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126 7.3. EPOCHS BY RECOVERY From equation 7.2, we know that ∃a ∈ A : R[a] ̸= no∧a ∈ Q∧a ∈ Q′. Combining this with the above result, we learn that ∃a ∈ A : R[a] = ( ,v) ∧ R[a] = ( ,v′). This requires that v = v′ thus we have a contradiction. 7.3.5 Examples We will now examine three examples of epochs by recovery using three different classes of quorums systems. Example: All aboard Paxos with epochs by recovery Algorithm 27: Proposer algorithm with epochs by recovery and a fixed quorum. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 state : • Q: fixed phase two quorum QA ← ∅ ife=nilthen e←0 else e←e+1 /* Start of Phase 1 for proposal e */ send prepare( e) to acceptors switch do case promise( e, ,w) received from acceptor a ∈ Q if w ̸= nil then v←w else v←γ case timeout goto line 1 /* Start Phase 2 for proposal (e,v) */ send propose( e,v) to acceptors while QA ̸⊇ Q do switch do case accept( e ,v) received from acceptor a QA ← QA ∪ {a} case timeout goto line 1 return vPDF Image | Distributed consensus
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