Our first 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 finite 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 realizability is in EXPSPACE.

Our second set of results concerns verification of MSC-graphs. While checking properties of a graph G, besides verifying all the scenarios in the set L(G) of MSCs specified 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 ML(G) is NP-complete, but checking ML^w(G) has a quadratic solution. For temporal logic specifications, considering the closure makes the verification problem harder: while checking LTL properties of L(G) is PSPACE-complete for bounded graphs G, checking even simple “local” properties of L^w(G) is undecidable.