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

Yannis Coutouly; Emmanuel Godard

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arXiv · 2304.05486

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

Yannis Coutouly·Emmanuel Godard

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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.

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BibTeX RIS

Yannis Coutouly, Emmanuel Godard. 2023-04-11. A Topology by Geometrization for Sub-Iterated Immediate Snapshot Message Adversaries and Applications to Set-Agreement. https://arxiv.org/abs/2304.05486

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