Tight Bounds on Channel Reliability via Generalized Quorum Systems (Extended Version)

TL;DR

This paper introduces generalized quorum systems that enable atomic register implementations under arbitrary process-channel failure patterns, relaxing classical connectivity constraints and proposing new logical clocks for reliable state tracking.

Contribution

It extends the theory of quorum systems to include channel failures, providing necessary and sufficient conditions for fault-tolerant distributed objects with weak connectivity.

Findings

Characterizes conditions for atomic objects under channel failures

Introduces logical clocks for unidirectional quorum communication

Establishes bounds on channel reliability for fault tolerance

Abstract

Communication channel failures are a major concern for the developers of modern fault-tolerant systems. However, while tight bounds for process failures are well-established, extending them to include channel failures has remained an open problem. We introduce \emph{generalized quorum systems} - a framework that characterizes the necessary and sufficient conditions for implementing atomic registers, atomic snapshots, lattice agreement and consensus under arbitrary patterns of process-channel failures. Generalized quorum systems relax the connectivity constraints of classical quorum systems: instead of requiring bidirectional reachability for every pair of write and read quorums, they only require some write quorum to be \emph{unidirectionally} reachable from some read quorum. This weak connectivity makes implementing registers particularly challenging, because it precludes the traditional request/response pattern of quorum access, making classical solutions like ABD inapplicable. To address this, we introduce novel logical clocks that allow write and read quorums to reliably track state updates without relying on bi-directional connectivity.