ω-automata are finite state automata that accept infinite strings. The class of ω-regular languages is exactly the set accepted by nondeterministic Buchi and L-automata, and deterministic Muller, Rabln, and Streett automata. The languages accepted by deterministic Buchi automata (DBA) form a strict subset of the class of ω-regular languages. Landweber characterized deterministic ω-automata whose languages are realizable by DBA. We provide an alternative proof of Landweber’s theorem and give polynomial time algorithms to check if a language L specified as a deterministic Muller, L-, Streett, or Rabin automaton can be realized as a DBA. We identify a sub-class of deterministic Muller, L-, Streett, and Rabin automata, called Buchi-type automata, which can be converted to an equivalent DBA on the same transition structure in polynomial time. For this subset of ω-automata, our transformation yields the most efficient algorithms for checking language inclusion-important for computer verification of reactive systems. We prove that a deterministic L-(DLA) or Rabin automaton (DRA), unlike deterministic Muller or Streett automata, is Buchi.type if and only if its language is realizable as a DBA. Therefore, for languages that are realizable as DBA, DBA are as compact as DRA or DLA.
CITATION STYLE
Krishnan, S. C., Puri, A., & Brayton, R. K. (1994). Deterministic ω automata vis-a-vis deterministic buchi automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 834 LNCS, pp. 378–386). Springer Verlag. https://doi.org/10.1007/3-540-58325-4_202
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