 
Summary: A modular approach to sharedmemory consensus, with
applications to the probabilisticwrite model
James Aspnes
Yale University
May 14, 2011
Abstract
We show that consensus can be solved by an alternating sequence of adoptcommit ob
jects [2, 25], which detect agreement, and conciliators, which ensure agreement with some
probability. We observe that most known randomized consensus algorithms have this structure.
We give a deterministic implementation of an mvalued adoptcommit object for an un
bounded number of processes that uses lg m + (log log m) space and individual work. We also
give a randomized conciliator for any number of values in the probabilisticwrite model with
n processes that guarantees agreement with constant probability while using one multiwriter
register, O(log n) expected individual work, and (n) expected total work. Combining these
objects gives a consensus protocol for the probabilisticwrite model that uses O(log m + log n)
individual work and O(n log m) total work. No previous protocol in this model uses sublinear
individual work or linear total work for constant m.
1 Introduction
The consensus problem [29] is to devise a protocol so that n processes, each with a private input,
can agree on a single common output that is equal to some process's input. For asynchronous
