An Algorithmic Approach to the Asynchronous Computability Theorem

The asynchronous computability theorem (ACT) uses concepts from combinatorial topology to characterize which tasks have wait-free solutions in read-write memory. A task can be expressed as a relation between two chromatic simplicial complexes. The theorem states that a task has a protocol (algorithm) if and only if there is a certain chromatic simplicial map compatible with that relation. While the original proof of the ACT relied on an involved combinatorial argument, Borowsky and Gafni later proposed an alternative proof that relied on a algorithmic construction, termed the "convergence algorithm". The description of this algorithm was incomplete, and presented without proof. In this paper, we give the first complete description, along with a proof of correctness.Comment: 16 pages, 2 figure

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