Handbook of Automated Reasoning

A Büchi-automaton is a finite ω-automaton, that is, a fair transition system where the set S of states is finite. A transition system (or labelled transition system) is a fair transition system where S _acc = S _rec = S. A weakly fair transition system is an ω-automaton where S _rec = S and S _acc = {s | ∀a, s′(s, a, s′) ∉ Δ}. That is, in a weakly fair transition system all states are recurring, and states are accepting iff they axe terminal. Usually, when talking about labelled and weakly fair transition systems, we omit the redundant components S _acc and S _rec .

A (finite or infinite) nonempty word $\sigma \triangleq \left({\sigma }_0,{\sigma }_1,\dots \right)$ is accepted by an automaton $\left(S,\text{Δ},S_0,S_{acc},S_{rec}\right)$ , if there ...