Bayesian Statistical Model Checking for Continuous Stochastic Logic

Abstract

In this paper, we propose a Bayesian approach to statistical model-checking (SMC) of discrete-time Markov chains with respect to continuous stochastic logic (CSL) specifications. While Bayesian approaches for simpler logic without nested probabilistic operators and Frequentist approaches for nested logic have been previously explored, the Bayesian approach for CSL consisting of nested probabilistic operators has not been addressed. The challenge in the nested case arises from the fact that unlike in probabilistic model-checking (PMC), where we obtain a definitive answer for the model-checking problem for the sub-formulas, instead, we only obtain a correct answer with a certain confidence, which needs to be factored into the recursive SMC algorithm. Here, we propose a Bayesian test based algorithm for CSL that has nested probabilistic operators. We have implemented our algorithm in a Python Toolbox. Our experimental evaluation shows that our Bayesian SMC approach performs better than both the frequentist SMC approach and PMC algorithms.