On Decidability of 2-process Affine Models

TL;DR

This paper investigates the computational capabilities of 2-process affine models, establishing that task solvability is decidable and providing a hierarchy of model equivalence classes.

Contribution

It proves that task computability in 2-process affine models is decidable and classifies these models into a complete hierarchy of five equivalence classes.

Findings

Task solvability in 2-process affine models is decidable.

A hierarchy of five equivalence classes of 2-process affine models is established.

The paper provides a complete classification of these models.

Abstract

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.