Many replication protocols are using a threshold model in which failures are independent and identically distributed (IID). In this model, one assumes that no more than t out of n components can fail. In many real systems, however, failures are not IID, and a straightforward application of threshold protocols yields suboptimal results. Here, we examine the problem of optimally transforming threshold protocols into survivor-set protocols tolerating dependent failures. In particular, we are interested in threshold protocols where the number of components n and the number of failures t are related by n > k · t, where k is a positive integer constant k. We develop an optimal transformation that translates any such threshold protocol to a survivor-set dependent failure model, and hence, to adversarial structures. Our transformation does not require authentication, self-verification or encryption. We characterize equivalence classes of adversarial structures, regarding solvability, using certain hierarchical properties based on set intersection.
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