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Sharp Congruences Adequate with Temporal Logics Combining Weak and Strong Modalities

Sharp Congruences Adequate with Temporal Logics Combining Weak and Strong Modalities

  • Frédéric Lang10,
  • Radu Mateescu10 &
  • Franco Mazzanti11 
  • Conference paper
  • Open Access
  • First Online: 17 April 2020

  • 6551 Accesses

  • 11 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12079)

Abstract

We showed in a recent paper that, when verifying a modal \(\mu \)-calculus formula, the actions of the system under verification can be partitioned into sets of so-called weak and strong actions, depending on the combination of weak and strong modalities occurring in the formula. In a compositional verification setting, where the system consists of processes executing in parallel, this partition allows us to decide whether each individual process can be minimized for either divergence-preserving branching (if the process contains only weak actions) or strong (otherwise) bisimilarity, while preserving the truth value of the formula. In this paper, we refine this idea by devising a family of bisimilarity relations, named sharp bisimilarities, parameterized by the set of strong actions. We show that these relations have all the nice properties necessary to be used for compositional verification, in particular congruence and adequacy with the logic. We also illustrate their practical utility on several examples and case-studies, and report about our success in the RERS 2019 model checking challenge.

Keywords

  • Bisimulation
  • Concurrency
  • Model checking
  • Mu-calculus

Grenoble INP—Institute of Engineering Univ. Grenoble Alpes.

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Author information

Authors and Affiliations

  1. Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LIG, 38000, Grenoble, France

    Frédéric Lang & Radu Mateescu

  2. ISTI-CNR, Pisa, Italy

    Franco Mazzanti

Authors
  1. Frédéric Lang
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  2. Radu Mateescu
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  3. Franco Mazzanti
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Correspondence to Frédéric Lang .

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Editors and Affiliations

  1. Johannes Kepler University, Linz, Austria

    Prof. Armin Biere

  2. University of Birmingham, Birmingham, UK

    Prof. David Parker

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Lang, F., Mateescu, R., Mazzanti, F. (2020). Sharp Congruences Adequate with Temporal Logics Combining Weak and Strong Modalities. In: Biere, A., Parker, D. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2020. Lecture Notes in Computer Science(), vol 12079. Springer, Cham. https://doi.org/10.1007/978-3-030-45237-7_4

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  • DOI: https://doi.org/10.1007/978-3-030-45237-7_4

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