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An affine model of computation is defined as a subset of iteratedimmediate-snapshot runs, capturing a wide variety of shared-memory systems,such as wait-freedom, t-resilience, k-concurrency, and fair shared-memoryadversaries. The question of whether a given task is solvable in a given affinemodel is, in general, undecidable. In this paper, we focus on affine modelsdefined for a system of two processes. We show that the task computability of2-process affine models is decidable and presents a complete hierarchy of thefive equivalence classes of 2-process affine models.

On Decidability of 2-process Affine Models