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.
Notes
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