In this paper, we generalize the lower bound on the number of rounds for Consensus algorithms assuming that processes fail dependently. This lower bound is general in the sense that it is independent of the failure assumptions for processes. In order to instantiate it, one needs to provide a necessary condition on process replication for a given failure model in terms of our abstractions to represent dependent failures. A surprising corollary of our generalization is that the lower bound on the number of rounds, in general, differs between the crash and the arbitrary failure models.
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