We present a comprehensive analysis of Round-Delayed Amnesiac Flooding (RDAF), a variant of Amnesiac Flooding that introduces round-based asynchrony through adversarial delays. We establish fundamental properties of RDAF, including termination characteristics for different graph types and decidability results under various adversarial models. Our key contributions include: (1) a formal model of RDAF incorporating round-based asynchrony, (2) a proof that flooding always terminates on acyclic graphs despite adversarial delays, (3) a construction showing non-termination is possible on any cyclic graph, (4) a demonstration that termination is undecidable with arbitrary computable adversaries, and (5) the introduction of Eventually Periodic Adversaries (EPA) under which termination becomes decidable. These results enhance our understanding of flooding in communication-delay settings and provide insights for designing robust distributed protocols.

翻译：本文对轮次延迟遗忘型泛洪传播（RDAF）进行了全面分析，该算法是遗忘型泛洪的一种变体，通过对抗性延迟引入基于轮次的异步性。我们建立了RDAF的基本性质，包括不同图结构下的终止特性以及各类对抗模型下的可判定性结果。核心贡献包括：（1）形式化构建了融合轮次异步性的RDAF模型；（2）证明在无环图上，即使存在对抗性延迟，泛洪过程仍可终止；（3）构造示例表明，任何有环图均可能发生非终止现象；（4）证明在任意可计算对抗者模型下，终止性问题不可判定；（5）提出最终周期对抗者模型（EPA），在该模型下终止性变为可判定。这些成果深化了对通信延迟场景下泛洪行为的理解，为设计鲁棒分布式协议提供了理论依据。