On Reasoning About Rings

Abstract

Distributed protocols are often composed of similar processes connected in a unidirectional ring network. Processes communicate by passing a token in a fixed direction; the process that holds the token is allowed to perform certain actions. Usually, correctness properties are expected to hold irrespective of the size of the ring. We show that the question of checking many useful correctness properties for rings of all sizes can be reduced to checking them on ring of sizes up to a small cutoff size. We apply our results to the verification of a mutual exclusion protocol and Milner's scheduler protocol.