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Parameter Synthesis Algorithms for Parametric Interval Markov Chains

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.
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https://hal.inria.fr/hal-01824814
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Submitted on : Wednesday, June 27, 2018 - 3:55:23 PM
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Laure Petrucci, Jaco Pol. Parameter Synthesis Algorithms for Parametric Interval Markov Chains. 38th International Conference on Formal Techniques for Distributed Objects, Components, and Systems (FORTE), Jun 2018, Madrid, Spain. pp.121-140, ⟨10.1007/978-3-319-92612-4_7⟩. ⟨hal-01824814⟩

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