An Asynchronous Computability Theorem for Fair Adversaries

Abstract: This paper proposes a simple topological characterization of a large class of fair adversarial 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. Fair adversaries include, but are not restricted to, the models of wait-freedom, t-resilience, and $k$-concurrency. Our results generalize and improve all previously derived topological characterizations of the ability of a model to solve distributed tasks.