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Fair Equivalence Relations

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FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1974))

Abstract

Equivalence between designs is a fundamental notion in verification. The linear and branching approaches to verification induce different notions of equivalence. When the designs aremodeled by fair state-transition systems, equivalence in the linear paradigm corresponds to fair trace equivalence, and in the branching paradigm corresponds to fair bisimulation. In this work we study the expressive power of various types of fairness conditions. For the linear paradigm, it is known that the Büchi condition is sufficiently strong (that is, a fair system that uses Rabin or Streett fairness can be translated to an equivalent Büchi system). We show that in the branching paradigm the expressiveness hierarchy depends on the types of fair bisimulation one chooses to use. We consider three types of fair bisimulation studied in the literature: ∃- bisimulation, game-bisimulation, and ∀-bisimulation. We show that while game- bisimulation and ∀-bisimulation have the same expressiveness hierarchy as tree automata, ∃-bisimulation induces a different hierarchy. This hierarchy lies between the hierarchies of word and tree automata, and it collapses at Rabin conditions of index one, and Streett conditions of index two.

Supported in part by NSF grants CCR-9700061 and CCR-9988322, and by a grant from the Intel Corporation.

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Author information

Authors and Affiliations

  1. Hebrew University, School of Engineering and Computer Science, 91904, Jerusalem, Israel

    Orna Kupferman

  2. Department of Computer Science, Weizmann Institute of Science, 76100, Rehovot, Israel

    Nir Piterman

  3. Department of Computer Science, Rice University, 77251-1892, TX, Houston, USA

    Moshe Y. Vardi

Authors
  1. Orna Kupferman
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  2. Nir Piterman
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  3. Moshe Y. Vardi
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, Hauz Khas, 110016, New Delhi, India

    Sanjiv Kapoor  & Sanjiva Prasad  & 

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Kupferman, O., Piterman, N., Vardi, M.Y. (2000). Fair Equivalence Relations. In: Kapoor, S., Prasad, S. (eds) FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2000. Lecture Notes in Computer Science, vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44450-5_12

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  • DOI: https://doi.org/10.1007/3-540-44450-5_12

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  • Print ISBN: 978-3-540-41413-1

  • Online ISBN: 978-3-540-44450-3

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