Byzantine agreement enables n processes to agree on a common L-bit value, despite t > 0 arbitrary failures. A long line of work has been dedicated to improving the worst-case bit complexity of Byzantine agreement in synchrony. This has culminated in COOL, an error-free (deterministically secure against a computationally unbounded adversary) algorithm that achieves a near-optimal bit complexity of O(nL + n^2 log n). COOL satisfies strong validity: if all correct processes propose the same value, only that value can be decided. Thus, whenever correct processes do not a priori agree, COOL might decide on "bottom", thus limiting its application in today's state machine replication (SMR) and blockchain protocols. In this work, we focus on the aforementioned limitation. Can we design an error-free near-optimal Byzantine agreement algorithm applicable in today's SMR and blockchain protocols? Can we design an error-free near-optimal agreement algorithm with external validity (a.k.a. validated agreement) stipulating that only values valid according to a predetermined predicate can be decided? This paper answers the question affirmatively. Namely, we present EXT, an error-free synchronous Byzantine agreement algorithm that satisfies external (along with strong) validity while exchanging O(n log n L + n^2 log n) bits in the worst case. Importantly, EXT is optimally resilient (tolerates t < n / 3 failures) and terminates in optimal O(n) rounds. Perhaps surprisingly, we construct EXT by exploiting existing concepts: (1) the recursive framework proposed by Berman, Garay and Perry and Coan and Welch and recently restated by Momose and Ren, (2) the aforementioned COOL algorithm introduced by Chen, and (3) the data dissemination primitive introduced by Das, Xiang and Ren.

翻译：拜占庭共识使得n个进程能够在存在t > 0个任意故障的情况下，就一个共同的L比特值达成一致。大量工作致力于改进同步拜占庭共识的最坏情况比特复杂度。最终产生了COOL算法，这是一种无错误（确定性安全，能够抵御计算能力无上限的对手）算法，实现了O(nL + n² log n)的近最优比特复杂度。COOL满足强有效性：如果所有正确进程提议相同值，则只能判定该值。因此，当正确进程未预先达成一致时，COOL可能判定为"空值"，从而限制了其在当代状态机复制(SMR)和区块链协议中的应用。本文聚焦上述局限性。能否设计一种适用于当代SMR和区块链协议的无错误近最优拜占庭共识算法？能否设计一种满足外部有效性（即验证共识）的无错误近最优共识算法，规定只有符合预定谓词的有效值才能被判定？本文给出肯定回答。我们提出EXT算法，这是一种满足外部有效性（同时具有强有效性）的无错误同步拜占庭共识算法，其最坏情况比特交换量为O(n log n L + n² log n)。重要的是，EXT具有最优鲁棒性（容忍t < n/3个故障），并在最优O(n)轮内终止。或许令人惊讶的是，我们通过利用现有概念构建EXT：(1) Berman、Garay与Perry、Coan与Welch提出，近期由Momose与Ren重新阐述的递归框架，(2) Chen提出的上述COOL算法，以及(3) Das、Xiang与Ren引入的数据分发原语。