Partial synchrony based on set timeliness

Abstract

We introduce a new model of partial synchrony for read-write shared memory systems. This model is based on the notion of set timeliness--a natural and straightforward generalization of the seminal concept of timeliness in the partially synchrony model of Dwork, Lynch and Stockmeyer [8].Despite its simplicity, the concept of set timeliness is powerful enough to describe the first partially synchronous system for read/write shared memory that separates consensus and set agreement: we show that this system has enough timeliness for solving set agreement but not enough for solving consensus.Set timeliness also allows us to define a family of partially synchronous systems of n processes, denoted Skn (1 ≤ k ≤ n − 1), which closely matches the family of k-anti-Ω failure detectors that were recently shown to be the weakest failure detectors for the k-set agreement problem: We prove that for 1 ≤ k ≤ n − 1, Skn is synchronous enough to implement k-anti-Ω but not enough to implement (k − 1)-anti-Ω.The results above show that set timeliness can be used to study and compare the partial synchrony requirements of problems that are strictly weaker than consensus.