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Probabilistic Hybrid Systems Verification via SMT and Monte Carlo Techniques

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Hardware and Software: Verification and Testing (HVC 2016)

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Abstract

We develop numerically rigorous Monte Carlo approaches for computing probabilistic reachability in hybrid systems subject to random and nondeterministic parameters. Instead of standard simulation we use \(\delta \)-complete SMT procedures, which enable formal reasoning for nonlinear systems up to a user-definable numeric precision. Monte Carlo approaches for probability estimation assume that sampling is possible for the real system at hand. However, when using \(\delta \)-complete simulation one instead samples from an overapproximation of the real random variable. In this paper, we introduce a Monte Carlo-SMT approach for computing probabilistic reachability confidence intervals that are both statistically and numerically rigorous. We apply our technique to hybrid systems involving nonlinear differential equations.

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Acknowledgements

F.S. was supported by award N00014-13-1-0090 of the US Office of Naval Research; P.Z. was supported by EPSRC grant EP/N031962/1.

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Authors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Fedor Shmarov & Paolo Zuliani

Authors
  1. Fedor Shmarov
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  2. Paolo Zuliani
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Correspondence to Paolo Zuliani .

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Editors and Affiliations

  1. IAIK, Graz University of Technology, Graz, Austria

    Roderick Bloem

  2. IBM Research Labs, Haifa, Israel

    Eli Arbel

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Shmarov, F., Zuliani, P. (2016). Probabilistic Hybrid Systems Verification via SMT and Monte Carlo Techniques. In: Bloem, R., Arbel, E. (eds) Hardware and Software: Verification and Testing. HVC 2016. Lecture Notes in Computer Science(), vol 10028. Springer, Cham. https://doi.org/10.1007/978-3-319-49052-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-49052-6_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49051-9

  • Online ISBN: 978-3-319-49052-6

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