Distributed consensus

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Distributed consensus ( distributed-consensus )

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110 6.2. EPOCH DEPENDENT ALGORITHM Proof of lemma 24. Consider any epoch f where f < e and any one of its phase two quorums Q where Q ∈ Qf2 . Prove that D[Q] ̸= nil. There are two mechanisms by which the revision C quorum intersection requirement with Q may be satisfied. Consider the case that an acceptor has promised in e with the proposal (g, w) for some epoch g where g ≥ f and for some value w. D[Q] will be set to either no or w, depending on whether additional proposals for epochs ≥ f and with different value have been received (Algorithm 20, lines 8-11). Consider the case that an acceptor a ∈ Q has promised in e with the proposal (g, w) for some epoch g and some value w. Consider the case that (g, w) = nil. D[Q] will be set to no (Algorithm 20, lines 4-5). Consider the case that (g, w) ̸= nil. Duetothetotalorderingofepochs,eitherg g or f < g. Consider the case that f = g. From value uniqueness (Lemma 9), we know that only one value can be proposed per epoch thus w = x. Consider the case that f > g. For the quorum in epoch g, D[Q] will only be set to value x if there is no proposal with a higher epoch and different value (Algorithm 20, lines 8-9). This cannot be true since we have assumed that w ̸= x. The same applies to epoch f if f < g.

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