On Decidability of 2-process Affine Models

An affine model of computation is defined as a subset of iterated immediate-snapshot runs, capturing a wide variety of shared-memory systems, such as wait-freedom, t-resilience, k-concurrency, and fair shared-memory adversaries. The question of whether a given task is solvable in a given affine model is, in general, undecidable. In this paper, we focus on affine models defined for a system of two processes. We show that the task computability of 2-process affine models is decidable and presents a complete hierarchy of the five equivalence classes of 2-process affine models

An Asynchronous Computability Theorem for Fair Adversaries

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