Büchi automaton

In computer science and automata theory, a Büchi automaton is a type of ω-automaton, which extends a finite automaton to infinite inputs. It accepts an infinite input sequence if there exists a run of the automaton that visits (at least) one of the final states infinitely often. Büchi automata recognize the omega-regular languages, the infinite word version of regular languages. It is named after the Swiss mathematician Julius Richard Büchi who invented this kind of automaton in 1962.

Büchi automata are often used in model checking as an automata-theoretic version of a formula in linear temporal logic.

Formal definition

Formally, a deterministic Büchi automaton is a tuple A = (Q,Σ,δ,q₀,F) that consists of the following components:

Q is a finite set. The elements of Q are called the states of A.

Σ is a finite set called the alphabet of A.

δ: Q × Σ → Q is a function, called the transition function of A.

q₀ is an element of Q, called the initial state of A.

F⊆Q is the acceptance condition. A accepts exactly those runs in which at least one of the infinitely often occurring states is in F.

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Büchi automaton

Formal definition

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