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84 4.2. QUORUM INTERSECTION ACROSS EPOCHS p1 a1 a2 a3 p2 e : 0, E : {2, . . . } propose(0,A) accept(0) QA : {a1} accept(0) QA :{a1,a2} epro:0 eacc :0 vacc :A epro:0 eacc :0 vacc :A epro:1 eacc :1 o:1 epro:1 eacc :1 epro:0 eacc :0 vacc :A epr eacc :1 (0, A) decided e : 1, E : {3, . . . } prepare(1) promise(1,0,A) QP : {a3}, emax:0 v:A promise(1,0,A) QP :{a2,a3} propose(1,A) accept(1) QA : {a3} accept(1) QA :{a2,a3} (1, A) decided Figure 4.3: Example of a proposer successfully skipping phase one using the minimum epoch. its phase one. This proposer may then propose a value, different to the decided value during its phase two. This situation does not cause a violation in safety since the proposer’s phase two will be unsuccessful since the phase two quorum will intersect with the phase one of the higher epoch. An example of this case is shown in Figure 4.4. Figure 4.4 shows the same execution as Figure 2.3, however now the proposer p1 skips over the first phase one. More generally, the implication of this result is that phase one quorums are required only to intersect with the phase two quorums of previous epochs, instead of all phase two quorums. One application of this result is that if we vary phase two quorums with epochsPDF Image | Distributed consensus
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