The combined power of conditions and failure detectors to solve asynchronous set agreement

• Authors: Achour Mostefaoui;Sergio Rajsbaum;Michel Raynal
• Venue: Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
• Year: 2005

An approach to cope with the impossibility of solving agreement problems in asynchronous systems made up of n processes and prone to t process crashes is to use failure detectors. An orthogonal approach that has been used is to consider conditions that restrict the possible inputs to such a problem. This paper considers a system with both failure detectors and conditions. The aim is to identify the failure detector class that abstracts away the synchrony needed to solve k-set agreement for a given condition.Three main contributions are presented. The first is a new class of failure detectors denoted Φty, 0≤ y≤ t. The processes can invoke a primitive queryy(S) with a set of process ids S. Roughly speaking, queryy(S) returns true only when all processes in S have crashed, provided t-y. It is shown that the classic Chandra and Toueg's failure detectors are incomparable to the Φty failure detectors. The second contribution is a generic condition-based protocol for Φty that solves k-set agreement. It can be instantiated with any (t-d)-legal condition C and solves k-set agreement for k=1+max(0,d-y); termination is guaranteed for inputs in C. (A condition is x-legal if and only if it can be used to solve x-fault tolerant asynchronous consensus.) A variant of the protocol that terminates always is described. Finally, a corresponding lower bound is presented showing that there is no Φty-based k-set agreement protocol for (t-d)-legal conditions with k≤ max(0,d-y).