M-Consensus Sample Clauses

M-Consensus. The M-Consensus problem is formalized in terms of proposers, acceptors, learners, and a v-map set whose Domain and Value sets equal the set of proposers and the set of proposable commands, respec- tively. As proposers propose commands, learners learn v- maps from proposers to commands or to Nil . Learners may learn different v-maps, but they must be always com- patible. A learner can only learn another v-map if it is an extension of the previously learned one. Eventually, all nonfaulty learners must learn the same complete non- trivial v-map. Formally, the properties of M-Consensus are the following, where learned [l ] is the v-map learned by learner l , initially ⊥ [37]: Nontriviality For any learner l , learned [l ] is always a nontrivial v-map and the range of learned [l ] contains only proposed commands. Stability For any learner l , if learned [l ] = v at some time, then v ± learned [l ] at all later times. Consistency The set of learned v-maps is always com- patible and has a nontrivial least upper bound. Liveness For any proposer p and learner l , if p, l and a quorum of acceptors are nonfaulty and p proposes a value, then eventually learned [l ] is complete. The similarity between the specification of M- Consensus and Consensus is not coincidental. These problems are, in fact, equivalent: one can solve con- sensus by deterministically choosing a proposal from the M-Consensus solution and, conversely and, conversely, one solve M-Consensus by building v-map whose range equals the decision of consensus. As a result, all lower- bounds of consensus are valid for M-Consensus, as for example, the Quorum Requirement for asynchronous al- gorithms (Assumption 1). ≤
Sample 1
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