computer science, the syntacticmonoid 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 syntacticmonoids 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 syntacticmonoid. In probability theory, semigroups are associated with Markov processes...
language has a syntacticmonoid 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 syntacticmonoid describing the Dyck...
recognized by some finite syntacticmonoid 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*...
quotient Σ ∗ / R {\displaystyle \Sigma ^{*}/R} , resulting in the syntacticmonoid of the Dyck language. The class Cl ( ϵ ) {\displaystyle \operatorname...
and only if its syntacticmonoid is finite and aperiodic. A consequence of the Krohn–Rhodes theorem is that every finite aperiodic monoid divides a wreath...
semigroup of M.: 78 For a regular language, the syntacticmonoid 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...
strings x and y. Thus, the trace monoid is a syntacticmonoid.[non sequitur See Talk:Trace monoid#As SyntacticMonoids] Independence: if u a ≡ v b {\displaystyle...
Regular language S-attributed grammar Star height Star height problem Syntacticmonoid 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 ∼...
It can be shown that a language L is star-free if and only if its syntacticmonoid is aperiodic (Schützenberger (1965)). Star height problem Generalized...
A subset of N {\displaystyle N} is recognizable if and only if its syntacticmonoid is finite. The set R E C ( N ) {\displaystyle \mathrm {REC} (N)} of...
splicing rules that respect a regular language can be determined from the syntacticmonoid of the language. Anderson (2006) p. 236 Anderson (2006) p. 242 Anderson...
reduced to the syntactic manipulation of formal languages in this way. The field of formal language theory studies primarily the purely syntactic aspects of...
Repeated function composition forms a monoid. For the transition functions, this monoid is known as the transition monoid, or sometimes the transformation...
the HTTP protocol Traces, the equivalence classes of strings of a trace monoid, studied in trace theories of concurrent computation Digital traces, the...
the case. For example, a monoid may be viewed as a category with a single object, whose morphisms are the elements of the monoid. The second fundamental...
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