Synthesis of Temporal Causality

We present an automata-based algorithm to synthesize \(\omega \) -regular causes for \(\omega \) -regular effects on executions of a reactive system, such as counterexamples uncovered by a model checker. Our theory is a generalization of temporal causality, which has recently been proposed as a framework for drawing causal relationships between trace properties on a given trace. So far, algorithms exist only for verifying a single causal relationship and, as an extension, cause synthesis through enumeration, which is complete only for a small fragment of effect properties. This work presents the first complete cause-synthesis algorithm for the class of \(\omega \) -regular effects. We show that in this case, causes are guaranteed to be \(\omega \) -regular themselves and can be computed as, e.g., nondeterministic Büchi automata. We demonstrate the practical feasibility of this algorithm with a prototype tool and evaluate its performance for cause synthesis and cause checking.