Reachability in parametric Interval Markov Chains using constraints

Anicet Bart, Benoît Delahaye, Paulin Fournier, Didier Lime, Éric Monfroy, Charlotte Truchet
2018 Theoretical Computer Science  
Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that
more » ... th semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -consistency, qualitative reachability and quantitative reachability -that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results.
doi:10.1016/j.tcs.2018.06.016 fatcat:7tlcirehbzbihccomofo4joobu