Generating Diagnoses for Probabilistic Model Checking Using Causality

One of the major advantages of model checking over other formal methods of verification is its ability to generate an error trace when the specification is falsified in the model. We call this trace a counterexample. In probabilistic model checking (PMC), counterexample generation has a quantitative aspect. The counterexample is a set of paths in which a path formula holds, and their accumulated probability mass violates the probability bound. In this paper, we address the complementary task of counterexample generation, which is the counterexample diagnosis. We propose an aided-diagnostic method for probabilistic counterexamples based on the notion of causality. Given a counterexample for a probabilistic CTL (PCTL) formula that does not hold over Discrete Time Markov Chain (DTMC) model, this method guides the user to the most responsible causes in the counterexample.