Diagnosis of Probabilistic Models using Causality and Regression

The counterexample in probabilistic model checking (PMC) is a set of paths in which a path formula holds, and their accumulated probability violates the probability bound. However, understanding the counterexample is not an easy task. In this paper we address the complementary task of counterexample generation, which is the counterexample analysis. We propose an aided-diagnostic method for probabilistic counterexamples based on the notions of causality and regression analysis. Given a counterexample for a Probabilistic CTL (PCTL)/Continuous Stochastic Logic (CSL) formula that does not hold over Discrete Time Markov Chain (DTMC)/Continuous Time Markov Logic (CTMC) model, this method generates the causes of the violation, and describes their contribution to the error in the form of a regression model.