Whereas distributed computing research has been very successful in exploring the solvability/impossibility border of distributed computing problems like consensus in representative classes of computing models with respect to model parameters like failure bounds, this is not the case for characterizing necessary and sufficient communication requirements. In this paper, we introduce network abstractions as a novel approach for modeling communication requirements in asynchronous distributed systems. A network abstraction of a run is a sequence of directed graphs on the set of processes, where the $i$-th graph defines the potential message chains that may arise in the $i$-th portion of the run. Formally, it is defined via associating (potential) message sending times with the corresponding message receiving times in a message schedule. Network abstractions allow to reason about the future causal cones that might arise in a run, hence also facilitate reasoning about liveness properties, and are inherently compatible with temporal epistemic reasoning frameworks. We demonstrate the utility of our approach by providing necessary and sufficient network abstractions for solving the canonical firing rebels with relay (FRR) problem, and variants thereof, in asynchronous systems with up to $f$ byzantine processes. FRR is not only a basic primitive in clock synchronization and consensus algorithms, but also integrates several distributed computing problems, namely triggering events, agreement and even stabilizing agreement, in a single problem instance.

翻译：尽管分布式计算研究在探索代表性计算模型类中（如共识问题）的可解性/不可解性边界方面取得了巨大成功，但针对必要且充分的通信需求表征仍存在不足。本文提出网络抽象这一新颖方法，用于建模异步分布式系统中的通信需求。运行的网络抽象是进程集合上的有向图序列，其中第i个图定义了运行第i部分可能出现的潜在消息链。形式上，它通过将消息调度中的（潜在）消息发送时间与对应接收时间相关联来定义。网络抽象能够推演运行中可能出现的未来因果锥，从而促进活性属性的推理，并天然兼容时间认知推理框架。我们通过为典型的中继触发反叛（FRR）问题及其变体提供必要且充分的网络抽象，验证了该方法的实用性——该问题在最多包含f个拜占庭进程的异步系统中求解。FRR不仅是时钟同步与共识算法的基本原语，更在一个问题实例中融合了触发事件、共识乃至稳定性共识等多个分布式计算问题。