A Characterization of Consensus Solvability for Closed Message Adversaries

Authors Kyrill Winkler , Ulrich Schmid , Yoram Moses

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Kyrill Winkler
  • TU Wien, Vienna, Austria
Ulrich Schmid
  • TU Wien, Vienna, Austria
Yoram Moses
  • Technion, Haifa, Israel

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Kyrill Winkler, Ulrich Schmid, and Yoram Moses. A Characterization of Consensus Solvability for Closed Message Adversaries. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Dynamic networks
  • Consensus
  • Message Adversary


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