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Parameter Synthesis Algorithms for Parametric Interval Markov Chains

  • Laure Petrucci
  • Jaco van de Pol
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Notes

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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Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.LIPN, CNRS UMR 7030, Université Paris 13, Sorbonne Paris CitéVilletaneuseFrance
  2. 2.Formal Methods and ToolsUniversity of TwenteEnschedeThe Netherlands

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