Brief Announcement: Compact Topology of Shared-Memory Adversaries

The paper proposes a simple topological characterization of a large class of adversarial distributed-computing models via affine tasks: sub-complexes of the second iteration of the standard chromatic subdivision. We show that the task computability of a model in the class is precisely captured by iterations of the corresponding affine task. While an adversary is in general defined as a non-compact set of infinite runs, its affine task is just a finite subset of runs of the 2-round iterated immediate snapshot (IIS) model. Our results generalize and improve all previously derived topological characterizations of distributed-computing models.