Timed Pattern Matching

Given a timed regular expression and a dense-time Boolean signal we compute the set of all matches of the expression in the signal, that is, the set of all segments of the signal that satisfy the regular expression. The set of matches is viewed as a set of points in a two-dimensional space with each point indicating the beginning and end of a matching segment on the real time axis. Our procedure, which works by induction on the structure of the expression, is based on the following result that we prove in this paper: the set of all matches of a timed regular expression by a signal of finite variability and duration can be written as a finite union of zones.