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DOI: 10.4230/LIPIcs.OPODIS.2024.21
No Symmetric Broadcast Abstraction Characterizes k-Set-Agreement in Message-Passing Systems

Authors: Sylvain Gay, Achour Mostéfaoui, and Matthieu Perrin

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
This paper explores the relationship between broadcast abstractions and the k-set agreement (k-SA) problem in crash-prone asynchronous distributed systems. It specifically investigates whether any broadcast abstraction is computationally equivalent to k-SA in message-passing systems. A key contribution of the paper is the delineation of the realm of "meaningful" broadcast abstractions, through the introduction of two new symmetry properties: compositionality and content-neutrality, inspired by the principle of network neutrality. Such preciseness in definition is essential for this paper’s scope, as our aim is not to characterize the computing power of a specific broadcast abstraction, but rather to explore the domain of broadcast abstractions as a whole, in search of a broadcast abstraction with certain characteristics. The paper’s main contribution is the proof that no broadcast abstraction, which is both content-neutral and compositional, is computationally equivalent to k-set agreement when 1 < k < n, in the crash-prone asynchronous message-passing model. To the best of our knowledge, this result represents the first instance of showing that a coordination problem cannot be expressed by an equivalent broadcast abstraction. It does not establish the absence of an implementation, but rather the absence of a specification that possesses certain properties.
Cite as

Sylvain Gay, Achour Mostéfaoui, and Matthieu Perrin. No Symmetric Broadcast Abstraction Characterizes k-Set-Agreement in Message-Passing Systems. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gay_et_al:LIPIcs.OPODIS.2024.21,
  author =	{Gay, Sylvain and Most\'{e}faoui, Achour and Perrin, Matthieu},
  title =	{{No Symmetric Broadcast Abstraction Characterizes k-Set-Agreement in Message-Passing Systems}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.21},
  URN =		{urn:nbn:de:0030-drops-225573},
  doi =		{10.4230/LIPIcs.OPODIS.2024.21},
  annote =	{Keywords: Agreement problem, Asynchronous system, Broadcast abstraction, Communication abstraction, Compositionality, Message-passing system, Network neutrality, Process crash, k-Set agreement, Wait-free model, Total order broadcast}
}
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