Bounds for Mutual Exclusion with only Processor Consistency

Abstract

Most weak memory consistency models are incapable of supporting a solution to mutual exclusion using only read and write operations to shared variables. Processor Consistency-Goodman's version (PC-G) is an exception. Ahamad et al.[1] showed that Peterson's mutual exclusion algorithm is correct for PC-G, but Lamport's bakery algorithm is not. In this paper, we derive a lower bound on the number and type (single- or multi-writer) of variables that a mutual exclusion algorithm must use in order to be correct for PC-G. We show that any such solution for n processes must use at least one multi-writer and n single-writers. This lower bound is tight when n = 2, and is tight when n > 2 for solutions that do not provide fairness. We show that Burns' algorithm is an unfair solution for mutual exclusion in PC-G that achieves our bound. However, five other known algorithms that use the same number and type of variables do not guarantee mutual exclusion when the memory consistency model is only PC-G, as opposed to the Sequential Consistency model for which they were designed. A corollary of this investigation is that, in contrast to Sequential Consistency, multi-writers cannot be implemented from single-writers in PC-G.