computer science, the syntactic monoid M ( L ) {\displaystyle M(L)} of a formal language L {\displaystyle L} is the smallest monoid that recognizes the...

is a free monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation...

natural link between finite semigroups and finite automata via the syntactic monoid. In probability theory, semigroups are associated with Markov processes...

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...

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...

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*...

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...

quotient Σ ∗ / R {\displaystyle \Sigma ^{*}/R} , resulting in the syntactic monoid of the Dyck language. The class Cl ⁡ ( ϵ ) {\displaystyle \operatorname...

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 ...

Associated with any semiautomaton is a monoid called the characteristic monoid, input monoid, transition monoid or transition system of the semiautomaton...

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...

Transformation semigroup Monoid Aperiodic monoid Free monoid Monoid (category theory) Monoid factorisation Syntactic monoid Structure Group (mathematics)...

prove that a language is not regular. Syntactic monoid Brzozowski, Janusz; Szykuła, Marek; Ye, Yuli (2018), "Syntactic Complexity of Regular Ideals", Theory...

algebra MV-algebra In Computer science: Max-plus algebra Syntactic monoid Transition monoid Abstract algebra Outline of abstract algebra Universal algebra...

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...

Regular language S-attributed grammar Star height Star height problem Syntactic monoid Syntax (logic) Tree-adjoining grammar Anagram Case sensitivity Infinite...

{\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 ∼...

algebraic characterization of star-free languages by means of aperiodic syntactic monoids. In particular star-free languages are a proper decidable subclass...

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...

reduced to the syntactic manipulation of formal languages in this way. The field of formal language theory studies primarily the purely syntactic aspects of...

Schützenberger characterized star-free languages as those with aperiodic syntactic monoids. They can also be characterized logically as languages definable in...

considered equivalent. In first-order syntactic unification, variables range over first-order terms and equivalence is syntactic. This version of unification has...

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...

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...

Synesthesia Synoecism Synonymy Synoptic philosophy Syntactic ambiguity Syntactic monoid Syntactic predicate Syntax Syntax (logic) Synthese Synthetic a...

Repeated function composition forms a monoid. For the transition functions, this monoid is known as the transition monoid, or sometimes the transformation...

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...

the HTTP protocol Traces, the equivalence classes of strings of a trace monoid, studied in trace theories of concurrent computation Digital traces, the...

instance literally equal to each input expression, the process is called "syntactical anti-unification", otherwise "E-anti-unification", or "anti-unification...

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...