Parameterized model checking of ring-based message passing systems

The Parameterized Model Checking Problem (PMCP) is to decide whether a temporal property holds for a uniform family of systems, U-n, comprised of finite, but arbitrarily many, copies of a template process U. Unfortunately, it is undecidable in general [3]. In this paper, we consider the PMCP for systems comprised of processes arranged in a ring that communicate by passing messages via tokens whose values can be updated at most a bounded number of times. Correctness properties are expressed using the stuttering-insensitive linear time logic LTL\X. For bidirectional rings we show how to reduce reasoning about rings with an arbitrary number of processes to rings with up to a certain finite cutoff number of processes. This immediately yields decidability of the PMCP at hand. We go on to show that for unidirectional rings small cutoffs can be achieved, making the decision procedure provably efficient. As example applications, we consider protocols for the leader election problem.