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

Authors: Yannis Coutouly and Emmanuel Godard

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)


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 complete and explicit characterization and lower bounds for solving set-agreement for general sub-IIS message adversaries. In order to have this characterization, we introduce a new topological approach for such general adversaries, closely associating executions to geometric simplicial complexes. This way, it is possible to define and explicitly construct a topology directly on the considered sets of executions. We believe this topology by geometrization to be of independent interest and a good candidate to investigate distributed computability in general sub-IIS message adversaries, as this could provide both simpler and more powerful ways of using topology for distributed computability.

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Yannis Coutouly and Emmanuel Godard. A Topology by Geometrization for Sub-Iterated Immediate Snapshot Message Adversaries and Applications to Set-Agreement. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 15:1-15:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{coutouly_et_al:LIPIcs.DISC.2023.15,
  author =	{Coutouly, Yannis and Godard, Emmanuel},
  title =	{{A Topology by Geometrization for Sub-Iterated Immediate Snapshot Message Adversaries and Applications to Set-Agreement}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.15},
  URN =		{urn:nbn:de:0030-drops-191417},
  doi =		{10.4230/LIPIcs.DISC.2023.15},
  annote =	{Keywords: topological methods, geometric simplicial complex, set-agreement}
}
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