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

  • Authors:

  • Ulrich Ultes-Nitsche

  • Affiliations:

  • Department of Computer Science, University of Fribourg, Boulevard de Pérolles 90, CH-1700 Fribourg, Switzerland

  • Venue:
  • Information Processing Letters
  • Year:
  • 2007

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Abstract

Buchi automata are finite automata that accept languages of infinitely long strings, so-called @w-languages. It is well known that, unlike in the finite-string case, deterministic and non-deterministic Buchi automata accept different @w-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 @w-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 @w-language.