Brief Announcement: Weak Synchrony Models and Failure Detectors for Message Passing (k-)Set Agreement

Abstract

Motivation. In recent years, the quest for weak system assumptions, which add just enough synchrony resp. failure information to purely asynchronous systems to circumvent impossibility results, has been an active research topic in distributed computing. Most work in this area has been devoted to (1) identifying weak(est) failure detectors (FDs), and (2) identifying synchrony assumptions just strong enough to implement these weak FDs.

Due to the FLP impossibility result [1], the first focus of this research has been the consensus problem. More recently, k-set agreement (termed set agreement for k = n−1) has been identified as a promising target for further exploring the solvability border in asynchronous systems. As for (1), anti- ${\it \Omega}$ [2] was shown to be the weakest FD for set agreement in shared memory systems: Whereas ${\it \Omega}$ (the weakest FD for solving consensus [3]) outputs the id of one correct process infinitely often, anti-${\it \Omega}$ outputs the id of one correct process only finitely often. Subsequently, a generalization called anti-${\it \Omega}_k$ that returns n−k processes has been shown to be the weakest FD for k-set agreement in shared memory system [4,5]. For message passing systems, only the weakest FD for set agreement is known, namely, the “loneliness” failure detector $\cal{L}$ [6]. Concerning (2), a class of shared memory models for implementing anti-${\it \Omega}_k$ was presented in [7].

This research was supported by the Austrian BM:vit’s FIT-IT programme (proj. no. 812205) and by Austrian Science Foundation (FWF) (proj. no. P20529).