Network Abstractions for Characterizing Communication Requirements in Asynchronous Distributed Systems

TL;DR

This paper introduces network abstractions as a new method to characterize communication requirements in asynchronous distributed systems, enabling better understanding of problem solvability and liveness properties.

Contribution

It proposes a novel network abstraction framework that models communication in asynchronous systems and applies it to solve the firing rebels with relay problem with Byzantine processes.

Findings

Network abstractions effectively model communication in asynchronous systems.

Necessary and sufficient conditions for solving the FRR problem are derived.

Framework facilitates reasoning about liveness and causal properties.

Abstract

Whereas distributed computing research has been very successful in exploring the solvability/impossibility border of distributed computing problems like consensus in representative classes of computing models with respect to model parameters like failure bounds, this is not the case for characterizing necessary and sufficient communication requirements. In this paper, we introduce network abstractions as a novel approach for modeling communication requirements in asynchronous distributed systems. A network abstraction of a run is a sequence of directed graphs on the set of processes, where the $i$-th graph specifies some ``potential'' message chains that can be guaranteed to arise in the $i$-th portion of the run. Formally, they are defined via associating message sending times with the end-to-end delays that would arise if the message was indeed sent by the sender's protocol. Network abstractions also allow to reason about future causal cones that might arise in a run, hence also facilitate reasoning about liveness properties, and are inherently compatible with temporal epistemic reasoning frameworks. We demonstrate the utility of our approach by providing necessary and sufficient network abstractions for solving the canonical firing rebels with relay (FRR) problem, and variants thereof, in asynchronous message-passing systems with up to $f$ byzantine processes connected via point-to-point links. FRR is not only a basic primitive in clock synchronization and consensus algorithms, but also integrates several distributed computing problems, namely triggering events, agreement and even stabilizing agreement, in a single problem instance.