A power-set construction for reducing Buchi automata to non-determinism degree two
Buchi automata are finite automata that accept languages of infinitely long strings, so-called omega-languages. It is well known that, unlike in the finite-string case, deterministic and non-deterministic Buchi automata accept different omega-language classes, i.e., that determination of a non-deterministic Buchi automaton using the classical power-set construction will yield in general a deterministic Buchi automaton which accepts a superset of the omega-language accepted by the given non-deterministic automaton. In this paper, a power-set construction to a given Buchi 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 Buchi automaton of non-determinism degree two and the given Buchi automaton of arbitrary non-determinism degree will accept the same omega-language. (c) 2006 Elsevier B.V. All rights reserved.
buchi automata non-determinism formal languages regular omega-languages