Stochastic Timed Automata
Nathalie Bertrand,Patricia Bouyer,Thomas Brihaye,Quentin Menet,Christel Baier,Marcus Groesser,Marcin Jurdziński +6 more
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TLDR
Correctness of the abstraction holds when automata are almost-surely fair, which it is shown, is the case for two large classes of systems, single- clock automata and so-called weak-reactive automata.Abstract:
A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property $\Phi$, we want to decide whether A satisfies $\Phi$ with probability 1. In this paper, we identify several classes of automata and of properties for which this can be decided. The proof relies on the construction of a finite abstraction, called the thick graph, that we interpret as a finite Markov chain, and for which we can decide the almost-sure model-checking problem. Correctness of the abstraction holds when automata are almost-surely fair, which we show, is the case for two large classes of systems, single- clock automata and so-called weak-reactive automata. Techniques employed in this article gather tools from real-time verification and probabilistic verification, as well as topological games played on timed automata.read more
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