License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2019.17
URN: urn:nbn:de:0030-drops-118038
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Winkler, Kyrill ; Schmid, Ulrich ; Moses, Yoram

A Characterization of Consensus Solvability for Closed Message Adversaries

LIPIcs-OPODIS-2019-17.pdf (0.6 MB)


Distributed computations in a synchronous system prone to message loss can be modeled as a game between a (deterministic) distributed algorithm versus an omniscient message adversary. The latter determines, for each round, the directed communication graph that specifies which messages can reach their destination. Message adversary definitions range from oblivious ones, which pick the communication graphs arbitrarily from a given set of candidate graphs, to general message adversaries, which are specified by the set of sequences of communication graphs (called admissible communication patterns) that they may generate. This paper provides a complete characterization of consensus solvability for closed message adversaries, where every inadmissible communication pattern has a finite prefix that makes all (infinite) extensions of this prefix inadmissible. Whereas every oblivious message adversary is closed, there are also closed message adversaries that are not oblivious. We provide a tight non-topological, purely combinatorial characterization theorem, which reduces consensus solvability to a simple condition on prefixes of the communication patterns. Our result not only non-trivially generalizes the known combinatorial characterization of the consensus solvability for oblivious message adversaries by Coulouma, Godard, and Peters (Theor. Comput. Sci., 2015), but also provides the first combinatorial characterization for this important class of message adversaries that is formulated directly on the prefixes of the communication patterns.

BibTeX - Entry

  author =	{Kyrill Winkler and Ulrich Schmid and Yoram Moses},
  title =	{{A Characterization of Consensus Solvability for Closed Message Adversaries}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Pascal Felber and Roy Friedman and Seth Gilbert and Avery Miller},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-118038},
  doi =		{10.4230/LIPIcs.OPODIS.2019.17},
  annote =	{Keywords: Dynamic networks, Consensus, Message Adversary}

Keywords: Dynamic networks, Consensus, Message Adversary
Collection: 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)
Issue Date: 2020
Date of publication: 11.02.2020

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