[KNP09d] M. Kwiatkowska, G. Norman and D. Parker. Stochastic Games for Verification of Probabilistic Timed Automata. Technical report RR-09-05, Oxford University Computing Laboratory. June 2009. [pdf] [bib]
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Notes: This is an extended version, including proofs, of [KNP09c].
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Abstract. Probabilistic timed automata (PTAs) are used for formal modelling and veri cation of systems with probabilistic, nondeterministic and real-time behaviour. For non-probabilistic timed automata, forwards reachability is the analysis method of choice, since it can be implemented extremely efficiently. However, for PTAs, such techniques are only able to compute upper bounds on maximum reachability probabilities. In this paper, we propose a new approach to the analysis of PTAs using abstraction and stochastic games. We show how efficient forwards reachability techniques can be extended to yield both lower and upper bounds on maximum (and minimum) reachability probabilities. We also present abstraction-re nement techniques that are guaranteed to improve the precision of these probability bounds, providing a fully automatic method for computing the exact values. We have implemented these techniques and applied them to a set of large case studies. We show that, in comparison to alternative approaches to verifying PTAs, such as backwards reachability and digital clocks, our techniques exhibit superior performance and scalability.