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. Processor Consistency-Goodman's version 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 Burn's 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 are incorrect for PC-G. A corollary of this investigation is that, in contrast to Sequential Consistency, multi-writers cannot be implemented from single-writers in PC-G.