Document Open Access Logo

A General Class of Reductions and Extension-Based Proofs

Authors Yusong Shi , Weidong Liu

PDF

File

Thumbnail PDF
PDF
LIPIcs.OPODIS.2024.19.pdf
  • Filesize: 0.91 MB
  • 17 pages

Document Identifiers

Subject Classification

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
  • Reductions
  • Impossibility proofs
  • Extension-based proof

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

The concept of extension-based proofs models the idea of a valency argument which is widely used in distributed computing. Extension-based proofs have been shown to be limited in power: there is no extension-based proof of the impossibility of a wait-free protocol for (n,k)-set agreement among n > k ≥ 2 processes. 
Previous work used a restricted class of reductions to show that there are no extension-based proofs of the impossibility of wait-free protocols for some other distributed computing problems. It is known that for a restricted class of reductions, if a task 𝒯 reduces to 𝒮 and 𝒯 has an augmented extension-based proof that it is impossible to solve in the NIS model, then so does 𝒮. We introduce multiple-instance extension-based proofs and show that, if 𝒯 reduces to multiple instances of 𝒮, instead of just one instance and 𝒯 has an augmented extension-based proof, then 𝒮 has a multiple-instance extension-based proof that it is impossible to solve in the NIIS model. We introduce a new version of extension-based proofs that can further our understanding of extension-based proofs and their limitations.

Cite As Get BibTex

Yusong Shi and Weidong Liu. A General Class of Reductions and Extension-Based Proofs. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.19

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. 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. 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.
  3. 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.
  4. 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.
  5. Hagit Attiya, Armando Castañeda, and Sergio Rajsbaum. Locally solvable tasks and the limitations of valency arguments. Journal of Parallel and Distributed Computing, 176:28-40, 2023. URL: https://doi.org/10.1016/j.jpdc.2023.02.002.
  6. Hagit Attiya, Pierre Fraigniaud, Ami Paz, and Sergio Rajsbaum. One Step Forward, One Step Back: FLP-Style Proofs and the Round-Reduction Technique for Colorless Tasks. In Rotem Oshman, editor, 37th International Symposium on Distributed Computing (DISC 2023), volume 281 of Leibniz International Proceedings in Informatics (LIPIcs), pages 4:1-4:23, Dagstuhl, Germany, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.DISC.2023.4.
  7. Elizabeth Borowsky and Eli Gafni. Generalized flp impossibility result for t-resilient asynchronous computations. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, STOC '93, pages 91-100, New York, NY, USA, 1993. Association for Computing Machinery. URL: https://doi.org/10.1145/167088.167119.
  8. Elizabeth Borowsky and Eli Gafni. Immediate atomic snapshots and fast renaming. In Proceedings of the Twelfth Annual ACM Symposium on Principles of Distributed Computing, PODC '93, pages 41-51, New York, NY, USA, 1993. Association for Computing Machinery. URL: https://doi.org/10.1145/164051.164056.
  9. Elizabeth Borowsky and Eli Gafni. A simple algorithmically reasoned characterization of wait-free computation (extended abstract). In Proceedings of the Sixteenth Annual ACM Symposium on Principles of Distributed Computing, PODC '97, pages 189-198, New York, NY, USA, 1997. Association for Computing Machinery. URL: https://doi.org/10.1145/259380.259439.
  10. Kayman Brusse and Faith Ellen. Reductions and extension-based proofs. In Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing, PODC'21, pages 497-507, New York, NY, USA, 2021. Association for Computing Machinery. URL: https://doi.org/10.1145/3465084.3467906.
  11. Soma Chaudhuri. More choices allow more faults: Set consensus problems in totally asynchronous systems. Inf. Comput., 105(1):132-158, July 1993. URL: https://doi.org/10.1006/inco.1993.1043.
  12. Michael J. Fischer, Nancy A. Lynch, and Michael S. Paterson. Impossibility of distributed consensus with one faulty process. J. ACM, 32(2):374-382, April 1985. URL: https://doi.org/10.1145/3149.214121.
  13. Eli Gafni, Sergio Rajsbaum, and Maurice Herlihy. Subconsensus tasks: Renaming is weaker than set agreement. In Proceedings of the 20th International Conference on Distributed Computing, DISC'06, pages 329-338, Berlin, Heidelberg, 2006. Springer-Verlag. URL: https://doi.org/10.1007/11864219_23.
  14. Maurice Herlihy and Nir Shavit. The topological structure of asynchronous computability. J. ACM, 46(6):858-923, November 1999. URL: https://doi.org/10.1145/331524.331529.
  15. Gunnar Hoest and Nir Shavit. Towards a topological characterization of asynchronous complexity. In Proceedings of the Sixteenth Annual ACM Symposium on Principles of Distributed Computing, PODC '97, pages 199-208, New York, NY, USA, 1997. Association for Computing Machinery. URL: https://doi.org/10.1145/259380.259440.
  16. Shihao Liu. The Impossibility of Approximate Agreement on a Larger Class of Graphs. In Eshcar Hillel, Roberto Palmieri, and Etienne Rivière, editors, 26th International Conference on Principles of Distributed Systems (OPODIS 2022), volume 253 of Leibniz International Proceedings in Informatics (LIPIcs), pages 22:1-22:20, Dagstuhl, Germany, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2022.22.
  17. Michael Saks and Fotios Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. Comput., 29(5):1449-1483, March 2000. URL: https://doi.org/10.1137/S0097539796307698.
  18. Yusong Shi and Weidong Liu. Colorless tasks and extension-based proofs, 2024. URL: https://arxiv.org/abs/2303.14769.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact