Coupling and Importance Sampling for Statistical Model Checking

Abstract : Statistical model-checking is an alternative verification technique applied on stochastic systems whose size is beyond numerical analysis ability. Given a model (most often a Markov chain) and a formula, it provides a confidence interval for the probability that the model satisfies the formula. One of the main limitations of the statistical approach is the computation time explosion triggered by the evaluation of very small probabilities. In order to solve this problem we develop a new approach based on importance sampling and coupling. The corresponding algorithms have been implemented in our tool cosmos. We present experimentation on several relevant systems, with estimated time reductions reaching a factor of 10^120.