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International Symposium on Automated Technology for Verification and Analysis

ATVA 2006: Automated Technology for Verification and Analysis pp 322–336Cite as

Ranked Predicate Abstraction for Branching Time: Complete, Incremental, and Precise

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4218))

Abstract

Predicate abstraction frameworks are a powerful means of combating the state explosion problem in model checking as they automatically synthesize abstract models that either verify compliance with a property, give rise to a genuine counter-example or produce a spurious counter-example that drives refinement of the abstract model. Prominent tools for safety (e.g. Blast) and termination (e.g. Terminator) checking rely on this approach. This paper presents such an abstraction framework for all properties of the modal μ-calculus based on ranked predicate abstraction. We show that our framework is incremental and confluent and should therefore allow good refinement heuristics. Moreover, ranked predicate abstractions are proved to be precise (i.e. optimal as abstractions) and also complete in that all properties true in a model are also true in a finite-state, ranked predicate abstraction of that model. This completeness relates to known characterizations of relative completeness for predicate abstraction with branching time.

This work is in part financially supported by the DFG project Refism (FE 942/1-1).

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Author information

Authors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Germany

    Harald Fecher

  2. Department of Computing, Imperial College London, United Kingdom

    Michael Huth

Authors
  1. Harald Fecher
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  2. Michael Huth
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Editor information

Editors and Affiliations

  1. VERIMAG, 2 Avenue de Vignate, Centre Equitation, 38610, Grenoble-Gières, France

    Susanne Graf

  2. Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Wenhui Zhang

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Fecher, H., Huth, M. (2006). Ranked Predicate Abstraction for Branching Time: Complete, Incremental, and Precise. In: Graf, S., Zhang, W. (eds) Automated Technology for Verification and Analysis. ATVA 2006. Lecture Notes in Computer Science, vol 4218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11901914_25

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  • DOI: https://doi.org/10.1007/11901914_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-47237-7

  • Online ISBN: 978-3-540-47238-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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