Querying streams using regular expressions: some semantics, decidability, and efficiency issues

This paper analyzes the decidability and complexity problems that arise when matching regular expressions on infinite streams of sets of symbols. We show that in important application domains, several apparently obvious semantics lead to detecting spurious events (events that are mere artifacts of the semantics) or to missing events of potential interest. We single out a class of semantics, of interest in many applications, which we dub use-and-throw: In a use-and-throw semantics, an elementary event can participate in the creation of at most one detected complex event. Many areas of research have identified this as a desirable requirement (we give the examples of databases and video surveillance), but hitherto there has been no systematic study of the characteristics of these semantics, in particular their decidability and algorithmic complexity. This paper is meant to provide at least some initial answers on this subject. We analyze several semantics, provide polynomial algorithms for them, and prove their correctness and their properties.