Counterexamples in Probabilistic LTL Model Checking for Markov Chains

We propose a way of presenting and computing a counterexample in probabilistic LTL model checking for discrete-time Markov chains. In qualitative probabilistic model checking, we present a counterexample as a pair (α,γ), where α,γ are finite words such that all paths that extend α and have infinitely many occurrences of γ violate the specification. In quantitative probabilistic model checking, we present a counterexample as a pair (W,R), where W is a set of such finite words α and R is a set of such finite words γ. Moreover, we suggest how the counterexample presented helps the user identify the underlying error in the system by means of an interactive game with the model checker.