A Divide-and-Conquer Strategy for Regular Model Checking

Regular model checking is being developed for algorithmic verification of several classes of infinite-state systems whose configurations can be modeled as words over a finite alphabet. Examples include parameterized systems consisting of an arbitrary number of homogeneous finite-state processes connected in a linear or ring-formed topology, and systems that operate on queues, stacks, integers, and other linear data structures. The main idea is to use regular languages as the representation of sets of configurations, and finite-state transducers to describe transition relations. In general, the verification problems considered are undecidable, so the work has consisted in developing semi-algorithms, and decidability results for restricted cases. In previous work, algorithms have been developed for computing the set of reachable states or the transitive closure of a transducer. Practical experience with these algorithms is that they often work well for simple transducers satisfying certain structural conditions. If the system under verification is modeled in terms of a set of small actions (program statements), then the transitive closure of each can be computed and used in a standard reachability analysis or fixpoint computation of a transitive closure. However, for arbitrary transducers, some divide-and-conquer strategy is needed to split a transducer into subparts whose transitive closure can be computed efficiently. In this paper, we present a systematic method for extracting subparts of a transition relation, each of whose transitive closure can be computed efficiently. This method works also in the case where the system model is not structured as a set of small actions, which, e.g., is the case when the model is the result of the transformation of a temporal logic specification, for which manual extraction is difficult. We have implemented the approach, and evaluated its performance on both safety and liveness properties of some parameterized synchronization protocols from the literature. In particular, we are able to obtain better results for proving liveness (non-starvation) properties of these protocols.