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A Hierarchy of Unrestricted Deterministic Objects with Consensus Number 1

Author Warren Zhu

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LIPIcs.OPODIS.2025.4.pdf
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  • 17 pages

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
Keywords
  • Shared Memory
  • Wait-free
  • Set Agreement
  • Consensus Hierarchy

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Abstract

The consensus number of a shared object is the maximum number of processes that can solve consensus in a wait-free manner using copies of the object and registers. In 2016, to prove that an object is not fully characterized by its consensus number, Afek, Ellen and Gafni showed that for all integers n ≥ 2, there exists an infinite sequence of deterministic objects of consensus number n with strictly increasing computational power. In 2018, Daian, Losa, Afek, and Gafni constructed an infinite sequence of deterministic objects of consensus number 1 with strictly decreasing computational power, but the single operation that each of these objects supports is restricted in how it can be used during an execution. As restrictions can have an effect on an object’s consensus number, it was left as an open question whether the same result holds without this restriction.
In this paper, we construct an infinite sequence of unrestricted deterministic objects with strictly decreasing computational power. All objects in this sequence have consensus number 1.

Cite As Get BibTex

Warren Zhu. A Hierarchy of Unrestricted Deterministic Objects with Consensus Number 1. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.OPODIS.2025.4

Author Details

Warren Zhu
  • Department of Computer Science, University of Toronto, Canada

Funding

This work was supported in part by the Natural Science and Engineering Research Council grant RGPIN-2020-04178.

Acknowledgements

I want to thank my advisor Faith Ellen for her many helpful discussions. I also want to thank Sam Toueg and Roei Tell for their feedback and advice.

References

  1. Yehuda Afek, Hagit Attiya, Danny Dolev, Eli Gafni, Michael Merritt, and Nir Shavit. Atomic snapshots of shared memory. J. ACM, 40(4):873-890, September 1993. URL: https://doi.org/10.1145/153724.153741.
  2. Yehuda Afek, Faith Ellen, and Eli Gafni. Deterministic objects: Life beyond consensus. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC '16, pages 97-106, 2016. URL: https://doi.org/10.1145/2933057.2933116.
  3. David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg. On the number of objects with distinct power and the linearizability of set agreement objects. In 31st International Symposium on Distributed Computing (DISC 2017), volume 91 of Leibniz International Proceedings in Informatics (LIPIcs), pages 12:1-12:14, 2017. URL: https://doi.org/10.4230/LIPIcs.DISC.2017.12.
  4. David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg. On the classification of deterministic objects via set agreement power. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC '18, pages 71-80, 2018. URL: https://doi.org/10.1145/3212734.3212775.
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  9. Carole Delporte-Gallet, Hugues Fauconnier, Eli Gafni, and Petr Kuznetsov. Set-Consensus Collections are Decidable. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016), volume 70 of Leibniz International Proceedings in Informatics (LIPIcs), pages 7:1-7:15, 2017. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2016.7.
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