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A General Class of Reductions and Extension-Based Proofs

Authors Yusong Shi , Weidong Liu

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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

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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 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

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