Consistency in Parametric Interval Probabilistic Timed Automata

• Published in: Journal of logical and algebraic methods in programming Vol. 110; p. 100459
• Main Authors: André, Étienne, Delahaye, Benoît, Fournier, Paulin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2020; Elsevier
• Subjects: Computer Science; Embedded Systems; Logic in Computer Science; Parametric probabilistic timed automata; Parametric verification; Timed probabilistic systems; Parametric probabilistic timed automata; Timed probabilistic systems; Parametric verification
• ISSN: 2352-2208
• DOI: 10.1016/j.jlamp.2019.04.007

We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the consistency problem that amounts to deciding whether a given specification admits at least one implementation. In the context of Interval Probabilistic Timed Automata (with no timing parameters), we show that this problem is decidable and propose a constructive algorithm for its resolution. We show that the existence of timing parameter valuations ensuring consistency is undecidable in the general context, but still exhibit a syntactic condition on parameters to ensure decidability. We also propose procedures that resolve both the consistency and the consistent reachability problems when the parametric probabilistic zone graph is finite.