Consensus is one of the most fundamental problems in distributed computing. This paper studies the consensus problem in a synchronous dynamic directed network, in which communication is controlled by an oblivious message adversary. The question when consensus is possible in this model has already been studied thoroughly in the literature from a combinatorial perspective, and is known to be challenging. This paper presents a topological perspective on consensus solvability under oblivious message adversaries, which provides interesting new insights. Our main contribution is a topological characterization of consensus solvability, which also leads to explicit decision procedures. Our approach is based on the novel notion of a communication pseudosphere, which can be seen as the message-passing analog of the well-known standard chromatic subdivision for wait-free shared memory systems. We further push the elegance and expressiveness of the "geometric" reasoning enabled by the topological approach by dealing with uninterpreted complexes, which considerably reduce the size of the protocol complex, and by labeling facets with information flow arrows, which give an intuitive meaning to the implicit epistemic status of the faces in a protocol complex.

翻译：共识是分布式计算中最基本的问题之一。本文研究同步有向动态网络中的共识问题，在该网络中通信由一种遗忘性消息敌手控制。从组合学视角出发，文献已对这一模型下共识何时可解进行了深入研究，并公认该问题颇具挑战性。本文从拓扑学视角诠释遗忘性消息敌手下的共识可解性，提供了新颖的见解。我们的主要贡献在于对共识可解性给出了一种拓扑刻画，该刻画亦能导出显式的判定程序。我们的方法基于"通信伪球"这一新概念，可视为著名的等待无关共享内存系统标准着色细分在消息传递场景下的类比。通过处理未解释复合体（显著缩小协议复合体的规模）以及用信息流箭头标记面（为协议复合体中各面隐含的认知状态赋予直观意义），我们进一步彰显了拓扑方法所赋予的"几何"推理的优雅性与表现力。