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Byzantine state-machine replication (SMR) ensures the consistency ofreplicated state in the presence of malicious replicas and lies at the heart ofthe modern blockchain technology. Byzantine SMR protocols often guaranteesafety under all circumstances and liveness only under synchrony. However,guaranteeing liveness even under this assumption is nontrivial. So far we havelacked systematic ways of incorporating liveness mechanisms into Byzantine SMRprotocols, which often led to subtle bugs. To close this gap, we introduce amodular framework to facilitate the design of provably live and efficientByzantine SMR protocols. Our framework relies on a view abstraction generatedby a special SMR synchronizer primitive to drive the agreement on commandordering. We present a simple formal specification of an SMR synchronizer andits bounded-space implementation under partial synchrony. We also apply ourspecification to prove liveness and analyze the latency of three Byzantine SMRprotocols via a uniform methodology. In particular, one of these results yieldswhat we believe is the first rigorous liveness proof for the algorithmic coreof the seminal PBFT protocol.

Liveness and Latency of Byzantine State-Machine Replication (Extended Version)