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

Expected Linear Round Synchronization: The Missing Link for Linear Byzantine SMR