 
Summary: Lower Bounds for Randomized Consensus
under a Weak Adversary
Hagit Attiya
Keren Censor Hillel
April 26, 2010
Abstract
This paper studies the inherent tradeoff between termination probability and total step complexity
of randomized consensus algorithms. It shows that for every integer k, the probability that an fresilient
randomized consensus algorithm of n processes does not terminate with agreement within k(nf) steps
is at least 1
ck , for some constant c. A corresponding result is proved for MonteCarlo algorithms that may
terminate in disagreement.
The lower bound holds for asynchronous systems, where processes communicate either by message
passing or through shared memory, under a very weak adversary that determines the schedule in ad
vance, without observing the algorithm's actions. This complements algorithms of Kapron et al. [26],
for messagepassing systems, and of Aumann et al. [7,8], for sharedmemory systems.
A preliminary version of this paper appeared in Proceedings of the 27th Annual ACM Symposium on Principles of Distributed
Computing, pages 315324, 2008. This research is supported in part by the Israel Science Foundation (grant number 953/06).
