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Formal Verification of Executable Complementation and Equivalence Checking for Büchi Automata

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Integrated Formal Methods (IFM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12546))

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Abstract

We develop a complementation procedure and an equivalence checker for nondeterministic Büchi automata. Both are formally verified using the proof assistant Isabelle/Hol. The verification covers everything from the abstract correctness proof down to the generated Sml code.

The complementation follows the rank-based approach. We formalize the abstract algorithm and use refinement to derive an executable implementation. In conjunction with a product operation and an emptiness check, this enables deciding language-wise equivalence between nondeterministic Büchi automata. We also improve and extend our library for transition systems and automata presented in previous research.

Finally, we develop a command-line executable providing complementation and equivalence checking as a verified reference tool. It can be used to test the output of other, unverified tools. We also include some tests that demonstrate that its performance is sufficient to do this in practice.

Research supported by Dfg grant Cava (Computer Aided Verification of Automata, ES 139/5-1, NI 491/12-1, SM 73/2-1) and Cava2 (Verified Model Checkers, KR 4890/1-1, LA 3292/1-1).

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Authors and Affiliations

  1. Technische Universität München, Munich, Germany

    Julian Brunner

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  1. Julian Brunner
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Correspondence to Julian Brunner .

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  1. University of Surrey, Guildford, UK

    Brijesh Dongol

  2. Royal Institute of Technology - KTH, Stockholm, Sweden

    Elena Troubitsyna

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Brunner, J. (2020). Formal Verification of Executable Complementation and Equivalence Checking for Büchi Automata. In: Dongol, B., Troubitsyna, E. (eds) Integrated Formal Methods. IFM 2020. Lecture Notes in Computer Science(), vol 12546. Springer, Cham. https://doi.org/10.1007/978-3-030-63461-2_13

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  • DOI: https://doi.org/10.1007/978-3-030-63461-2_13

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