Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models containing first-order state variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the first-order state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol.
We present regular model checking, a framework for algorithmic verification of infinite-state systems with, e.g., queues, stacks, integers, or a parameterized linear topology. States are represented by strings over a finite alphabet and the transition relation by a regular length-preserving relation on strings. Major problems in the verification of parameterized and infinite-state systems are to compute the set of states that are reachable from some set of initial states, and to compute the transitive closure of the transition relation. We present two complementary techniques for these problems. One is a direct automata-theoretic construction, and the other is based on widening. Both techniques are incomplete in general, but we give sufficient conditions under which they work. We also present a method for verifying ω-regular properties of parameterized systems, by computation of the transitive closure of a transition relation. The paper shows that, by an appropriate choice of a rich assertional language, it is possible to extend the utility of symbolic model checking beyond the realm of BDD-represented finite-state systems into the domain of infinite-state systems, leading to a powerful technique for uniform verification of unbounded (parameterized) process networks.