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Parameter Synthesis Algorithms for Parametric Interval Markov Chains

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Book cover Formal Techniques for Distributed Objects, Components, and Systems (FORTE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10854))

Abstract

This paper considers the consistency problem for Parametric Interval Markov Chains. In particular, we introduce a co-inductive definition of consistency, which improves and simplifies previous inductive definitions considerably. The equivalence of the inductive and co-inductive definitions has been formally proved in the interactive theorem prover PVS.

These definitions lead to forward and backward algorithms, respectively, for synthesizing an expression for all parameters for which a given PIMC is consistent. We give new complexity results when tackling the consistency problem for IMCs (i.e. without parameters). We provide a sharper upper bound, based on the longest simple path in the IMC. The algorithms are also optimized, using different techniques (dynamic programming cache, polyhedra representation, etc.). They are evaluated on a prototype implementation. For parameter synthesis, we use Constraint Logic Programming and the PARMA library for convex polyhedra.

This research was conducted with the support of PHC Van Gogh project PAMPAS.

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Notes

  1. 1.

    In the following, for the sake of readability, we do not consider linear combinations of parameters as bounds of the intervals. However, allowing them would not change the results.

  2. 2.

    The complete text of the proofs, their PVS formalisation, Prolog programs, and experimental data can be found at http://fmt.cs.utwente.nl/~vdpol/PIMC2018.zip.

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Acknowledgement

The authors would like to thank the reviewers for their extensive comments, which helped them to improve the paper. They acknowledge the support of University Paris 13 and of the Van Gogh project PAMPAS, that covered their mutual research visits.

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Authors and Affiliations

  1. LIPN, CNRS UMR 7030, Université Paris 13, Sorbonne Paris Cité, Villetaneuse, France

    Laure Petrucci

  2. Formal Methods and Tools, University of Twente, Enschede, The Netherlands

    Jaco van de Pol

Authors
  1. Laure Petrucci
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  2. Jaco van de Pol
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Corresponding authors

Correspondence to Laure Petrucci or Jaco van de Pol .

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Editors and Affiliations

  1. Technische Universität Dresden, Dresden, Germany

    Christel Baier

  2. Departamento de Informática, Universidade Nova de Lisboa, Caparica, Portugal

    Luís Caires

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Petrucci, L., van de Pol, J. (2018). Parameter Synthesis Algorithms for Parametric Interval Markov Chains. In: Baier, C., Caires, L. (eds) Formal Techniques for Distributed Objects, Components, and Systems. FORTE 2018. Lecture Notes in Computer Science(), vol 10854. Springer, Cham. https://doi.org/10.1007/978-3-319-92612-4_7

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  • DOI: https://doi.org/10.1007/978-3-319-92612-4_7

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  • Online ISBN: 978-3-319-92612-4

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