Beyond Canonical Rounds: Communication Abstractions for Optimal Byzantine Resilience

We study communication abstractions for asynchronous Byzantine fault tolerance with optimal failure resilience, where n > 3f. Two classic patterns -- canonical asynchronous rounds and communication-closed layers -- have long been considered as general frameworks for designing distributed algorithms, making asynchronous executions appear synchronous and enabling modular reasoning. We show that these patterns are inherently limited in the critical resilience regime 3f 3f), and supports modular reductions. Specifically, we present the first optimally-resilient algorithm for connected consensus by reducing it to gather. Our results demonstrate that while round-based abstractions are analytically convenient, they obscure the true complexity of Byzantine fault-tolerant algorithms. Richer communication patterns such as gather provide a better foundation for modular, optimal-resilience design.