Work on \emph{optimal} protocols for \emph{Eventual Byzantine Agreement} (EBA) -- protocols that, in a precise sense, decide as soon as possible in every run and guarantee that all nonfaulty agents decide on the same value -- has focused on emph{full-information protocols} (FIPs), where agents repeatedly send messages that completely describe their past observations to every other agent. While it can be shown that, without loss of generality, we can take an optimal protocol to be an FIP, full information exchange is impractical to implement for many applications due to the required message size. We separate protocols into two parts, the \emph{information-exchange protocol} and the \emph{action protocol}, so as to be able to examine the effects of more limited information exchange. We then define a notion of optimality with respect to an information-exchange protocol. Roughly speaking, an action protocol $P$ is optimal with respect to an information-exchange protocol $\mathcal{E}$ if, with $P$, agents decide as soon as possible among action protocols that exchange information according to $\mathcal{E}$. We present a knowledge-based EBA program for omission failures all of whose implementations are guaranteed to be correct and are optimal if the information exchange satisfies a certain safety condition. We then construct concrete programs that implement this knowledge-based program in two settings of interest that are shown to satisfy the safety condition. Finally, we show that a small modification of our program results in an FIP that is both optimal and efficiently implementable, settling an open problem posed by Halpern, Moses, and Waarts (SIAM J. Comput., 2001).

翻译：关于《最优最终拜占庭协议》（EBA）的研究——即能在每一次运行中尽可能早地达成决策，且保证所有非故障节点就同一值达成一致的协议——此前主要聚焦于《全信息协议》（FIP），其中各节点反复向其他所有节点发送完整描述其历史观测的消息。虽然理论上可以证明，不失一般性地可将最优协议视为FIP，但对许多应用而言，全信息交换因消息规模过大而难以实际部署。本文将协议拆分为《信息交换协议》与《动作协议》两部分，从而能够考察有限信息交换的影响。进而定义了相对于信息交换协议的最优性概念：粗略而言，动作协议$P$相对于信息交换协议$\mathcal{E}$是最优的，当且仅当在所有按$\mathcal{E}$进行信息交换的动作协议中，采用$P$的节点能尽可能早地达成决策。针对遗漏失败模型，我们提出一个基于知识的EBA程序，其所有实现均保证正确，且在满足特定安全条件的信息交换下达到最优。随后，我们在两个满足该安全条件的重要场景中构建具体的程序，实现了该基于知识的程序。最后，我们对程序进行微小修改，得到一个既最优又可高效实现的FIP，从而解决了由Halpern、Moses和Waarts提出的开放问题（SIAM J. Comput., 2001）。