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On Bounded Specifications

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2250))

Abstract

Bounded model checking methodologies check the correctness of a system with respect to a given specification by examining computations of a bounded length. Results from set-theoretic topology imply that sets in Σω that are both open and closed (clopen sets) are precisely bounded sets: membership of a word in a clopen set can be determined by examining a bounded prefix of it. Clopen sets correspond to specifications that are both safety and co-safety. In this paper we study bounded specifications from this perspective. We consider both the linear and the branching frameworks. In the linear framework, we show that when clopen specifications are given by word automata or temporal logic formulas, we can identify a bound and translate the specification to bounded formalisms such as cycle-free automata and bounded LTL. In the branching framework, we show that while clopen sets of trees with infinite branching degrees may not be bounded, we can extend the results from the linear framework to clopen specifications given by tree automata or temporal logic formulas, even for trees with infinite branching degrees. There, we can identify a bound and translate clopen specifications to cycle-free automata and modal logic. Finally, we show how our results imply that the bottom levels of the μ-calculus hierarchy coalesce.

Supported in part by BSF grant 9800096.

Supported in part by NSF grants CCR-9700061, CCR-9988322, IIS-9908435, IIS-9978135, and EIA-0086264 by BSF grant 9800096, and by a grant from the Intel Corporation.

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Author information

Authors and Affiliations

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

    Orna Kupferman

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

    MosheY. Vardi

Authors
  1. Orna Kupferman
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  2. MosheY. Vardi
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Editor information

Editors and Affiliations

  1. Department of Software, Technical University of Catalonia, Jordi Girona 1, 08034, Barcelona, Spain

    Robert Nieuwenhuis

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

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Kupferman, O., Vardi, M. (2001). On Bounded Specifications. In: Nieuwenhuis, R., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2001. Lecture Notes in Computer Science(), vol 2250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45653-8_2

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  • DOI: https://doi.org/10.1007/3-540-45653-8_2

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  • Print ISBN: 978-3-540-42957-9

  • Online ISBN: 978-3-540-45653-7

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