A Topology by Geometrization for Sub-Iterated Immediate Snapshot Message Adversaries and Applications to Set-Agreement

TL;DR

This paper introduces a novel topological framework based on geometric simplicial complexes to analyze general message adversaries in the IIS model, enabling simpler characterization and lower bounds for set-agreement problems.

Contribution

It develops a new topological approach for arbitrary subsets of IIS executions, providing a more straightforward and powerful method for distributed computability analysis.

Findings

Complete characterization of set-agreement solvability under sub-IIS adversaries

Lower bounds established for set-agreement in the generalized adversary model

Simplified topological methods for analyzing distributed computability

Abstract

The Iterated Immediate Snapshot model (IIS) is a central model in the message adversary setting. We consider general message adversaries whose executions are arbitrary subsets of the executions of the IIS message adversary. We present a new topological approach for such general adversaries, based upon geometric simplicial complexes. We are able to define a topology directly on the considered sets of executions, which gives both simpler and more powerful ways of using topology for distributed computability. As application of this new framework, we present a complete characterization and lower bounds for solving set-agreement for general sub-IIS message adversaries.