Deterministic Ω automata vis-a-vis deterministic Buchi automata
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 Müller, Rabin, 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 Müller, 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.
KeywordsAcceptance Condition Finite State Automaton Strongly Connect Component Fairness Constraint State Transition Graph
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- 3.A. Aziz et al. HSIS: A BDD-Based Environment for Formal Verification. In Proc. of the Design Automation Conf., 1994. To Appear.Google Scholar
- 4.S. C. Krishnan, A. Puri, and R. K. Brayton. Deterministic Ω-automata vis-a-vis Deterministic Buchi Automata. Technical report, Electronics Research Lab, Univ. of California, Berkeley, CA 94720. preprint.Google Scholar
- 5.R. P. Kurshan. Complementing Deterministic Büchi Automata in Polynomial Time. Journal of Computer and System Sciences, 35:59–71, 1987.Google Scholar
- 6.R. P. Kurshan. Automata-Theoretic Verification of Coordinating Processes. Princeton University Press, 1993. To appear.Google Scholar
- 7.M.O. Rabin and D.Scott. Finite Automata and their Decision Problems. In IBM Journal of Research and Development, volume 3, pages 115–125, 1959.Google Scholar
- 8.Shmuel Safra. Complexity of Automata on Infinite Objects. PhD thesis, The Weizmann Institute of Science, Rehovot, Israel, March 1989.Google Scholar
- 9.W. Thomas. Automata on Infinite Objects. In J. van Leeuwen, editor, Formal Models and Semantics, volume B of Handbook of Theoretical Computer Science, pages 133–191. Elsevier Science, 1990.Google Scholar