The disagreement power of an adversary

Abstract

At the heart of distributed computing lies the fundamental result that the level of agreement that can be obtained in an asynchronous shared memory model where t processes can crash is exactly t+1. In other words, an adversary that can crash any subset of size at most t can prevent the processes from agreeing on t values. But what about the rest (22n − n) adversaries that might crash certain combination of processes and not others?This paper presents a precise way to characterize such adversaries by introducing the notion of disagreement power: the biggest integer k for which the adversary can prevent processes from agreeing on k values. We show how to compute the disagreement power of an adversary and how this notion enables to derive n classes of adversaries.We use our characterization to also close the question of the weakest failure detector for k-set agreement. So far, the result has been obtained for two extreme cases: consensus and n−1-set agreement. We answer this question for any k.