Round-Delayed Amnesiac Flooding

TL;DR

This paper analyzes a variant of flooding protocols called Round-Delayed Amnesiac Flooding, focusing on termination properties under various adversarial delay models in distributed systems.

Contribution

It introduces a formal model of RDAF, proves termination on acyclic graphs, shows non-termination on cyclic graphs, and explores decidability under different adversarial conditions.

Findings

Flooding terminates on acyclic graphs despite delays.

Non-termination can occur on cyclic graphs with delays.

Termination is undecidable with arbitrary adversaries.

Abstract

We present a comprehensive analysis of Round-Delayed Amnesiac Flooding (RDAF), a variant of Amnesiac Flooding that introduces round-based asynchrony through adversarial delays. We establish fundamental properties of RDAF, including termination characteristics for different graph types and decidability results under various adversarial models. Our key contributions include: (1) a formal model of RDAF incorporating round-based asynchrony, (2) a proof that flooding always terminates on acyclic graphs despite adversarial delays, (3) a construction showing non-termination is possible on any cyclic graph, (4) a demonstration that termination is undecidable with arbitrary computable adversaries, and (5) the introduction of Eventually Periodic Adversaries (EPA) under which termination becomes decidable. These results enhance our understanding of flooding in communication-delay settings and provide insights for designing robust distributed protocols.