On the weakest information on failures to solve mutual exclusion and consensus in asynchronous crash-prone read/write systems

Abstract

Mutual exclusion and consensus are among the most important coordination problems encountered in asynchronous concurrent systems, whether processes communicate using read/write registers or message passing. Unfortunately, neither can be solved in crash-prone systems, as soon as even a single process may crash. Hence, an important question: which is the weakest information on failures that must be given to the processes so that these problems can be solved whatever the number of crashes. This approach to circumvent impossibility results is known under the name failure detectors.Considering mutual exclusion and consensus in a crash-prone asynchronous system where the processes communicate through read/write registers, this article answers the previous question by presenting two failure detectors. The first, called Quasi-Perfect (QP) allows mutual exclusion to be solved in the presence of any number of process crashes. The second, called Ω⁎, allows consensus to be solved in the general model where not all but an a priori unknown subset of processes participates in consensus. In addition to algorithms solving each of the previous problems with the help of the associated failure detector, the article shows that QP and Ω⁎ provides the weakest information on failures needed to solve mutex exclusion and participant-restricted consensus respectively.