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Tight Conditions for Binary-Output Tasks Under Crashes

Authors Timothé Albouy , Antonio Fernández Anta , Chryssis Georgiou , Nicolas Nicolaou , Junlang Wang

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LIPIcs.OPODIS.2025.5.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed solvability
  • Asynchrony
  • Synchrony
  • Impossibility proofs
  • Binary-output tasks
  • Crash tolerance
  • Disagreement

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Abstract

This paper explores necessary and sufficient system conditions to solve distributed tasks with binary outputs (i.e., tasks with output values in {0,1}). We focus on the distinct output sets of values a task can produce (intentionally disregarding validity and value multiplicity), considering that some processes may output no value. In a distributed system with n processes, of which up to t ≤ n can crash, we provide a complete characterization of the tight conditions on n and t under which every class of tasks with binary outputs is solvable, for both synchronous and asynchronous systems. This output-set approach yields highly general results: it unifies multiple distributed computing problems, such as binary consensus and symmetry breaking, and it produces impossibility proofs that hold for stronger task formulations, including those that consider validity, account for value multiplicity, or move beyond binary outputs.

Cite As Get BibTex

Timothé Albouy, Antonio Fernández Anta, Chryssis Georgiou, Nicolas Nicolaou, and Junlang Wang. Tight Conditions for Binary-Output Tasks Under Crashes. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.OPODIS.2025.5

Author Details

Timothé Albouy
  • IMDEA Software Institute, Madrid, Spain
Antonio Fernández Anta
  • IMDEA Software Institute, Madrid, Spain
  • IMDEA Networks Institute, Madrid, Spain
Chryssis Georgiou
  • University of Cyprus, Nicosia, Cyprus
Nicolas Nicolaou
  • Algolysis Ltd, Nicosia, Cyprus
Junlang Wang
  • IMDEA Networks Institute, Madrid, Spain
  • Universidad Carlos III de Madrid, Spain

Funding

This work has been partially supported by the Spanish Ministry of Science and Innovation under grants SocialProbing (TED2021-131264B-I00) and DRONAC (PID2022-140560OB-I00), the ERDF "A way of making Europe", NextGenerationEU, and the Spanish Government’s "Plan de Recuperación, Transformación y Resiliencia". This work is part of the grant CEX2024-001471-M funded by MICIU/AEI/10.13039/501100011033.

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