The unbeatability of a consensus protocol, introduced by Halpern et al. (SIAM J Comput 31:838–865, 2001), is a stronger notion of optimality than the accepted notion of early stopping protocols. Using a novel knowledge-based analysis, this paper derives the first explicit unbeatable consensus protocols in the literature, for the standard synchronous message-passing model with crash failures. These protocols strictly dominate the best kno-wn protocols for uniform and for Nonuniform Consensus, in some cases improving on them by a large margin. The analysis provides a new understanding of the logical structure of consensus, and of the distinction between uniform and nonuniform Consensus. All protocols presented in this paper have very concise descriptions, and are shown to be efficiently implementable.

Halpern 等人介绍的共识协议的无与伦比性。（SIAM J Comput 31:838–865, 2001）是一个比公认的提前停止协议概念更强的最优性概念。使用一种新颖的基于知识的分析，本文推导出了文献中第一个明确的无与伦比的共识协议，用于具有崩溃故障的标准同步消息传递模型。这些协议严格控制了最知名的统一和非统一共识协议，在某些情况下大大改进了它们。该分析提供了对共识的逻辑结构以及统一和非统一共识之间的区别的新理解。本文中提出的所有协议都有非常简洁的描述，并且被证明可以有效地实现。