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Improving SMT Solver Integrations for the Validation of B and Event-B Models

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Book cover Formal Methods for Industrial Critical Systems (FMICS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12863))

Abstract

ProB provides a constraint solver for the B-method written in Prolog and optionally can make use of different backends based on SAT or SMT solving. One such solver integration translates B and Event-B operators to SMT-LIB using the C interface of the Z3 solver. This translation uses quantifiers to axiomatise operators when translating to SMT-LIB, which are not well-handled by Z3. Several relational constraints such as the transitive closure are not supported since their translations were too involved.

In this paper, we substantially improve the translation to SMT-LIB by employing a more constructive rather than axiomatised style using Z3’s lambda functions. Thereby, we are able to translate more set-theoretic B and Event-B operators to SMT-LIB, and improve the overall performance. We further extend ProB’s interface to Z3 to run different solver configurations in parallel, e.g., either using the former or new translation. Empirical results show that the new translation to SMT-LIB and the parallel integration of different configurations of the Z3 solver have improved the performance of constraint solving.

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Notes

  1. 1.

    Z3 throws the error “internalization of exists is not supported”.

  2. 2.

    The benchmarks can be found in the following repository to reproduce the results: https://github.com/Joshua27/fmics2021_benchmarks.

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Acknowledgements

We would like to thank the reviewers of FMICS’2021 for their useful feedback.

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Authors and Affiliations

  1. Institut für Informatik, Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany

    Joshua Schmidt & Michael Leuschel

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  1. Joshua Schmidt
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Correspondence to Joshua Schmidt .

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  1. Technical University of Denmark, Kongens Lyngby, Denmark

    Alberto Lluch Lafuente

  2. KBR/NASA Ames Research Center, Moffett Field, CA, USA

    Anastasia Mavridou

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Schmidt, J., Leuschel, M. (2021). Improving SMT Solver Integrations for the Validation of B and Event-B Models. In: Lluch Lafuente, A., Mavridou, A. (eds) Formal Methods for Industrial Critical Systems. FMICS 2021. Lecture Notes in Computer Science(), vol 12863. Springer, Cham. https://doi.org/10.1007/978-3-030-85248-1_7

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  • DOI: https://doi.org/10.1007/978-3-030-85248-1_7

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