From Unreliable Objects to Reliable Objects: The Case of Atomic Registers and Consensus

Abstract

A concurrent object is an object that can be concurrently accessed by several processes. It has been shown by Maurice Herlihy that any concurrent object O defined by a sequential specification can be wait-free implemented from reliable atomic registers (shared variables) and consensus objects. Wait-free means that any invocation of an operation of the object O issued by a non-faulty process does terminate, whatever the behavior of the other processes (e.g., despite the fact they are very slow or even have crashed).

So, an important issue consists in providing reliable atomic registers and reliable consensus objects despite the failures experienced by the base objects from which these atomic registers and consensus objects are built. This paper considers self-implementations, i.e., the case where a reliable atomic register (resp., consensus object) is built from unreliable atomic registers (resp., unreliable consensus objects). The paper addresses the object failure model where the base objects can suffer responsive or nonresponsive crash failures. When there are solutions the paper presents corresponding algorithms, and when there is no solution, it presents the corresponding impossibility result. The paper has a tutorial flavor whose aim is to make the reader familiar with important results when one has to build resilient concurrent objects. To that aim, the paper use both algorithms from the literature and new algorithms.