computer science, the syntactic monoid M ( L ) {\displaystyle M(L)} of a formal language L {\displaystyle L} is the smallest monoid that recognizes the...
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is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation...
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Semigroup (redirect from Monoid theory)
natural link between finite semigroups and finite automata via the syntactic monoid. In probability theory, semigroups are associated with Markov processes...
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language has a syntactic monoid that recognizes that language. For the case of a regular language, that monoid is isomorphic to the transition monoid associated...
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Bicyclic semigroup (redirect from Bicyclic monoid)
it is in fact a monoid, it is usually referred to as simply a semigroup. It is perhaps most easily understood as the syntactic monoid describing the Dyck...
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recognized by some finite syntactic monoid M, meaning it is the preimage {w ∈ Σ* | f(w) ∈ S} of a subset S of a finite monoid M under a monoid homomorphism f: Σ*...
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strings x and y. Thus, the trace monoid is a syntactic monoid.[non sequitur See Talk:Trace monoid#As Syntactic Monoids] Independence: if u a ≡ v b {\displaystyle...
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quotient Σ ∗ / R {\displaystyle \Sigma ^{*}/R} , resulting in the syntactic monoid of the Dyck language. The class Cl ( ϵ ) {\displaystyle \operatorname...
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Transformation semigroup (redirect from Transformation monoid)
semigroup of M.: 78 For a regular language, the syntactic monoid is isomorphic to the transformation monoid of the minimal automaton of the language.: 81 ...
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Semiautomaton (redirect from Transition monoid)
Associated with any semiautomaton is a monoid called the characteristic monoid, input monoid, transition monoid or transition system of the semiautomaton...
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Aperiodic semigroup (redirect from Aperiodic monoid)
and only if its syntactic monoid is finite and aperiodic. A consequence of the Krohn–Rhodes theorem is that every finite aperiodic monoid divides a wreath...
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Transformation semigroup Monoid Aperiodic monoid Free monoid Monoid (category theory) Monoid factorisation Syntactic monoid Structure Group (mathematics)...
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prove that a language is not regular. Syntactic monoid Brzozowski, Janusz; Szykuła, Marek; Ye, Yuli (2018), "Syntactic Complexity of Regular Ideals", Theory...
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algebra MV-algebra In Computer science: Max-plus algebra Syntactic monoid Transition monoid Abstract algebra Outline of abstract algebra Universal algebra...
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A subset of N {\displaystyle N} is recognizable if and only if its syntactic monoid is finite. The set R E C ( N ) {\displaystyle \mathrm {REC} (N)} of...
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Regular language S-attributed grammar Star height Star height problem Syntactic monoid Syntax (logic) Tree-adjoining grammar Anagram Case sensitivity Infinite...
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String operations (section Syntactic relation)
{\displaystyle S\subset M} of a monoid M {\displaystyle M} defines an equivalence relation, called the right syntactic relation of S. It is given by ∼...
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algebraic characterization of star-free languages by means of aperiodic syntactic monoids. In particular star-free languages are a proper decidable subclass...
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It can be shown that a language L is star-free if and only if its syntactic monoid is aperiodic (Schützenberger (1965)). Star height problem Generalized...
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reduced to the syntactic manipulation of formal languages in this way. The field of formal language theory studies primarily the purely syntactic aspects of...
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Schützenberger characterized star-free languages as those with aperiodic syntactic monoids. They can also be characterized logically as languages definable in...
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Unification (computer science) (redirect from Syntactic unification)
considered equivalent. In first-order syntactic unification, variables range over first-order terms and equivalence is syntactic. This version of unification has...
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to the category of monoids. Here the task for the programmer is to construct an appropriate monoid, or perhaps to choose a monoid from a library. The...
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splicing rules that respect a regular language can be determined from the syntactic monoid of the language. Anderson (2006) p. 236 Anderson (2006) p. 242 Anderson...
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Synesthesia Synoecism Synonymy Synoptic philosophy Syntactic ambiguity Syntactic monoid Syntactic predicate Syntax Syntax (logic) Synthese Synthetic a...
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Repeated function composition forms a monoid. For the transition functions, this monoid is known as the transition monoid, or sometimes the transformation...
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are now defined. Let M and N be monoids, and let p and q be elements of the monoid M. Let φ be a morphism of monoids from M to N. It is said that the...
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the HTTP protocol Traces, the equivalence classes of strings of a trace monoid, studied in trace theories of concurrent computation Digital traces, the...
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Anti-unification (redirect from First-order syntactical anti-unification)
instance literally equal to each input expression, the process is called "syntactical anti-unification", otherwise "E-anti-unification", or "anti-unification...
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bicyclic monoid. Thus semi-Thue systems constitute a natural framework for solving the word problem for monoids and groups. In fact, every monoid has a presentation...
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