A Simple Object that Spans the Whole Consensus Hierarchy

TL;DR

This paper introduces a simple, generic object called a sliding window register that generalizes atomic read/write registers, capturing the entire consensus hierarchy and serving as an educational tool for understanding Herlihy's hierarchy.

Contribution

It presents a natural, simple object that spans the whole consensus hierarchy, providing a clear pedagogical introduction to Herlihy's model.

Findings

The object is a sliding window register of size k.

Its consensus number is exactly k.

It offers a unified view of the consensus hierarchy.

Abstract

This paper presents a simple generalization of the basic atomic read/write register object, whose genericity parameter spans the whole set of integers and is such that its k-parameterized instance has exactly consensus number k. This object, whose definition is pretty natural, is a sliding window register of size k. Its interest lies in its simplicity and its genericity dimension which provides a global view capturing the whole consensus hierarchy. Hence, this short article must be seen as a simple pedagogical introduction to Herlihy's consensus hierarchy.