The weakest failure detector for solving consensus

We determine what information about failures is necessary and sufficient to solve Consensus in asynchronous distributed systems subject to crash failures. In Chandra and Toueg [1996] it is shown that ◇script W sign, a failure detector that provides surprisingly little information about which processes have crashed, is sufficient to solve Consensus in asynchronous systems with a majority of correct processes. In this paper, we prove that to solve Consensus, any failure detector has to provide at least as much information as ◇script W sign. Thus, ◇script W sign is indeed the weakest failure detector for solving Consensus in asynchronous systems with a majority of correct processes.