Propositional Dynamic Logic for Message-Passing Systems

Abstract

We examine a bidirectional propositional dynamic logic (PDL) for finite andinfinite message sequence charts (MSCs) extending LTL and TLC-. By this kind ofmulti-modal logic we can express properties both in the entire future and inthe past of an event. Path expressions strengthen the classical until operatorof temporal logic. For every formula defining an MSC language, we construct acommunicating finite-state machine (CFM) accepting the same language. The CFMobtained has size exponential in the size of the formula. This synthesisproblem is solved in full generality, i.e., also for MSCs with unboundedchannels. The model checking problem for CFMs and HMSCs turns out to be inPSPACE for existentially bounded MSCs. Finally, we show that, for PDL withintersection, the semantics of a formula cannot be captured by a CFM anymore