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A unified approach for showing language containment and equivalence between various types of ω-automata

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CAAP '90 (CAAP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 431))

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Abstract

We consider the language containment and equivalence problems for six different types of ω-automata: Büchi, Muller, Rabin, Streett, the L-automata of Kurshan, and the ∀-automata of Manna and Pnueli. We give a six by six matrix in which each row and column is associated with one of these types of automata. The entry in the i th row and j th column is the complexity of showing containment between the i th type of automaton and the j th. Thus, for example, we give the complexity of showing language containment and equivalence between a Büchi automaton and a Muller or Streett automaton. Our results are obtained by a uniform method that associates a formula of the logic CTL* with each type of automaton. Our algorithms use a model checking procedure for the logic with the formulas obtained from the automata. The results of our paper are important for verification of finite state concurrent systems with fairness constraints. A natural way of reasoning about such systems is to model the finite state program by one ω-automaton and its specification by another.

This research was partially supported by NSF grant CCR-87-226-33

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh

    E. M. Clarke & I. A. Browne

  2. AT&T Bell Laboratories, Murray Hill

    R. P. Kurshan

Authors
  1. E. M. Clarke
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  2. I. A. Browne
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  3. R. P. Kurshan
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A. Arnold

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© 1990 Springer-Verlag Berlin Heidelberg

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Clarke, E.M., Browne, I.A., Kurshan, R.P. (1990). A unified approach for showing language containment and equivalence between various types of ω-automata. In: Arnold, A. (eds) CAAP '90. CAAP 1990. Lecture Notes in Computer Science, vol 431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52590-4_43

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  • DOI: https://doi.org/10.1007/3-540-52590-4_43

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52590-5

  • Online ISBN: 978-3-540-47042-7

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