AI 中文总结
研究混合故障模型下两消息延迟提交的容错，证明n至少为5f+3c+1的紧密界限，还展示更具弹性的提交路径，最多f个 equivocators时保证核心活性，违反则进入同步恢复。
AI 中文摘要
经典部分同步状态机复制，如PBFT，在n至少3f+1时容忍f个拜占庭副本，每个请求用三个通信步骤。近期协议如Minimmit在更强规模假设下实现两消息延迟决策。本文研究混合模型下两消息延迟提交的容错，证明紧密界限并展示更具弹性路径，给出特定参数下的容忍率。
英文摘要
Classical partially synchronous state machine replication, as in PBFT, tolerates f Byzantine replicas among n at least 3f+1 using three communication steps per request. Recent protocols such as Minimmit achieve two-message-delay decisions under stronger size assumptions, notably n at least 5f+1 when any silent replica must be counted as a potential equivocator. Hydrangea and Kudzu treat mixed Byzantine and crash faults, focusing on providing a fast-path under optimistic conditions while maintaining a fall-back commitment path similar to PBFT. In this paper, we also consider a mixed model, but focus on studying the fault tolerance of the 2-message-delay commit. For this, we prove a tight bound of n at least 5f+3c+1. Extending this result, we also show that there exists a more resilient commit path that allows an extra f_abc < n-3f-2c alive-but-corrupt faults at 4-message-delays. Core liveness is claimed in executions with at most f equivocators; if this regime is violated (e.g., AbC-induced forks), the protocol enters synchronous recovery, where only the resilient-path safety guarantee is preserved. As a result, for f=16, c=6, and n=99, we obtain a commit path that tolerates 22% of replicas failing for liveness, 16% equivocating for 1-RTT safety, and 54% equivocating for 2-RTT safety.
