State Machine Replication (SMR) solutions often divide time into rounds, with a designated leader driving decisions in each round. Progress is guaranteed once all correct processes synchronize to the same round, and the leader of that round is correct. Recently suggested Byzantine SMR solutions such as HotStuff, and LibraBFT achieve progress with a linear message complexity and a constant time complexity once such round synchronization occurs. But round synchronization itself incurs an additional cost. By Dolev and Reischuk’s lower bound, any deterministic solution must have \(\Omega (n^2)\) communication complexity. Yet the question of randomized round synchronization with an expected linear message complexity remained open. We present an algorithm that, for the first time, achieves round synchronization with expected linear message complexity and expected constant latency. Existing protocols can use our round synchronization algorithm to solve Byzantine SMR with the same asymptotic performance.

状态机复制 (SMR) 解决方案通常将时间分为几轮，由指定的领导者在每轮中推动决策。一旦所有正确的进程同步到同一轮，并且该轮的领导者是正确的，进度就得到保证。最近提出的拜占庭 SMR 解决方案（例如 HotStuff 和 LibraBFT）一旦发生这种轮同步，就可以在线性消息复杂度和恒定时间复杂度上取得进展。但轮同步本身会产生额外的成本。根据 Dolev 和 Reischuk 的下限，任何确定性解决方案都必须具有\(\Omega (n^2)\)通信复杂性。然而，随机轮同步与预期线性消息复杂性的问题仍然悬而未决。我们提出了一种算法，首次实现了具有预期线性消息复杂性和预期恒定延迟的轮同步。现有协议可以使用我们的轮同步算法来解决具有相同渐近性能的拜占庭SMR。