Symbolically bounding the drift in time-constrained MSC graphs

Abstract

Verifying systems involving both time and concurrency rapidly leads to undecidability, and requires restrictions to become effective. This paper addresses the emptiness problem for time-constrained MSC-Graphs (TC-MSC graphs for short), that is, checking whether there is a timed execution compatible with a TC-MSC graph specification. This problem is known to be undecidable in general [11], and decidable for some regular specifications [11]. We establish decidability of the emptiness problem under the condition that, for a given K, no path of the TC-MSC graph forces any node to take more than K time units to complete. We prove that this condition can be effectively checked. The proofs use a novel symbolic representation for runs, where time constraints are encoded as a system of inequalities. This allows us to handle non-regular specifications and improve efficiency w.r.t. using interleaved representations. © 2012 Springer-Verlag.