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Fair Equivalence Relations

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Book cover Verification: Theory and Practice

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2772))

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 are modeled 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: 3-bisimulation, gamebisimulation, and V-bisimulation. We show that while game-bisimulation and V-bisimulation have the same expressiveness hierarchy as tree automata, 3-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.

This author is grateful to Zohar Manna for introducing him to logic in computer science. 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. School of Eng. and Computer Science, Hebrew University, Jerusalem, 91904, Israel

    Orna Kupferman

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

    Nir Piterman

  3. Department of Computer Science, Rice University, Houston, TX, 77251-1892, 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. School of Computer Science, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Nachum Dershowitz

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Kupferman, O., Piterman, N., Vardi, M.Y. (2003). Fair Equivalence Relations. In: Dershowitz, N. (eds) Verification: Theory and Practice. Lecture Notes in Computer Science, vol 2772. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39910-0_30

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  • DOI: https://doi.org/10.1007/978-3-540-39910-0_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21002-3

  • Online ISBN: 978-3-540-39910-0

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