Consensus using Asynchronous Failure Detectors

TL;DR

This paper clarifies how asynchronous failure detectors enable solving crash-tolerant consensus in asynchronous systems, providing a detailed model and proof that $ ext{Omega}$ is the weakest such detector needed.

Contribution

It offers a detailed, automata-theoretic proof that $ ext{Omega}$ is the weakest asynchronous failure detector for consensus, clarifying the underlying mechanisms.

Findings

Demonstrates the exact role of failure detectors in consensus

Provides a detailed automata-based proof of $ ext{Omega}$'s weakness

Addresses assumptions in previous proofs

Abstract

The FLP result shows that crash-tolerant consensus is impossible to solve in asynchronous systems, and several solutions have been proposed for crash-tolerant consensus under alternative (stronger) models. One popular approach is to augment the asynchronous system with appropriate failure detectors, which provide (potentially unreliable) information about process crashes in the system, to circumvent the FLP impossibility. In this paper, we demonstrate the exact mechanism by which (sufficiently powerful) asynchronous failure detectors enable solving crash-tolerant consensus. Our approach, which borrows arguments from the FLP impossibility proof and the famous result from CHT, which shows that $\Omega$ is a weakest failure detector to solve consensus, also yields a natural proof to $\Omega$ as a weakest asynchronous failure detector to solve consensus. The use of I/O automata theory in our approach enables us to model execution in a more detailed fashion than CHT and also addresses the latent assumptions and assertions in the original result in CHT.