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Probabilistic automaton : In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also genera... |
Probabilistic automaton : For a given initial state and input character, a deterministic finite automaton (DFA) has exactly one next state, and a nondeterministic finite automaton (NFA) has a set of next states. A probabilistic automaton (PA) instead has a weighted set (or vector) of next states, where the weights must... |
Probabilistic automaton : The probabilistic automaton may be defined as an extension of a nondeterministic finite automaton ( Q , Σ , δ , q 0 , F ) ,F) , together with two probabilities: the probability P of a particular state transition taking place, and with the initial state q 0 replaced by a stochastic vector giv... |
Probabilistic automaton : The set of languages recognized by probabilistic automata are called stochastic languages. They include the regular languages as a subset. Let F = Q accept ⊆ Q \subseteq Q be the set of "accepting" or "final" states of the automaton. By abuse of notation, Q accept can also be understood to be... |
Probabilistic automaton : Every regular language is stochastic, and more strongly, every regular language is η-stochastic. A weak converse is that every 0-stochastic language is regular; however, the general converse does not hold: there are stochastic languages that are not regular. Every η-stochastic language is stoc... |
Probabilistic automaton : The p-adic languages provide an example of a stochastic language that is not regular, and also show that the number of stochastic languages is uncountable. A p-adic language is defined as the set of strings L η ( p ) = (p)=\n_n_\ldots \vert 0\leq n_<p0.n_n_n_\ldots >\eta \ in the letters 0 , ... |
Probabilistic automaton : The probabilistic automaton has a geometric interpretation: the state vector can be understood to be a point that lives on the face of the standard simplex, opposite to the orthogonal corner. The transition matrices form a monoid, acting on the point. This may be generalized by having the poin... |
Probabilistic automaton : Salomaa, Arto (1969). "Finite nondeterministic and probabilistic automata". Theory of Automata. Oxford: Pergamon Press. |
Pumping lemma for regular languages : In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages. Informally, it says that all sufficiently long strings in a regular language may be pumped—that is, have a middle section of the stri... |
Pumping lemma for regular languages : Let L be a regular language. Then there exists an integer p ≥ 1 depending only on L such that every string w in L of length at least p ( p is called the "pumping length") can be written as w = x y z (i.e., w can be divided into three substrings), satisfying the following c... |
Pumping lemma for regular languages : The pumping lemma is often used to prove that a particular language is non-regular: a proof by contradiction may consist of exhibiting a string (of the required length) in the language that lacks the property outlined in the pumping lemma. Example: The language L = b^:n\geq 0\ ove... |
Pumping lemma for regular languages : For every regular language there is a finite-state automaton (FSA) that accepts the language. The number of states in such an FSA are counted and that count is used as the pumping length p . For a string of length at least p , let q 0 be the start state and let q 1 , . . . , q p... |
Pumping lemma for regular languages : If a language L is regular, then there exists a number p ≥ 1 (the pumping length) such that every string u w v in L with | w | ≥ p can be written in the form u w v = u x y z v with strings x , y and z such that | x y | ≤ p , | y | ≥ 1 and u x y i z v zv is in L for ever... |
Pumping lemma for regular languages : While the pumping lemma states that all regular languages satisfy the conditions described above, the converse of this statement is not true: a language that satisfies these conditions may still be non-regular. In other words, both the original and the general version of the pumpin... |
Pumping lemma for regular languages : Ogden's lemma Pumping lemma for context-free languages Pumping lemma for regular tree languages |
Pumping lemma for regular languages : Lawson, Mark V. (2004). Finite automata. Chapman and Hall/CRC. ISBN 978-1-58488-255-8. Zbl 1086.68074. Sipser, Michael (1997). "1.4: Nonregular Languages". Introduction to the Theory of Computation. PWS Publishing. pp. 77–83. ISBN 978-0-534-94728-6. Zbl 1169.68300. Hopcroft, John E... |
Quantum finite automaton : In quantum computing, quantum finite automata (QFA) or quantum state machines are a quantum analog of probabilistic automata or a Markov decision process. They provide a mathematical abstraction of real-world quantum computers. Several types of automata may be defined, including measure-once ... |
Quantum finite automaton : There is a simple, intuitive way of understanding quantum finite automata. One begins with a graph-theoretic interpretation of deterministic finite automata (DFA). A DFA can be represented as a directed graph, with states as nodes in the graph, and arrows representing state transitions. Each ... |
Quantum finite automaton : Measure-once automata were introduced by Cris Moore and James P. Crutchfield. They may be defined formally as follows. As with an ordinary finite automaton, the quantum automaton is considered to have N possible internal states, represented in this case by an N -state qudit | ψ ⟩ . More pr... |
Quantum finite automaton : Consider the classical deterministic finite automaton given by the state transition table The quantum state is a vector, in bra–ket notation | ψ ⟩ = a 1 | S 1 ⟩ + a 2 | S 2 ⟩ = [ a 1 a 2 ] |S_\rangle +a_|S_\rangle =a_\\a_\end with the complex numbers a 1 , a 2 ,a_ normalized so that [ a 1 ∗ a... |
Quantum finite automaton : Measure-many automata were introduced by Kondacs and Watrous in 1997. The general framework resembles that of the measure-once automaton, except that instead of there being one projection, at the end, there is a projection, or quantum measurement, performed after each letter is read. A formal... |
Quantum finite automaton : As of 2019, most quantum computers are implementations of measure-once quantum finite automata, and the software systems for programming them expose the state-preparation of | ψ ⟩ , measurement P and a choice of unitary transformations U α , such the controlled NOT gate, the Hadamard trans... |
Quantum finite automaton : The above constructions indicate how the concept of a quantum finite automaton can be generalized to arbitrary topological spaces. For example, one may take some (N-dimensional) Riemann symmetric space to take the place of C P N P^ . In place of the unitary matrices, one uses the isometries ... |
Quantum finite automaton : Quantum Markov chain Blum–Shub–Smale machine Real computer == Notes == |
Quotient automaton : In computer science, in particular in formal language theory, a quotient automaton can be obtained from a given nondeterministic finite automaton by joining some of its states. The quotient recognizes a superset of the given automaton; in some cases, handled by the Myhill–Nerode theorem, both langu... |
Quotient automaton : A (nondeterministic) finite automaton is a quintuple A = ⟨Σ, S, s0, δ, Sf⟩, where: Σ is the input alphabet (a finite, non-empty set of symbols), S is a finite, non-empty set of states, s0 is the initial state, an element of S, δ is the state-transition relation: δ ⊆ S × Σ × S, and Sf is the set of ... |
Quotient automaton : For example, the automaton A shown in the first row of the table is formally defined by ΣA = , SA = , sA0 = a, δA = , and SAf = . It recognizes the finite set of strings ; this set can also be denoted by the regular expression "1+10+100". The relation (≈) = , more briefly denoted as a≈b,c≈d, is an ... |
Quotient automaton : For every automaton A and every equivalence relation ≈ on its states set, L(A/≈) is a superset of (or equal to) L(A).: 6 Given a finite automaton A over some alphabet Σ, an equivalence relation ≈ can be defined on Σ* by x ≈ y if ∀ z ∈ Σ*: xz ∈ L(A) ↔ yz ∈ L(A). By the Myhill–Nerode theorem, A/≈ is ... |
Quotient automaton : Quotient group Quotient category |
Regular language : In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augme... |
Regular language : The collection of regular languages over an alphabet Σ is defined recursively as follows: The empty language Ø is a regular language. For each a ∈ Σ (a belongs to Σ), the singleton language is a regular language. If A is a regular language, A* (Kleene star) is a regular language. Due to this, the em... |
Regular language : All finite languages are regular; in particular the empty string language = Ø* is regular. Other typical examples include the language consisting of all strings over the alphabet which contain an even number of a's, or the language consisting of all strings of the form: several a's followed by seve... |
Regular language : A regular language satisfies the following equivalent properties: it is the language of a regular expression (by the above definition) it is the language accepted by a nondeterministic finite automaton (NFA) it is the language accepted by a deterministic finite automaton (DFA) it can be generated by ... |
Regular language : The regular languages are closed under various operations, that is, if the languages K and L are regular, so is the result of the following operations: the set-theoretic Boolean operations: union K ∪ L, intersection K ∩ L, and complement L, hence also relative complement K − L. the regular operations... |
Regular language : Given two deterministic finite automata A and B, it is decidable whether they accept the same language. As a consequence, using the above closure properties, the following problems are also decidable for arbitrarily given deterministic finite automata A and B, with accepted languages LA and LB, respe... |
Regular language : In computational complexity theory, the complexity class of all regular languages is sometimes referred to as REGULAR or REG and equals DSPACE(O(1)), the decision problems that can be solved in constant space (the space used is independent of the input size). REGULAR ≠ AC0, since it (trivially) conta... |
Regular language : To locate the regular languages in the Chomsky hierarchy, one notices that every regular language is context-free. The converse is not true: for example, the language consisting of all strings having the same number of a's as b's is context-free but not regular. To prove that a language is not regula... |
Regular language : Let s L ( n ) (n) denote the number of words of length n in L . The ordinary generating function for L is the formal power series S L ( z ) = ∑ n ≥ 0 s L ( n ) z n . (z)=\sum _s_(n)z^\ . The generating function of a language L is a rational function if L is regular. Hence for every regular language... |
Regular language : The notion of a regular language has been generalized to infinite words (see ω-automata) and to trees (see tree automaton). Rational set generalizes the notion (of regular/rational language) to monoids that are not necessarily free. Likewise, the notion of a recognizable language (by a finite automat... |
Regular language : Kleene, S.C.: Representation of events in nerve nets and finite automata. In: Shannon, C.E., McCarthy, J. (eds.) Automata Studies, pp. 3–41. Princeton University Press, Princeton (1956); it is a slightly modified version of his 1951 RAND Corporation report of the same title, RM704. Sakarovitch, J (19... |
Regular language : Complexity Zoo: Class REG |
Self-verifying finite automaton : In automata theory, a self-verifying finite automaton (SVFA) is a special kind of a nondeterministic finite automaton (NFA) with a symmetric kind of nondeterminism introduced by Hromkovič and Schnitger. Generally, in self-verifying nondeterminism, each computation path is concluded wit... |
Self-verifying finite automaton : An SVFA is represented formally by a 6-tuple, A=(Q, Σ, Δ, q0, Fa, Fr) such that (Q, Σ, Δ, q0, Fa) is an NFA, and Fa, Fr are disjoint subsets of Q. For each word w = a1a2 … an, a computation is a sequence of states r0,r1, …, rn, in Q with the following conditions: r0 = q0 ri+1 ∈ Δ(ri, a... |
Self-verifying finite automaton : Each DFA is a SVFA, but not vice versa. Jirásková and Pighizzini proved that for every SVFA of n states, there exists an equivalent DFA of g ( n ) = Θ ( 3 n / 3 ) ) states. Furthermore, for each positive integer n, there exists an n-state SVFA such that the minimal equivalent DFA has e... |
Semiautomaton : In mathematics and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states, a set Σ called the input alphabet, and a function T: Q × Σ → Q called the transition function. Associated with any semiautomaton is a monoid... |
Semiautomaton : A transformation semigroup or transformation monoid is a pair ( M , Q ) consisting of a set Q (often called the "set of states") and a semigroup or monoid M of functions, or "transformations", mapping Q to itself. They are functions in the sense that every element m of M is a map m : Q → Q . If s and ... |
Semiautomaton : A semiautomaton is a triple ( Q , Σ , T ) where Σ is a non-empty set, called the input alphabet, Q is a non-empty set, called the set of states, and T is the transition function T : Q × Σ → Q . When the set of states Q is a finite set—it need not be—, a semiautomaton may be thought of as a determinis... |
Semiautomaton : If the set of states Q is finite, then the transition functions are commonly represented as state transition tables. The structure of all possible transitions driven by strings in the free monoid has a graphical depiction as a de Bruijn graph. The set of states Q need not be finite, or even countable. A... |
Semiautomaton : A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. American Mathematical Society, volume 2 (1967), ISBN 978-0-8218-0272-4. F. Gecseg and I. Peak, Algebraic Theory of Automata (1972), Akademiai Kiado, Budapest. W. M. L. Holcombe, Algebraic Automata Theory (1982), Cambridge University P... |
Separating words problem : In theoretical computer science, the separating words problem is the problem of finding the smallest deterministic finite automaton that behaves differently on two given strings, meaning that it accepts one of the two strings and rejects the other string. It is an open problem how large such ... |
Separating words problem : The two strings 0010 and 1000 may be distinguished from each other by a three-state automaton in which the transitions from the start state go to two different states, both of which are terminal in the sense that subsequent transitions from these two states always return to the same state. Th... |
Separating words problem : For proving bounds on this problem, it may be assumed without loss of generality that the inputs are strings over a two-letter alphabet. For, if two strings over a larger alphabet differ then there exists a string homomorphism that maps them to binary strings of the same length that also diff... |
Separating words problem : The problem of bounding the size of an automaton that distinguishes two given strings was first formulated by Goralčík & Koubek (1986), who showed that the automaton size is always sublinear. Later, Robson (1989) proved the upper bound O(n2/5(log n)3/5) on the automaton size that may be requi... |
Separating words problem : Several special cases of the separating words problem are known to be solvable using few states: If two binary words have differing numbers of zeros or ones, then they can be distinguished from each other by counting their Hamming weights modulo a prime of logarithmic size, using a logarithmi... |
State complexity : State complexity is an area of theoretical computer science dealing with the size of abstract automata, such as different kinds of finite automata. The classical result in the area is that simulating an n -state nondeterministic finite automaton by a deterministic finite automaton requires exactly 2... |
State complexity : Finite automata can be deterministic and nondeterministic, one-way (DFA, NFA) and two-way (2DFA, 2NFA). Other related classes are unambiguous (UFA), self-verifying (SVFA) and alternating (AFA) finite automata. These automata can also be two-way (2UFA, 2SVFA, 2AFA). All these machines can accept exact... |
State complexity : Given a binary regularity-preserving operation on languages ∘ and a family of automata X (DFA, NFA, etc.), the state complexity of ∘ is an integer function f ( m , n ) such that for each m-state X-automaton A and n-state X-automaton B there is an f ( m , n ) -state X-automaton for L ( A ) ∘ L ( B... |
State complexity : State complexity of finite automata with a one-letter (unary) alphabet, pioneered by Chrobak, is different from the multi-letter case. Let g ( n ) = e Θ ( n ln n ) ) be Landau's function. |
State complexity : Surveys of state complexity were written by Holzer and Kutrib and by Gao et al. New research on state complexity is commonly presented at the annual workshops on Descriptional Complexity of Formal Systems (DCFS), at the Conference on Implementation and Application of Automata (CIAA), and at various c... |
Suffix automaton : In computer science, a suffix automaton is an efficient data structure for representing the substring index of a given string which allows the storage, processing, and retrieval of compressed information about all its substrings. The suffix automaton of a string S is the smallest directed acyclic gr... |
Suffix automaton : The concept of suffix automaton was introduced in 1983 by a group of scientists from University of Denver and University of Colorado Boulder consisting of Anselm Blumer, Janet Blumer, Andrzej Ehrenfeucht, David Haussler and Ross McConnell, although similar concepts had earlier been studied alongside ... |
Suffix automaton : Usually when speaking about suffix automata and related concepts, some notions from formal language theory and automata theory are used, in particular: "Alphabet" is a finite set Σ that is used to construct words. Its elements are called "characters"; "Word" is a finite sequence of characters ω = ω ... |
Suffix automaton : Formally, deterministic finite automaton is determined by 5-tuple A = ( Σ , Q , q 0 , F , δ ) =(\Sigma ,Q,q_,F,\delta ) , where: Σ is an "alphabet" that is used to construct words, Q is a set of automaton "states", q 0 ∈ Q \in Q is an "initial" state of automaton, F ⊂ Q is a set of "final" states ... |
Suffix automaton : Initially the automaton only consists of a single state corresponding to the empty word, then characters of the string are added one by one and the automaton is rebuilt on each step incrementally. |
Suffix automaton : The suffix automaton is closely related to other suffix structures and substring indices. Given a suffix automaton of a specific string one may construct its suffix tree via compacting and recursive traversal in linear time. Similar transforms are possible in both directions to switch between the suf... |
Suffix automaton : Suffix automaton of the string S may be used to solve such problems as: Counting the number of distinct substrings of S in O ( | S | ) on-line, Finding the longest substring of S occurring at least twice in O ( | S | ) , Finding the longest common substring of S and T in O ( | T | ) , Countin... |
Suffix automaton : Media related to Suffix automaton at Wikimedia Commons Suffix automaton article on E-Maxx Algorithms in English |
Synchronizing word : In computer science, more precisely, in the theory of deterministic finite automata (DFA), a synchronizing word or reset sequence is a word in the input alphabet of the DFA that sends any state of the DFA to one and the same state. That is, if an ensemble of copies of the DFA are each started in di... |
Synchronizing word : Given a DFA, the problem of determining if it has a synchronizing word can be solved in polynomial time using a theorem due to Ján Černý. A simple approach considers the power set of states of the DFA, and builds a directed graph where nodes belong to the power set, and a directed edge describes th... |
Synchronizing word : The problem of estimating the length of synchronizing words has a long history and was posed independently by several authors, but it is commonly known as the Černý conjecture. In 1969, Ján Černý conjectured that (n − 1)2 is the upper bound for the length of the shortest synchronizing word for any ... |
Synchronizing word : The road coloring problem is the problem of labeling the edges of a regular directed graph with the symbols of a k-letter input alphabet (where k is the outdegree of each vertex) in order to form a synchronizable DFA. It was conjectured in 1970 by Benjamin Weiss and Roy Adler that any strongly conn... |
Synchronizing word : A transformation semigroup is synchronizing if it contains an element of rank 1, that is, an element whose image is of cardinality 1. A DFA corresponds to a transformation semigroup with a distinguished generator set. |
Synchronizing word : Rystsov, I. C. (2004), "Černý's conjecture: retrospects and prospects", Proc. Worksh. Synchronizing Automata, Turku (WSA 2004). Jürgensen, H. (2008), "Synchronization", Information and Computation, 206 (9–10): 1033–1044, doi:10.1016/j.ic.2008.03.005 Volkov, Mikhail V. (2008), "Synchronizing Automat... |
Thompson's construction : In computer science, Thompson's construction algorithm, also called the McNaughton–Yamada–Thompson algorithm, is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). This NFA can be used to match strings against the regular expression. This ... |
Thompson's construction : The algorithm works recursively by splitting an expression into its constituent subexpressions, from which the NFA will be constructed using a set of rules. More precisely, from a regular expression E, the obtained automaton A with the transition function Δ respects the following properties: A... |
Thompson's construction : Two examples are now given, a small informal one with the result, and a bigger with a step by step application of the algorithm. |
Thompson's construction : Thompson's is one of several algorithms for constructing NFAs from regular expressions; an earlier algorithm was given by McNaughton and Yamada. Converse to Thompson's construction, Kleene's algorithm transforms a finite automaton into a regular expression. Glushkov's construction algorithm is... |
Thompson's construction : Regular expressions are often used to specify patterns that software is then asked to match. Generating an NFA by Thompson's construction, and using an appropriate algorithm to simulate it, it is possible to create pattern-matching software with performance that is O ( m n ) , where m is t... |
Tree transducer : In theoretical computer science and formal language theory, a tree transducer (TT) is an abstract machine taking as input a tree, and generating output – generally other trees, but models producing words or other structures exist. Roughly speaking, tree transducers extend tree automata in the same way... |
Tree transducer : A TOP T is a tuple (Q, Σ, Γ, I, δ) such that: Q is a finite set, the set of states; Σ is a finite ranked alphabet, called the input alphabet; Γ is a finite ranked alphabet, called the output alphabet; I is a subset of Q, the set of initial states; and δ is a set of rules of the form q ( f ( x 1 , … , ... |
Tree transducer : As in the simpler case of tree automata, bottom-up tree transducers are defined similarly to their top-down counterparts, but proceed from the leaves of the tree to the root, instead of from the root to the leaves. Thus the main difference is in the form of the rules, which are of the form f ( q 1 ( x... |
Tree transducer : Comon, Hubert; Dauchet, Max; Gilleron, Rémi; Jacquemard, Florent; Lugiez, Denis; Löding, Christof; Tison, Sophie; Tommasi, Marc (November 2008). "Chapter 6: Tree Transducers". Tree Automata Techniques and Applications. Retrieved 11 February 2014. Hosoya, Haruo (4 November 2010). Foundations of XML Pro... |
Trie : In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's position within the trie det... |
Trie : The idea of a trie for representing a set of strings was first abstractly described by Axel Thue in 1912. Tries were first described in a computer context by René de la Briandais in 1959.: 336 The idea was independently described in 1960 by Edward Fredkin, who coined the term trie, pronouncing it (as "tree"), af... |
Trie : Tries are a form of string-indexed look-up data structure, which is used to store a dictionary list of words that can be searched on in a manner that allows for efficient generation of completion lists.: 1 A prefix trie is an ordered tree data structure used in the representation of a set of strings over a finit... |
Trie : Tries support various operations: insertion, deletion, and lookup of a string key. Tries are composed of nodes that contain links, which either point to other suffix child nodes or null. As for every tree, each node but the root is pointed to by only one other node, called its parent. Each node contains as many ... |
Trie : Tries can be represented in several ways, corresponding to different trade-offs between memory use and speed of the operations.: 341 Using a vector of pointers for representing a trie consumes enormous space; however, memory space can be reduced at the expense of running time if a singly linked list is used for ... |
Trie : Trie data structures are commonly used in predictive text or autocomplete dictionaries, and approximate matching algorithms. Tries enable faster searches, occupy less space, especially when the set contains large number of short strings, thus used in spell checking, hyphenation applications and longest prefix ma... |
Trie : NIST's Dictionary of Algorithms and Data Structures: Trie |
Tsetlin machine : A Tsetlin machine is an artificial intelligence algorithm based on propositional logic. |
Tsetlin machine : A Tsetlin machine is a form of learning automaton collective for learning patterns using propositional logic. Ole-Christoffer Granmo created and gave the method its name after Michael Lvovitch Tsetlin, who invented the Tsetlin automaton and worked on Tsetlin automata collectives and games. Collectives... |
Tsetlin machine : Original Tsetlin machine Convolutional Tsetlin machine Regression Tsetlin machine Relational Tsetlin machine Weighted Tsetlin machine Arbitrarily deterministic Tsetlin machine Parallel asynchronous Tsetlin machine Coalesced multi-output Tsetlin machine Tsetlin machine for contextual bandit problems Ts... |
Tsetlin machine : Keyword spotting Aspect-based sentiment analysis Word-sense disambiguation Novelty detection Intrusion detection Semantic relation analysis Image analysis Text categorization Fake news detection Game playing Batteryless sensing Recommendation systems Word embedding ECG analysis Edge computing Bayesian... |
Two-way finite automaton : In computer science, in particular in automata theory, a two-way finite automaton is a finite automaton that is allowed to re-read its input. |
Two-way finite automaton : A two-way deterministic finite automaton (2DFA) is an abstract machine, a generalized version of the deterministic finite automaton (DFA) which can revisit characters already processed. As in a DFA, there are a finite number of states with transitions between them based on the current charact... |
Two-way finite automaton : Formally, a two-way deterministic finite automaton can be described by the following 8-tuple: M = ( Q , Σ , L , R , δ , s , t , r ) where Q is the finite, non-empty set of states Σ is the finite, non-empty set of input symbols L is the left endmarker R is the right endmarker δ : Q × ( Σ ... |
Two-way finite automaton : A two-way nondeterministic finite automaton (2NFA) may have multiple transitions defined in the same configuration. Its transition function is δ : Q × ( Σ ∪ ) → 2 Q × )\rightarrow 2^ \ . Like a standard one-way NFA, a 2NFA accepts a string if at least one of the possible computations is acc... |
Two-way finite automaton : A two-way alternating finite automaton (2AFA) is a two-way extension of an alternating finite automaton (AFA). Its state set is Q = Q ∃ ∪ Q ∀ \cup Q_ where Q ∃ ∩ Q ∀ = ∅ \cap Q_=\emptyset . States in Q ∃ and Q ∀ are called existential resp. universal. In an existential state a 2AFA nondete... |
Two-way finite automaton : Two-way and one-way finite automata, deterministic and nondeterministic and alternating, accept the same class of regular languages. However, transforming an automaton of one type to an equivalent automaton of another type incurs a blow-up in the number of states. Christos Kapoutsis determine... |
Two-way finite automaton : Sweeping automata are 2DFAs of a special kind that process the input string by making alternating left-to-right and right-to-left sweeps, turning only at the endmarkers. Sipser constructed a sequence of languages, each accepted by an n-state NFA, yet which is not accepted by any sweeping auto... |
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