[KNP09c] Marta Kwiatkowska, Gethin Norman and David Parker. Stochastic Games for Verification of Probabilistic Timed Automata. In Proc. 7th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS'09), volume 5813 of LNCS, pages 212-227, Springer. September 2009. [pdf] [bib] [Presents game-based abstraction-refinement techniques for verifying PTAs, implemented in PRISM.]
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Notes: An full version of this paper with proofs can be found in [KNP09d]. The original publication is available at www.springerlink.com.
Abstract. Probabilistic timed automata (PTAs) are used for formal modelling and verification 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-refinement 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.