Regular sets of infinite message sequence charts

This paper resumes the study of regular sets of message sequence charts (MSC) initiated by Henriksen et al. [Technical Report, BRICS RS-99-52, 1999]. Differently from their results, we consider infinite MSCs. It is shown that for bounded sets of infinite MSCs, the notions of recognizability, axiomatizability in monadic second order logic, and acceptance by a deterministic message passing automaton with Muller acceptance condition coincide. We furthermore characterize the expressive power of first order logic and of its extension by modulo-counting quantifiers over bounded infinite MSCs. In order to prove our results, we exhibit a new connection to the theory of Mazurkiewicz traces using relabeling techniques. (C) 2003 Elsevier Science (USA). All rights reserved.