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122 7.3. EPOCHS BY RECOVERY Algorithm 26: Algorithm for possibleValues with epochs by recovery (Revision A). 1 2 3 4 5 6 7 8 9 10 11 12 13 func possibleValues(R): foreach Q ∈ Q2 do if ∃a∈Q:R[a]=nil then /* if acceptor in quorum returns nil then no decision */ D[Q] ← no elseif∃a∈Q,∃f,g∈E,∃w,x∈V: R[a]=(f,w)∧R[]=(g,x)∧g>f∧x̸=wthen /* if two acceptors return proposals with different values then no decision for quorums containing the acceptor with the lower proposal */ D[Q] ← no else if ∃a,b∈Q:∃f ∈E,∃w,x∈V : R[a]=(f,w)∧R[b]=(f,x)∧w̸=x)then /* if two acceptors in the same quorum return proposals with same number but different values then no decision */ D[Q] ← no else /* all proposals returned by quorum are for the same value thus this value maybe decided */ D[Q] ← only({w ∈ V |∃a ∈ Q : R[a] = ( , w)}) return{w∈V|∃Q∈Q2 :D[Q]=w} set D for quorum Q to no if two acceptors within the quorum have returned promises with the same epoch but different values (line 7-8, Algorithm 26). Thirdly, after satisfying the usual quorum intersection requirement, if there are multiple possibly decided values then the proposer must wait for additional promises to rule out values until only one or zero values remain. This is implemented by adding the condition on the cardinality of Vdec (line 10, Algorithm 25). 7.3.3 Safety We will prove the safety of Paxos revisions A with epochs allocated by recovery using the usual method. Our usual properties still hold, except from properties 1 & 4, restated below: Property 1. Proposers use unique epochs for each proposal.PDF Image | Distributed consensus
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