The disagreement power of an adversary

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 all the other ${2^{2^n - 1} - (n+1)}$ adversaries that are not uniform in this sense and might crash certain combination of processes and not others? This paper presents a precise way to classify all adversaries. We introduce 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 derive n equivalence classes of adversaries.