In the paper <a href="http://users.ece.cmu.edu/~koopman/roses/dsn04/koopman04_crc_poly_embedded.pdf" rel="nofollow"... | <p>Define the sets</p>
<p>$$\begin{align*}
P(d) &:= \{ p ~|~ \deg(p) \leq d \}\\
A_i(d) &:= \{ p \in P(d) ~|~ s(p) = i \}
\end{align*}$$</p>
<p>where $s(p)$ is the number of $1$ coefficients of the polynomial $p$. For a given CRC generator polynomial $g$, define</p>
<p>$$ U_i(d) := \{ p \in A_i(d) ~|~ \exist... | 66 |
word embeddings | join is the heart of the monad because it encompasses everything a monad can do that a functor cannot. Is this true? | https://cs.stackexchange.com/questions/99516/join-is-the-heart-of-the-monad-because-it-encompasses-everything-a-monad-can-do | <p>There is a controversy about Monad implementation in S.O .</p>
<p>The original question is,</p>
<p><a href="https://stackoverflow.com/questions/53109889/whats-so-special-about-monads-in-kleisli-category#">What's so special about Monads in Kleisli category?</a></p>
<blockquote>
<p>Is there any counterexample that Fun... | <p>I'm not sure I fully understand the question, but since it's my answer you're wondering about, I'll do my best to clarify my meaning.<sup>1</sup></p>
<blockquote>
<p>join is the heart of the monad because it encompasses everything a monad can do that a functor cannot. Is this true?</p>
</blockquote>
<p>Let's fin... | 67 |
graph theory | Research in Graph Theory versus Graph Algorithms | https://cs.stackexchange.com/questions/25847/research-in-graph-theory-versus-graph-algorithms | <p>I have a very generic question to ask. It is related to
research. I'm interested in Graph theory. I have done a course in
it. I have done some topics related to both graph theory as a point
of view of doing it as a mathematics student and also studied some
graph algorithms. I'm going for research internship in ... | <p><strong>Question 1</strong></p>
<p>I would say that the two areas are definitely not identical, however there is a huge overlap. Partly it depends on where you draw some very fuzzy lines. Let's start with:</p>
<ul>
<li><em>Graph Theory</em> is about the properties of graphs as mathematical objects</li>
<li><em>Gra... | 68 |
graph theory | Graph theory book for beginners | https://cs.stackexchange.com/questions/148733/graph-theory-book-for-beginners | <p>I need a book recommendation for graph theory which supposes background in set theory. I want to cover those questions first as graph theory is part of combinatorics. Can you recommend me a book which is beginner-friendly without going much into combinatorics?</p>
<p>I heard about Harris and West but these books use... | 69 | |
graph theory | Does spectral graph theory say anything about graph isomorphism | https://cs.stackexchange.com/questions/25988/does-spectral-graph-theory-say-anything-about-graph-isomorphism | <p>Is there research or are there results that discuss graph isomorphism in the context of spectral graph theory?</p>
<p>Two known theorems of spectral graph theory are:</p>
<ol>
<li><p>Two graphs are called isospectral or cospectral if the adjacency matrices of the graphs have equal multisets of eigenvalues.</p></li... | <p>Graph isomorphism has been mentioned along with primality testing as early as 1971 in Cook's famous paper on NP-completeness. Cook mentions that he was unable to prove the NP-completeness of both problems. Nowadays we known that primality testing is in P, but the status of graph isomorphism is still unknown. Most ex... | 70 |
graph theory | Repeated vertices in cycles (graph theory) | https://cs.stackexchange.com/questions/150806/repeated-vertices-in-cycles-graph-theory | <p>In graph theory, can a cycle contain repeated nodes/vertices not including the first and last ones? If so, can you please give an example?</p>
| <p>Usually cycles are assumed not to have any repeating vertices (other than the first and last vertices being identical). If repeating vertices are allowed, then one talks about <em>closed walks</em>. In order to stress that cycles have no repeating vertices, we call them <em>simple cycles</em>.</p>
<p>That said, term... | 71 |
graph theory | Is this a known problem in graph theory? | https://cs.stackexchange.com/questions/129198/is-this-a-known-problem-in-graph-theory | <p>My basic problem includes a graph where each node <span class="math-container">$i$</span> is associated with a weight <span class="math-container">$c_i$</span>, and the problem is to find a minimum (or maximum) weighted independent set with a fixed cardinality <span class="math-container">$p$</span>. This is I belie... | <p>If <span class="math-container">$G=(V,E)$</span>, with <span class="math-container">$V=\{v_1,v_2,...,v_n\}$</span> and weights <span class="math-container">$\{c_{i,j}, i=1,2,...,n, j=1,2,...,p\}$</span> is the given graph, then we can construct the <a href="https://en.wikipedia.org/wiki/Strong_product_of_graphs" rel... | 72 |
graph theory | Standard or Top Text on Applied Graph Theory | https://cs.stackexchange.com/questions/2845/standard-or-top-text-on-applied-graph-theory | <p>I am looking for a reference text on applied graph theory and graph algorithms. Is there a standard text used in most computer science programs? If not, what are the most respected texts in the field? I have Cormen et al.</p>
| <p>For digraphs in particular, there's Band-Jensen & Gutin's <a href="http://www.cs.rhul.ac.uk/books/dbook/" rel="nofollow">"Digraphs: Theory, Algorithms and Applications"</a>. It covers quite a bit of material.</p>
<p>The first edition is free to download now that the second edition is out (There's a link to the ... | 73 |
graph theory | Looking for an esoteric graph theory algorithm | https://cs.stackexchange.com/questions/106743/looking-for-an-esoteric-graph-theory-algorithm | <p>So I'm sure this is an unusual question for this type of site, but I am to give a talk on algorithms for discrete graphs in a few weeks. It has been specified that the talk is to be on some algorithm which will be unfamiliar for those attending. It it to be some graph traversal algorithm at about the junior level. D... | 74 | |
graph theory | Relative Importance in Graph Theory | https://cs.stackexchange.com/questions/32203/relative-importance-in-graph-theory | <p>I am working on an algorithm that ranks a set of nodes in a graph with respect to how relative this node is to other predefined nodes (I call them query nodes). The way how the algorithm works is similar to recommendation algorithms. For instance, if i want to buy an item from an online store, the algorithm will loo... | <p>You can for instance take as <em>ground truth data</em> the movielens dataset, remove some rating links between users and movies. You can rank your algorithm by counting the number of link that you can guess right. Usually machine learning algorithm also guess the rating score.</p>
| 75 |
graph theory | graph theory single bar vs double bar size notation | https://cs.stackexchange.com/questions/167412/graph-theory-single-bar-vs-double-bar-size-notation | <p>A follow-up on <a href="https://stackoverflow.com/questions/15037679/what-do-the-absolute-value-bars-mean-in-graph-theory">https://stackoverflow.com/questions/15037679/what-do-the-absolute-value-bars-mean-in-graph-theory</a></p>
<p>What is the difference between single bar <span class="math-container">$|G|$</span> a... | <p>You are correct. <span class="math-container">$|G|$</span> denotes the number of vertices in <span class="math-container">$G$</span>, and <span class="math-container">$||G||$</span> denotes the number of edges in <span class="math-container">$G$</span>. Formally, for a graph <span class="math-container">$G = (V, E)$... | 76 |
graph theory | Is there a graph theory textbook that covers treewidth thoroughly? | https://cs.stackexchange.com/questions/132289/is-there-a-graph-theory-textbook-that-covers-treewidth-thoroughly | <p>Can someone recommend a graph theory textbook that covers treewidth thoroughly?</p>
<p>Something that focuses on the graph-theoretic structure of bounded treewidth graphs rather than solving problems on them. Don't need the strongest/newest results but would prefer something that</p>
<p>Preferably something that co... | <p>I don't know if the thing you are looking for exists, but here are at least some pointers:</p>
<p><a href="http://parameterized-algorithms.mimuw.edu.pl/parameterized-algorithms.pdf" rel="nofollow noreferrer"><em>Parameterized Algorithms</em> by Cygan <em>et al</em> (free PDF version)</a> has a chapter dedicated on t... | 77 |
graph theory | Approporiate algorithm for a graph theory problem | https://cs.stackexchange.com/questions/109576/approporiate-algorithm-for-a-graph-theory-problem | <p>So I have recently ran into a graph theory problem and was unable to find a matching algorithm for the problem or reword the problem to match some existing algorithm.</p>
<p>The problem is pretty straightforward - given a weighted directed graph, pick edges to maximize the sum of all weights of the chosen edges. Ma... | 78 | |
graph theory | What is a min-max theorem in graph theory? | https://cs.stackexchange.com/questions/99039/what-is-a-min-max-theorem-in-graph-theory | <p>I'm currently studying a paper which uses extensively the term '<code>min-max theorems</code>' in graph theory, and claims to present a tool allowing to generalize these theorems. (here is the <a href="http://acta.bibl.u-szeged.hu/38618/1/math_041_fasc_001_002.pdf#page=65" rel="nofollow noreferrer">link</a> to the p... | <p>A min-max theorem is simply a theorem that says that the minimum value possible for one quantity is the maximum value possible for some other.
For example,</p>
<ul>
<li><p>Max-flow min-cut says that the value of the biggest flow between two vertices in a weighted graph is equal to the value of the minimum cut that ... | 79 |
graph theory | Is there a good analogy between spectral representation of a signal and graph theory? | https://cs.stackexchange.com/questions/140083/is-there-a-good-analogy-between-spectral-representation-of-a-signal-and-graph-th | <p>I am working on some time series problems where the Fourier representation of the signal in the frequency domain is also important. I am wondering if there is any connection between time series signals consisting of sinusoidal/inherently periodic functions (functions that can be cleanly represented by a sum of sinus... | 80 | |
graph theory | Graph Theory - Airline Schedule | https://cs.stackexchange.com/questions/77119/graph-theory-airline-schedule | <p>Suppose I have a number of airports which have a set number of routes. Large airports have 7, medium airports have 4, and small airports have 1.</p>
<p>First of all, what would I call a graph of this type where it is undirected, has no parallel edges, no loops, and every edge is connected to another (that is no rou... | 81 | |
graph theory | What graph theory algorithm(s) would help solve this problem? | https://cs.stackexchange.com/questions/88597/what-graph-theory-algorithms-would-help-solve-this-problem | <p>I have a directed graph with the following properties:</p>
<ol>
<li>Except for a few special progenitor nodes, every node has two parent nodes</li>
<li>Any node can have any whole number of child nodes</li>
<li>The graph is generated such that no node is a descendant of itself in the following way: I starting with ... | <p>Given two progenitor vertices $u$ and $v$, the following "modified flood fill" builds a set $P$ of additional vertices to include:</p>
<ul>
<li>While a vertex $x$ exists whose parents are both in the set $\{u, v\} \cup P$:
<ul>
<li>Add $x$ to $P$.</li>
</ul></li>
</ul>
<p>This will halt with $\{u, v\} \cup P$ bei... | 82 |
graph theory | Graph theory : Trees | https://cs.stackexchange.com/questions/126596/graph-theory-trees | <p>I need to determine all the trees on 25 vertices for which there exists an integer m ≥ 2, such
that the degree of each vertex gives the same remainder when divided by m.</p>
<p>Can somebody help ?</p>
| <p>Suppose <span class="math-container">$G = (V, E)$</span> is a tree with 25 vertices such that there exist some constants <span class="math-container">$c \geq 0$</span> and <span class="math-container">$m \geq 2$</span> such that <span class="math-container">$\operatorname{deg} v \equiv_m c$</span> for all <span clas... | 83 |
graph theory | Markov Inequality in graph theory | https://cs.stackexchange.com/questions/96407/markov-inequality-in-graph-theory | <p>Fix an optimal solution G∗ to k-Cycle-Free Subgraph. Partition the vertex set V of G randomly into two subsets, A and B, each of size n/2, and remove edges internal to A or B. In expectation, the fraction of edges in G∗ that remain after this process is 1/2. <strong><em>With probability at least 2/3 the fraction of ... | <p>Let $X$ denote the fraction of remaining edges. We know that $0 \leq X \leq 1$ and $\mathbb{E}[X] = 1/2$. Let us define $Y = 1 - X$, which is the fraction of edges inside $A$ and $B$. This is a non-negative random variable whose expectation is $\mathbb{E}[Y] = 1/2$. According to Markov's inequality,
$$
\Pr[X < 1/... | 84 |
graph theory | graph theory proof or disproving | https://cs.stackexchange.com/questions/118141/graph-theory-proof-or-disproving | <p>I was requested to prove or disprove the following statement
if a graph is conncted does it necessarily means that E>(V-1)(V-2)/2
v represents vertex and E the edges
I think I need to disprove it with overall disproval but how?</p>
| <p>If you think it's false, the easiest way to disprove it would be to find a counterexample. That is, find a graph where <span class="math-container">$E \leq \frac{1}{2}(V-1)(V-2)$</span>. Try some easy connected graphs (e.g. a straight-line path graph) and see if you can find a suitable graph.</p>
| 85 |
graph theory | Good resource for graph theory | https://cs.stackexchange.com/questions/116444/good-resource-for-graph-theory | <p>Frankly speaking I have many problem with symbols in graph such as (s:s') or v\S or some symbols such as those that I mentioned . Can anyone suggest a good resource or a good tutorial on the net that has been discussed about these symbols and have clarified these symbols ?</p>
| 86 | |
graph theory | How do programs like Apache Airflow/ Luigi determine shortest path and how does that relate to graph theory? | https://cs.stackexchange.com/questions/119602/how-do-programs-like-apache-airflow-luigi-determine-shortest-path-and-how-does | <p>I am looking for a simple layman's term explanation on how do programs like Apache Airflow or Luigi (or any Task/ETL schedulers) determine the shortest path to complete a certain task and make it possible to parallelize it? And how does that, if any, relate to graph theory?</p>
| 87 | |
graph theory | graph theory analogue of rectangular matrix | https://cs.stackexchange.com/questions/47092/graph-theory-analogue-of-rectangular-matrix | <p>Graphs are usually defined as a set of vertices $V$ together with a set of edges $E$ consisting of elements $V \times V$. I'm interested in a slight generalization of this, where instead one has two sets $V$, $W$ and the edges are taken from $V \times W$. The adjacency matrix of such an object would be rectangular, ... | <p>Such a graph is known as a <a href="https://en.wikipedia.org/wiki/Bipartite_graph">bipartite graph</a>. There is a whole theory about bipartite graphs, including a number of algorithms that are specialized for bipartite graphs.</p>
| 88 |
graph theory | Graph Theory Handshaking problem | https://cs.stackexchange.com/questions/27507/graph-theory-handshaking-problem | <p>Mr. and Mrs. Smith, a married couple, invited 9 other married couples to a party. (So the party consisted of 10
couples.) There was a round of handshaking, but no one shook hand with his or her spouse. Afterwards, Mrs.
Smith asked everyone except herself, “how many persons have you shaken hands with?” All 19 answers... | <p>Here is a solution for two couples, $m_1,w_1$ and $m_2,w_2$. The edges are $(m_1,w_2),(w_1,w_2)$. The degrees are $1,1,0,2$ (in the order $m_1,w_1,m_2,w_2$).</p>
<p>Here is a solution for three couples, $m_1,w_1,m_2,w_2,m_3,w_3$. The edges are $(m_1,w_2),(w_1,w_2),(m_1,w_3),(w_1,w_3),(m_2,w_3),(w_2,w_3)$. The degre... | 89 |
graph theory | Dependent Type Theory Implementation of a Graph | https://cs.stackexchange.com/questions/94003/dependent-type-theory-implementation-of-a-graph | <p>In Haskell you find <a href="http://www.cs.ox.ac.uk/duncan.coutts/papers/recursive_data_structures_in_haskell.pdf" rel="nofollow noreferrer">graphs defined like this</a>:</p>
<pre><code>data Graph a = GNode a (Graph a)
</code></pre>
<p><a href="https://hackage.haskell.org/package/algebraic-graphs" rel="nofollow no... | <p>So, there are two different things you are talking about.</p>
<ol>
<li>The <strong>definition</strong> of a graph</li>
<li>The <strong>encoding</strong> of a graph</li>
</ol>
<p>A Graph is always <em>defined</em> as a set of vertices and edges. This tells us what vertices are in the graph, and for any pair of vert... | 90 |
graph theory | graph theory conventions, difference between a PATH and a GRAPH? | https://cs.stackexchange.com/questions/112054/graph-theory-conventions-difference-between-a-path-and-a-graph | <p>Consider this example, I did my pseudocode in python</p>
<pre><code>findCycle(G):
for each edge e in E(G):
if isThereCycle(G-e):
G = G - e
return G
</code></pre>
<p>assume isthereCycle returns whether the graph <span class="math-container">$G$</span> has a cycle. </p>
<p>Input is a gr... | <p>Your algorithm returns a cycle rather than a path.</p>
<p>Here is a <a href="https://en.wikipedia.org/wiki/Cycle_graph" rel="nofollow noreferrer">cycle</a>:</p>
<p><a href="https://i.sstatic.net/Xt9sm.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Xt9sm.png" alt="cycle"></a></p>
<p>Here is a <a hr... | 91 |
graph theory | Playing with boxes: NP-hard? [Graph Theory] | https://cs.stackexchange.com/questions/153291/playing-with-boxes-np-hard-graph-theory | <p>You are playing with boxes on a <span class="math-container">$K_{1, n}$</span>-<span class="math-container">$\textbf{subdivision}$</span> graph <span class="math-container">$G:=(V, E)$</span> whose number of vertices is odd, i.e., <span class="math-container">$|V| \equiv 1$</span> (mod <span class="math-container">$... | 92 | |
graph theory | The equivalence relations cover problem (in graph theory) | https://cs.stackexchange.com/questions/27828/the-equivalence-relations-cover-problem-in-graph-theory | <p>An equivalence relation on a finite vertex set can be represented by an undirected graph that is a disjoint union of cliques. The vertex set represents the elements and an edge represents that two elements are equivalent.</p>
<p>If I have a graph $G$ and graphs $G_1,\dots,G_k$, we say that $G$ is covered by $G_1,\d... | <p>The problem is known as the <em>equivalence covering problem</em> in graph theory. It is upper bounded by the <em>clique covering number</em> (the minimum collection of cliques such that each edge of the graph is in <em>at least</em> one clique). There are many similar problems and definitions; one has to be very ca... | 93 |
graph theory | Category theory and graphs | https://cs.stackexchange.com/questions/23875/category-theory-and-graphs | <p>Could most categories , or a finite part of them be represented on a subset of a complete graph of N vertices (Kn) which is connected. and partly directed? Could all the axioms of category theory be written for such graphs?</p>
| <p>A category consists of:</p>
<ul>
<li><p>Objects.</p></li>
<li><p>Directed arrows between objects. There can be multiple arrows between any two given objects, or a unique arrow, or none.</p></li>
<li><p>A composition map for arrows that takes an arrow $f$ from $x$ to $y$ and another arrow $g$ from $y$ to $z$ and out... | 94 |
graph theory | Graph Theory applied to a physical logic puzzle | https://cs.stackexchange.com/questions/85965/graph-theory-applied-to-a-physical-logic-puzzle | <p>For Christmas my brother got me this puzzle:
<img src="https://i.sstatic.net/OqSnc.jpg" alt="puzzle"></p>
<p>The premise is that you have a metal medallion with a series of holes in it and a metal ring with a slit just large enough to slide it from hole to hole, barring obstacles, like the edge of the map and an ob... | 95 | |
graph theory | Graph theory, $n$ people sitting around table | https://cs.stackexchange.com/questions/44212/graph-theory-n-people-sitting-around-table | <p>$n$ people want to have dinner together around a table for $k$ nights so that no person has the same neighbor twice.</p>
<ol>
<li>How big can $k$ be in terms of $n$?</li>
<li>Does everybody get to sit next to everybody else?</li>
<li>How many seating arrangements are there?</li>
</ol>
| <p><em>Point 3.</em> If the seats are unlabelled, the number of arrangements is $\frac{(n-1)!}{2}$.</p>
<p><em>Explanation</em>: put a hat on one of the person and take it as the leader. Then you have $n-1$ choices for the person to his right and so on. But each arrangement is counted twice if you consider that circul... | 96 |
graph theory | Graph theory: determining maximum number of edges | https://cs.stackexchange.com/questions/101199/graph-theory-determining-maximum-number-of-edges | <p>Based on the question below, can someone please explain to me the reasoning behind why the maximum number of edge is 5/2|V|? I don't find the particular reasoning in the solution to be that helpful for why the maximum number is 5/2|V|. </p>
<p><a href="https://i.sstatic.net/OUIeL.png" rel="nofollow noreferrer"><img... | <p>The following identity is well-known:
<span class="math-container">$$
2|E| = \sum_{v \in V} d(v).
$$</span>
In words, if we sum all degrees in a graph, we get twice the number of edges. To see this, divide each edge <span class="math-container">$(x,y)$</span> into two halves: the <span class="math-container">$x$</sp... | 97 |
graph theory | Is Homomorphic Computation Possible Using Graph Theory | https://cs.stackexchange.com/questions/170640/is-homomorphic-computation-possible-using-graph-theory | <p><a href="https://www.zama.ai/" rel="nofollow noreferrer">Homomorphic encryption</a> allows to store data on a blockchain encrypted, but a smart contract is a program that is executed on a node on the blockchain, therefore the "source code" of the contract is not private; therefore it is desirable to build ... | 98 | |
graph theory | if (dis)proving a conjecture on graph theory can be done just by a counter example then can every (dis)proof be mapped actually to a counter-example? | https://cs.stackexchange.com/questions/27529/if-disproving-a-conjecture-on-graph-theory-can-be-done-just-by-a-counter-examp | <p>Suppose we have a conjecture on graph theory that can be (dis)proved by means of a counter example, then, is it true that every alternative (dis)proof of the conjecture can be mapped to a counter example? </p>
<p>This is in the general case, but for instance, can any proof that the hadwiger's conjecture is false be... | <p>Your question isn't entirely clear, but it seems you're asking if every false graph property has a counterexample. Obviously this is true: by definition there must be some graph for which the property doesn't hold. On the other hand, a proof that the property doesn't hold for all graphs may not necessarily give an e... | 99 |
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