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No Symmetric Broadcast Abstraction Characterizes k-Set-Agreement in Message-Passing Systems

Authors Sylvain Gay , Achour Mostéfaoui , Matthieu Perrin

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Author Details

Sylvain Gay
  • École Normale Supérieure, Paris, France
Achour Mostéfaoui
  • LS2N, Nantes Université, France
Matthieu Perrin
  • LS2N, Nantes Université, France

Funding

This work was partially supported by the French ANR project ByBloS (ANR-20-CE25-0002-01) and the CominLabs Labex project PriCLeSS (ANR-10-LABX-07-81).

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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) https://doi.org/10.4230/LIPIcs.OPODIS.2024.21

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Computer systems organization → Dependable and fault-tolerant systems and networks
  • Networks → Network properties
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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