More Choices Allow More Faults: Set Consensus Problems in Totally Asynchronous Systems

Abstract

We define k-set consensus problem as an extension of the consensus problem, where each processors decides on a single value such that the set of decided values in any run is of size at most k. We require the agreement condition that all values decided upon are initial values of some processor. We show that the problem has a simple ( k - 1 )-resilient protocol in a totally asynchronous system.