Parameterized Compositional Model Checking

Kedar S. Namjoshi, Richard J. Trefler

Abstract: The Parameterized Compositional Model Checking Problem (PCMCP) is to decide, using compositional proofs, whether a property holds for every instance of a parameterized family of process networks. Compositional analysis focuses attention on the neighborhood structure of processes in the network family. For the verification of safety properties, the PCMCP is shown to be much more tractable than the more general Parameterized Model Checking Problem (PMCP). For example, the PMCP is undecidable for ring networks while the PCMCP is decidable in polynomial time. This result generalizes to toroidal mesh networks and related networks for describing parallel architectures. Decidable models of the PCMCP are also shown for networks of control and user processes. The results are based on the demonstration of compositional cutoffs; that is, small instances whose compositional proofs generalize to the entire parametric family. There are, however, control-user models where the PCMCP and the PMCP are both undecidable.