Online Timed Pattern Matching using Automata

Abstract : We provide a procedure for detecting the sub-segments of an incrementally observed Boolean signal w that match a given temporal pattern phi. As a pattern specification language, we use timed regular expressions, a formalism well-suited for expressing properties of concurrent asynchronous behaviors embedded in metric time. We construct a timed automaton accepting the timed language denoted by phi and modify it slightly for the purpose of matching. We then apply zone-based reachability computation to this automaton while it reads w, and retrieve all the matching segments from the results. Since the procedure is automaton based, it can be applied to patterns specified by other formalisms such as timed temporal logics reducible to timed automata or directly encoded as timed automata. The procedure has been implemented and its performance on synthetic examples is demonstrated.