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Explaining Non-bisimilarity in a Coalgebraic Approach: Games and Distinguishing Formulas

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Coalgebraic Methods in Computer Science (CMCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12094))

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Abstract

Behavioural equivalences can be characterized via bisimulation, modal logics, and spoiler-duplicator games. In this paper we work in the general setting of coalgebra and focus on generic algorithms for computing the winning strategies of both players in a bisimulation game. The winning strategy of the spoiler (if it exists) is then transformed into a modal formula that distinguishes the given non-bisimilar states. The modalities required for the formula are also synthesized on-the-fly, and we present a recipe for re-coding the formula with different modalities, given by a separating set of predicate liftings. Both the game and the generation of the distinguishing formulas have been implemented in a tool called T-Beg.

Work by the first two authors supported by the DFG project BEMEGA (KO 2185/7-2). Work by the third author forms part of the DFG project ProbDL2 (SCHR 1118/6-2).

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Notes

  1. 1.

    Available at: https://www.uni-due.de/theoinf/research/tools_tbeg.php.

  2. 2.

    For a function \(f:X\rightarrow Y\), \( ker (f) = \{(x_0,x_1)\mid x_0,x_1\in X, f(x_0) = f(x_1)\} \subseteq X\times X\).

  3. 3.

    http://www.brics.dk/bisim/.

  4. 4.

    https://www.jeroenkeiren.nl/blog/on-games-and-simulations/.

  5. 5.

    https://www.nuget.org/packages/Microsoft.Msagl.GraphViewerGDI.

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Acknowledgements

We would like to thank the reviewers for the careful reading of the paper and their valuable comments. Furthermore we thank Thorsten Wißmann and Sebastian Küpper for inspiring discussions on (efficient) coalgebraic partition refinement and zippability.

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Authors and Affiliations

  1. University of Duisburg-Essen, Duisburg, Germany

    Barbara König & Christina Mika-Michalski

  2. Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Lutz Schröder

Authors
  1. Barbara König
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  2. Christina Mika-Michalski
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  3. Lutz Schröder
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Corresponding author

Correspondence to Christina Mika-Michalski .

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Editors and Affiliations

  1. Université de Paris, CNRS, IRIF, Paris, France

    Daniela Petrişan

  2. Radboud University, Nijmegen, The Netherlands

    Jurriaan Rot

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König, B., Mika-Michalski, C., Schröder, L. (2020). Explaining Non-bisimilarity in a Coalgebraic Approach: Games and Distinguishing Formulas. In: Petrişan, D., Rot, J. (eds) Coalgebraic Methods in Computer Science. CMCS 2020. Lecture Notes in Computer Science(), vol 12094. Springer, Cham. https://doi.org/10.1007/978-3-030-57201-3_8

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