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CHAPTER 4. QUORUM INTERSECTION REVISED 77 Algorithm 13: Proposer algorithm for Paxos revision A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 state : • Q2: set of quorums for phase two (configured, persistent) v,emax←nil QP,QA←∅ e ← min(E ) E←E\{e} /* Start Phase 1 for epoch e */ send prepare( e) to acceptors while∃Q∈Q2 :QP ∩Q=∅do switch do case promise( e,f,w) received from acceptor a QP ←QP ∩{a} if f ̸= nil ∧ (emax = nil ∨ f > emax) then emax ← f, v ← w case timeout goto line 1 if v=nilthen v←γ /* Start Phase 2 for proposal (e,v) */ send propose( e,v) to acceptors while∀Q∈Q2 :QA ̸⊇Qdo switch do case accept( e) received from acceptor a QA ← QA ∪ {a} case timeout goto line 1 return v From Table 2.3, we learn revising our proof of Lemma 11 is sufficient to prove the safety Paxos revisions A. Recall Lemma 11 from our safety proof for Classic Paxos (§2.6): Lemma 11 (Quorum intersection). If a value v is decided in epoch e then at least one acceptor which accepted proposal (e,v) will be required to promise in any future proposals > e. Lemma 11 proved that at least one acceptor which accepted a decided proposal will be required to promise in any subsequent proposals. This was trivially proven by Classic Paxos’s requirement that a quorum of acceptors participate in each phase of the algorithmPDF Image | Distributed consensus
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