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Locally Solvable Tasks and the Limitations of Valency Arguments

Authors Hagit Attiya , Armando Castañeda, Sergio Rajsbaum

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Author Details

Hagit Attiya
  • Computer Science Department, Technion, Haifa, Israel
Armando Castañeda
  • Instituto de Matemáticas, UNAM, Mexico City, Mexico
Sergio Rajsbaum
  • Instituto de Matemáticas, UNAM, Mexico City, Mexico


We thank Ulrich Schmid and the reviewers for helpful comments, and Dan Alistarh, James Aspnes, Faith Ellen, Rati Gelashvili and Leqi Zhu for helpful conversations.

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Hagit Attiya, Armando Castañeda, and Sergio Rajsbaum. Locally Solvable Tasks and the Limitations of Valency Arguments. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 18:1-18:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


An elegant strategy for proving impossibility results in distributed computing was introduced in the celebrated FLP consensus impossibility proof. This strategy is local in nature as at each stage, one configuration of a hypothetical protocol for consensus is considered, together with future valencies of possible extensions. This proof strategy has been used in numerous situations related to consensus, leading one to wonder why it has not been used in impossibility results of two other well-known tasks: set agreement and renaming. This paper provides an explanation of why impossibility proofs of these tasks have been of a global nature. It shows that a protocol can always solve such tasks locally, in the following sense. Given a configuration and all its future valencies, if a single successor configuration is selected, then the protocol can reveal all decisions in this branch of executions, satisfying the task specification. This result is shown for both set agreement and renaming, implying that there are no local impossibility proofs for these tasks.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Computing methodologies → Distributed algorithms
  • Computing methodologies → Concurrent algorithms
  • Theory of computation → Concurrent algorithms
  • Theory of computation → Distributed algorithms
  • Wait-freedom
  • Set agreement
  • Weak symmetry breaking
  • Impossibility proofs


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