[BBBK16] Benoit Barbot, Nicolas Basset, Marc Beunardeau and Marta Kwiatkowska. Uniform Sampling for Timed Automata with Application to Language Inclusion Measurement. In Proc. 13th International Conference on Quantitative Evaluation of SysTems (QEST 2016), volume 9826 of LNCS, pages 175-190, Springer. 2016. [pdf] [bib] [Develops Monte Carlo model checking techniques for timed automata using PRISM, SageMath and COSMOS.]
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Abstract. Monte Carlo model checking introduced by Smolka and Grosu is an approach to analyse non-probabilistic models using sampling and draw conclusions with a given confidence interval by applying statistical inference. Though not exhaustive, the method enables verification of complex models, even in cases where the underlying problem is undecidable. In this paper we develop Monte Carlo model checking techniques to evaluate quantitative properties of timed languages. Our approach is based on uniform random sampling of behaviours, as opposed to isotropic sampling that chooses the next step uniformly at random. The uniformity is defined with respect to volume measure of timed languages previously studied by Asarin, Basset and Degorre. We improve over their work by employing a zone graph abstraction instead of the region graph abstraction and incorporating uniform sampling within a zone-based Monte Carlo model checking framework. We implement our algorithms using tools PRISM, SageMath and COSMOS, and demonstrate their usefulness on statistical language inclusion measurement in terms of volume.