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Tight Bounds for Critical Sections in Processor Consistent Platforms
October 2006 (vol. 17 no. 10)
pp. 1072-1083

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. showed that Peterson's mutual exclusion algorithm is correct for PC-G, but Lamport's bakery algorithm is not. This paper derives a lower bound on the number of and type of (single or multiwriter) variables that a mutual exclusion algorithm must use in order to be correct for PC-G. Specifically, any such solution for n processes must use at least one multiwriter variable and n single-writer variables. Peterson's algorithm for two processes uses one multiwriter and two single-writer variables, and therefore establishes that this bound is tight for two processes. This paper presents a new n{\hbox{-}}{\rm{process}} algorithm for mutual exclusion that is correct for PC-G and achieves the bound for any n. While Peterson's algorithm is fair, this extension to arbitrary n is not fair. Six known algorithms that use the same number and type of variables are shown to fail to 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 our investigation is that, in contrast to Sequential Consistency, multiwriter variables cannot be implemented from single-writer variables in a PC-G system.

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Index Terms:
Memory consistency models, mutual exclusion, processor consistency, multiwriter/single-writer variables.
Citation:
Lisa Higham, Jalal Kawash, "Tight Bounds for Critical Sections in Processor Consistent Platforms," IEEE Transactions on Parallel and Distributed Systems, vol. 17, no. 10, pp. 1072-1083, Oct. 2006, doi:10.1109/TPDS.2006.146
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