A power-set construction for reducing Buechi automata to non-determinism degree two

摘要

Buechi automata are finite automata that accept languages of infinitely long strings, so-called ω-languages. It is well known that, unlike in the finite-string case, deterministic and non-deterministic Buechi automata accept different ω-language classes, i.e., that determination of a non-deterministic Buechi automaton using the classical power-set construction will yield in general a deterministic Buechi automaton which accepts a superset of the ω-language accepted by the given non-deterministic automaton. In this paper, a power-set construction to a given Buechi automaton is presented, which reduces the degree of non-determinism of the automaton to at most two, meaning that to each state and input symbol, there exist at most two distinct successor states. The constructed Buechi automaton of non-determinism degree two and the given Buechi automaton of arbitrary non-determinism degree will accept the same ω-language.