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Bounded Verification of Reachability of Probabilistic Hybrid Systems

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Quantitative Evaluation of Systems (QEST 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11024))

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Abstract

In this paper, we consider the problem of bounded reachability analysis of probabilistic hybrid systems which model discrete, continuous and probabilistic behaviors. The discrete and probabilistic dynamics are modeled using a finite state Markov decision process (MDP), and the continuous dynamics is incorporated by annotating the states of the MDP with differential equations/inclusions. We focus on polyhedral dynamical systems to model continuous dynamics. Our broad approach for computing probabilistic bounds on reachability consists of the computation of the exact minimum/maximum probability of reachability within k discrete steps in a polyhedral probabilistic hybrid system by reducing it to solving an optimization problem with satisfiability modulo theory (SMT) constraints.

We have implemented analysis algorithms in a Python toolbox, and use the Z3opt optimization solver at the backend. We report the results of experimentation on a case study involving the analysis of the probability of the depletion of the charge in a battery used in the nano-satellite.

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Acknowledgements

Pavithra Prabhakar was partially supported by NSF CAREER Award No. 1552668 and ONR YIP Award No. N000141712577.

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Authors and Affiliations

  1. Kansas State University, Manhattan, USA

    Ratan Lal & Pavithra Prabhakar

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  1. Ratan Lal
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  2. Pavithra Prabhakar
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Correspondence to Ratan Lal or Pavithra Prabhakar .

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Editors and Affiliations

  1. Macquarie University , Sydney, New South Wales, Australia

    Annabelle McIver

  2. University of Turin , Turin, Italy

    Andras Horvath

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Lal, R., Prabhakar, P. (2018). Bounded Verification of Reachability of Probabilistic Hybrid Systems. In: McIver, A., Horvath, A. (eds) Quantitative Evaluation of Systems. QEST 2018. Lecture Notes in Computer Science(), vol 11024. Springer, Cham. https://doi.org/10.1007/978-3-319-99154-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-99154-2_15

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