When developing fault-tolerant protocols, systems are usually modeled assuming that process failures are independent and identically distributed. In this paper, we present a system model that can represent correlated failures. We show that such a model is useful in that protocols can be made more efficient. Central to our approach is the idea of a core, which is a reliable minimal subset of processes. We present two probabilistic failure models for dependent failures and discuss them in terms of computing cores. For both, finding a smallest minimal core is NP-hard, but one of the two models can be strengthened in a natural way to make computing a minimal core in P.
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