The Iterated Immediate Snapshot model (IIS) is a central model in the message adversary setting. We consider general message adversaries whose executions are arbitrary subsets of the executions of the IIS message adversary. We present a new topological approach for such general adversaries, based upon geometric simplicial complexes. We are able to define a topology directly on the considered sets of executions, which gives both simpler and more powerful ways of using topology for distributed computability. As application of this new framework, we present a complete characterization and lower bounds for solving set-agreement for general sub-IIS message adversaries.

翻译：迭代即时快照模型（IIS）是消息对手设置中的核心模型。我们考虑一般的消息对手，其执行过程是IIS消息对手执行过程的任意子集。针对此类一般对手，我们提出了一种基于几何单纯复形的新拓扑方法。我们能够直接在所考虑的执行集上定义拓扑结构，从而为分布式可计算性提供更简单且更强大的拓扑应用方式。作为该新框架的应用，我们给出了解决一般子IIS消息对手下集合共识问题的完整刻画与下界分析。