Null Messages, Information and Coordination

TL;DR

This paper explores the role of null messages in synchronous systems, establishing conditions for information transfer and coordination, especially under crash failures, through new concepts like resilient message blocks.

Contribution

It introduces a refined definition of null messages, generalizes message chains, and defines resilient message blocks necessary for information transfer in crash-prone systems.

Findings

Null messages are crucial for information transfer in reliable systems.

Resilient message blocks are necessary for crash-prone systems.

A combination of resilient message blocks solves the Ordered Response problem.

Abstract

This paper investigates the role that null messages play in synchronous systems with and without failures, and provides necessary and sufficient conditions on the structure of protocols for information transfer and coordination there. We start by introducing a new and more refined definition of null messages. A generalization of message chains that allow these null messages is provided, and is shown to be necessary and sufficient for information transfer in reliable systems. Coping with crash failures requires a much richer structure, since not receiving a message may be the result of the sender's failure. We introduce a class of communication patterns called {\em resilient message blocks}, which impose a stricter condition on protocols than the {\em silent choirs} of Goren and Moses (2020). Such blocks are shown to be necessary for information transfer in crash-prone systems. Moreover, they are sufficient in several cases of interest, in which silent choirs are not. Finally, a particular combination of resilient message blocks is shown to be necessary and sufficient for solving the Ordered Response coordination problem.