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Approximate Probabilistic Verification of Hybrid Systems

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Hybrid Systems Biology (HSB 2015)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 9271))

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Abstract

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability 1. Based on this, we formulate a sequential hypothesis testing procedure for verifying–approximately–that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings.

S. Paul—The author would like to thank ERC grant 269427 that supported a part of this work.

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Authors and Affiliations

  1. Laboratory of Systems Pharmacology, Harvard Medical School, Boston, USA

    Benjamin M. Gyori & P. S. Thiagarajan

  2. Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, USA

    Bing Liu

  3. Institute de Recherche En Informatique de Toulouse, 31062, Toulouse, France

    Soumya Paul

  4. Department of Computer Science, National University of Singapore, Singapore, Singapore

    R. Ramanathan

Authors
  1. Benjamin M. Gyori
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  2. Bing Liu
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  3. Soumya Paul
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  4. R. Ramanathan
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  5. P. S. Thiagarajan
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Corresponding author

Correspondence to P. S. Thiagarajan .

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Editors and Affiliations

  1. University of Oxford, Oxford, United Kingdom

    Alessandro Abate

  2. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    David Šafránek

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Gyori, B.M., Liu, B., Paul, S., Ramanathan, R., Thiagarajan, P.S. (2015). Approximate Probabilistic Verification of Hybrid Systems. In: Abate, A., Šafránek, D. (eds) Hybrid Systems Biology. HSB 2015. Lecture Notes in Computer Science(), vol 9271. Springer, Cham. https://doi.org/10.1007/978-3-319-26916-0_6

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  • DOI: https://doi.org/10.1007/978-3-319-26916-0_6

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-26916-0

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