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共识等分布式计算问题在代表性计算模型类中关于故障界限等模型参数的可解性/不可解性边界方面非常成功，但在刻画必要且充分的通信需求方面却未达到同等水平。本文提出网络抽象这一新颖方法，用于对异步分布式系统中的通信需求进行建模。运行轨迹的网络抽象是进程集合上的一组有向图序列，其中第i个有向图定义了该运行轨迹第i部分中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消息接收时间相关联来定义。网络抽象能够对运行轨迹中可能出现的未来因果锥进行推理，因此也有助于对活性性质进行推理，并且天然兼容时态认知推理框架。我们通过为异步系统中最多存在f个拜占庭进程的情况下，解决经典的"叛乱者中继触发"（FRR）问题及其变体提供必要且充分的网络抽象，展示了该方法的有用性。FRR不仅是时钟同步和共识算法中的基本原语，更在单个问题实例中整合了触发事件、共识乃至稳定共识等多个分布式计算问题。