finite monoid

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• Finite-state machine — State machine redirects here. For infinite state machines, see State transition system. For fault tolerance methodology, see State machine replication. SFSM redirects here. For the Italian railway company, see Circumvesuviana. A finite state… …   Wikipedia

• Monoid — This article is about the mathematical concept. For the alien creatures in the Doctor Who adventure, see The Ark (Doctor Who). Coherence law for monoid unit In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a… …   Wikipedia

• Monoid ring — In abstract algebra, a monoid ring is a new ring constructed from some other ring and a monoid. Definition Let R be a ring and G be a monoid. Consider all the functions φ  : G → R such that the set {g: φ(g) ≠ 0} is finite. Let all such… …   Wikipedia

• Deterministic finite-state machine — An example of a Deterministic Finite Automaton that accepts only binary numbers that are multiples of 3. The state S0 is both the start state and an accept state. In the theory of computation and automata theory, a deterministic finite state… …   Wikipedia

• Nondeterministic finite-state machine — In the theory of computation, a nondeterministic finite state machine or nondeterministic finite automaton (NFA) is a finite state machine where for each pair of state and input symbol there may be several possible next states. This distinguishes …   Wikipedia

• Free monoid — In abstract algebra, the free monoid on a set A is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from A , with the binary operation of concatenation. It is usually denoted A lowast;. The identity… …   Wikipedia

• Syntactic monoid — In mathematics, the syntactic monoid M ( L ) of a formal language L is the smallest monoid that recognizes the language L .yntactic quotientGiven Ssubset M a subset of a monoid M , one may define sets that consist of formal left or right inverses …   Wikipedia

• Refinement monoid — In mathematics, a refinement monoid is a commutative monoid M such that for any elements a0, a1, b0, b1 of M such that a0+a1=b0+b1, there are elements c00, c01, c10, c11 of M such that a0=c00+c01, a1=c10+c11, b0=c00+c10, and b1=c01+c11. A… …   Wikipedia

• Aperiodic monoid — In mathematics, an aperiodic semigroup is a semigroup S such that for every x ∈ S , there exists a nonnegative integer n such that xn = xn + 1 .An aperiodic monoid is an aperiodic semigroup which is a monoid. This notion is in some sense… …   Wikipedia

• Trace monoid — In mathematics and computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters to always be in a fixed order,… …   Wikipedia

• Presentation of a monoid — In algebra, a presentation of a monoid (or semigroup) is a description of a monoid (or semigroup) in terms of a set Sigma; of generators and a set of relations on the free monoid Sigma; lowast; (or free semigroup Sigma;+) generated by Sigma;. The …   Wikipedia