Eventual Wait-Free Synchronization

TL;DR

This paper establishes a theoretical framework for eventually linearizable objects in shared memory, introducing the concept of eventual consensus number to classify their synchronization power and creating a hierarchy analogous to the consensus hierarchy.

Contribution

It introduces the notion of eventual consensus number and proves the universality of the n-process eventually linearizable fetch-and-cons object, advancing the theoretical understanding of eventual linearizability.

Findings

n-process eventually linearizable fetch-and-cons is universal

Defined the concept of eventual consensus number

Established a hierarchy of eventually linearizable objects

Abstract

Eventually linearizable objects are novel shared memory programming constructs introduced as an analogy to eventual consistency in message-passing systems. However, their behaviors in shared memory systems are so mysterious that very little general theoretical properties of them is known. In this paper, we lay the theoretical foundation of the study of eventually linearizable objects. We prove that the n-process eventually linearizable fetch-and-cons (n-FAC) object is universal and can be used to classify the eventually linearizable objects. In particular, we define the concept of eventual consensus number of an abstract data type and prove that the eventual consensus number can be used as a good characterization of the synchronization power of eventual objects. Thus we got a complete hierarchy of eventually linearizable objects, as a perfect analogy of the consensus hierarchy. In this way, the synchronization power of eventual linearizability become much more well understood.