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Brief Announcement: Colorless Tasks and Extension-Based Proofs

Authors Yusong Shi , Weidong Liu

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ACM Subject Classification
  • Theory of computation → Interactive proof systems
  • Theory of computation → Distributed algorithms
  • Theory of computation → Distributed computing models
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Colorless tasks
  • Impossibility proofs
  • Extension-based proof

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Abstract

The concept of extension-based proofs models the idea of a valency argument, which is widely used in distributed computing. Extension-based proofs are limited in power: it has been shown that there is no extension-based proof of the impossibility of a wait-free protocol for (n,k)-set agreement among n > k ≥ 2 processes. There are only a few tasks that have been proven to have no extension-based proof of the impossibility, since the techniques in these works are closely related to the specific task.
We give a necessary and sufficient condition for colorless tasks to have no extension-based proofs of the impossibility of wait-free protocols in the NIIS model. We introduce a general adversarial strategy decoupled from any concrete task specification. In this strategy, some properties of the chromatic subdivision that is widely used in distributed computing are proved.

Cite As Get BibTex

Yusong Shi and Weidong Liu. Brief Announcement: Colorless Tasks and Extension-Based Proofs. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 54:1-54:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.54

Author Details

Yusong Shi
  • Department of Computer Science and Technology, Tsinghua University, Beijing, China
Weidong Liu
  • Department of Computer Science and Technology, Tsinghua University, Beijing, China
  • Zhongguancun Laboratory, Beijing, China

Acknowledgements

We would like to thank Faith Ellen and Shihao Liu for helpful discussions and the anonymous reviewers for their comments.

References

  1. Dan Alistarh, James Aspnes, Faith Ellen, Rati Gelashvili, and Leqi Zhu. Why extension-based proofs fail. Proceedings of the 51’st Annual ACM Symposium on Theory of Computing (STOC), pages 986-996, 2019. URL: https://doi.org/10.1145/3313276.3316407.
  2. Dan Alistarh, James Aspnes, Faith Ellen, Rati Gelashvili, and Leqi Zhu. Why extension-based proofs fail. SIAM Journal on Computing, 52(4):913-944, 2023. URL: https://doi.org/10.1137/20M1375851.
  3. Dan Alistarh, Faith Ellen, and Joel Rybicki. Wait-free approximate agreement on graphs. In Structural Information and Communication Complexity: 28th International Colloquium, SIROCCO 2021, Wrocław, Poland, June 28 – July 1, 2021, Proceedings, pages 87-105, Berlin, Heidelberg, 2021. Springer-Verlag. URL: https://doi.org/10.1007/978-3-030-79527-6_6.
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  12. Yusong Shi and Weidong Liu. Colorless tasks and extension-based proofs, 2023. URL: https://arxiv.org/abs/2303.14769.
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