### Parameter Synthesis for Parametric Interval Markov Chains [chapter]

Benoît Delahaye, Didier Lime, Laure Petrucci
<span title="2015-12-25">2015</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Interval Markov Chains (IMCs) are the base of a classic probabilistic specification theory introduced by Larsen and Jonsson in 1991. They are also a popular abstraction for probabilistic systems. In this paper we study parameter synthesis for a parametric extension of Interval Markov Chains in which the endpoints of intervals may be replaced with parameters. In particular, we propose constructions for the synthesis of all parameter values ensuring several properties such as consistency and
more &raquo; ... stent reachability in both the existential and universal settings with respect to implementations. We also discuss how our constructions can be modified in order to synthesise all parameter values ensuring other typical properties. This work has been partially supported by project PACS ANR-14-CE28-0002 and Pays de la Loire research project AFSEC. Definition 3 (Satisfaction Relation [14]). Let I = (S, s 0 , ϕ, A, V I ) be an IMC and M = (T, t 0 , M, A, V M ) be a MC. A relation R ⊆ T ×S is a satisfaction relation if whenever tRs,
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-49122-5_18">doi:10.1007/978-3-662-49122-5_18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l73s4k7g3vc67gjs3dahudg7dq">fatcat:l73s4k7g3vc67gjs3dahudg7dq</a> </span>
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