Parametric Timed Pattern Matching

Given a log and a specification, timed pattern matching aims at exhibiting for which start and end dates a specification holds on that log. For example, "a given action is always followed by another action before a given deadline". This problem has strong connections with monitoring real-time systems. We address here timed pattern matching in the presence of an uncertain specification, i.e., that may contain timing parameters (e.g., the deadline can be uncertain or unknown). We want to know for which start and end dates, and for what values of the timing parameters, a property holds. For instance, we look for the minimum or maximum deadline (together with the corresponding start and end dates) for which the property holds. We propose two frameworks for parametric timed pattern matching. The first one is based on parametric timed model checking. In contrast to most parametric timed problems, the solution is effectively computable. The second one is a dedicated method; not only we largely improve the efficiency compared to the first method, but we further propose optimizations with skipping. Our experiment results suggest that our algorithms, especially the second one, are efficient and practically relevant.