Consistency in Parametric Interval Probabilistic Timed Automata

Abstract

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.

Tweaking the Odds in Probabilistic Timed Automata

“…In its adaptation to cpPTA [8], all v ∈ V must result in the same reachability probabilities. Parametric interval probabilistic timed automata [7] combine cpPTA with interval Markov chains [36], i.e. compared to cpPTA, the concrete probabilities are replaced by intervals of possible probabilities.…”

“…In contrast to parametric probabilities, intervals cannot express dependencies between the probabilities of different events (such as one event being twice as likely as another). For this model, research currently remains focused on the question of consistency [7].…”