The Disagreement Power of an Adversary
Résumé
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 ($2^{2^n} -n$) adversaries that might crash certain combination of processes and not others? Given any adversary, what is its disagreement power? i.e., the biggest $k$ for which it can prevent processes from agreeing on $k$ values. This paper answers this question. We present a general characterization of adversaries that enables to directly derive their disagreement power. 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 $k$ and any adversary.
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