On Model Checking for Non-Deterministic In nite-State Systems

We demonstrate that many known algorithms for model checking innnite-state systems can be derived uniformly from a reachability procedure that generates a \covering graph", a generalization of the Karp-Miller graph for Petri Nets. Each node of the covering graph has an associated non-empty set of reach-able states, which makes it possible to model check safety properties of the system on the covering graph. For systems with a well-quasi-ordered simulation relation , each innnite fair computation has a nite witness , which may be detected using the covering graph and combinatorial properties of the speciic innnite state system. These results explain many known de-cidability results in a simple, uniform manner. This is a strong indication that the covering graph construction is appropriate for the analysis of innnite state systems. We also consider the new application domain of parameterized broadcast protocols, and indicate how to apply the construction in this domain. This application is illustrated on an invalidation-based cache co-herency protocol, for which many safety properties can be proved fully automatically for an arbitrary number of processes.