Realizability and Veri cation of MSC Graphs

Scenario-based speciications such as message sequence charts (MSC) ooer an intuitive and visual way of describing design requirements. MSC-graphs allow convenient expression of multiple scenarios, and can be viewed as an early model of the system that can be subjected to a variety of analyses. Problems such as LTL model checking are known to be decidable for the class of bounded MSC-graphs. Our rst set of results concerns checking realizability of bounded MSC-graphs. An MSC-graph is realizable if there is a distributed implementation that generates precisely the behaviors in the graph. There are two notions of realizability, weak and safe, depending on whether or not we require the implementation to be deadlock-free. It is known that for a set of MSCs, weak realizability is coNP-complete while safe realizability has a polynomial-time solution. We establish that for bounded MSC-graphs, weak realizability is, surprisingly, undecidable, while safe is in Expspace. Our second set of results concerns veriication of MSC-graphs. While checking properties of a graph G, besides verifying all the scenarios in the set L(G) of MSCs speciied by G, it is desirable to verify all the scenarios in the set L w (G)|the closure of G, that contains the implied scenarios that any distributed implementation of G must include. For checking whether a given MSC M is a possible behavior, checking M 2 L(G) is NP-complete, but checking M 2 L w (G) has a quadratic solution. For temporal logic speciications, considering the closure makes the veriication problem harder: while checking LTL properties of L(G) is Pspace-complete and checking local properties has polynomial-time solutions, even for boolean combinations of local properties of L w (G), verifying acyclic graphs is coNP-complete and verifying bounded graphs is undecidable.