部分同步模型中状态机复制的二次最坏情况消息复杂度
Quadratic worst-case message complexity for State Machine Replication in the partial synchrony model
摘要：
我们考虑的消息复杂性的状态机复制协议处理拜占庭故障的部分同步模型。Dolev和Reischuk的结果给出了消息复杂度的二次下界，但不知道这个下界是否紧，已知最有效的协议给出了最坏情况的消息复杂度$O(n^3)$。我们描述了一个协议，满足Dolev和Reischuk的二次下界，同时也满足其他理想的属性。要指定这些属性，假设我们有$n$副本，其$f$显示拜占庭故障（使用$n\geq 3f+1$）。假设$Δ$是消息延迟的上限，即如果消息在时间$t$发送，则它在时间$ \text{max} \{ t, GST \} +Δ$接收。我们描述了一个确定性的协议，同时实现$O(n^2)$最坏情况下的消息复杂性，乐观的响应性，$O(fΔ)$的时间，以第一次确认后，$GST$和$O(n)$平均消息复杂性。
英文摘要：
We consider the message complexity of State Machine Replication protocols dealing with Byzantine failures in the partial synchrony model. A result of Dolev and Reischuk gives a quadratic lower bound for the message complexity, but it was unknown whether this lower bound is tight, with the most efficient known protocols giving worst-case message complexity $O(n^3)$. We describe a protocol which meets Dolev and Reischuk's quadratic lower bound, while also satisfying other desirable properties. To specify these properties, suppose that we have $n$ replicas, $f$ of which display Byzantine faults (with $n\geq 3f+1$). Suppose that $Δ$ is an upper bound on message delay, i.e. if a message is sent at time $t$, then it is received by time $ \text{max} \{ t, GST \} +Δ$. We describe a deterministic protocol that simultaneously achieves $O(n^2)$ worst-case message complexity, optimistic responsiveness, $O(fΔ)$ time to first confirmation after $GST$ and $O(n)$ mean message complexity.
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