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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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Submitted on : Wednesday, June 27, 2018 - 3:55:23 PM
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Laure Petrucci, Jaco van De 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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