Propositional Dynamic Logic for Message-Passing Systems

TL;DR

This paper introduces a bidirectional propositional dynamic logic for message sequence charts, enabling expressive property specification and synthesis of finite-state machines, with complexity results for model checking and limitations with intersection.

Contribution

It extends existing temporal logics with multi-modal capabilities for MSCs and provides a synthesis method for CFMs from PDL formulas, including complexity analysis.

Findings

CFMs can be synthesized from PDL formulas with exponential size.

Model checking for CFMs and HMSCs is in PSPACE for bounded MSCs.

PDL with intersection cannot be captured by CFMs.

Abstract

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