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Reducing Tarski to Unique Tarski (In the Black-Box Model)

Authors Xi Chen, Yuhao Li, Mihalis Yannakakis

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Author Details

Xi Chen
  • Columbia University, New York, NY, USA
Yuhao Li
  • Columbia University, New York, NY, USA
Mihalis Yannakakis
  • Columbia University, New York, NY, USA

Funding

  • Chen, Xi: Supported by NSF grants IIS-1838154, CCF-2106429 and CCF-2107187.
  • Li, Yuhao: Supported by NSF grants CCF-1563155, CCF-1703925, IIS-1838154, CCF-2106429 and CCF-2107187.
  • Yannakakis, Mihalis: Supported by NSF grants CCF-2107187 and CCF-2212233.

Acknowledgements

We would like to thank anonymous CCC reviewers for their helpful comments to improve the presentation of the paper.

Cite As Get BibTex

Xi Chen, Yuhao Li, and Mihalis Yannakakis. Reducing Tarski to Unique Tarski (In the Black-Box Model). In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CCC.2023.21

Abstract

We study the problem of finding a Tarski fixed point over the k-dimensional grid [n]^k. We give a black-box reduction from the Tarski problem to the same problem with an additional promise that the input function has a unique fixed point. It implies that the Tarski problem and the unique Tarski problem have exactly the same query complexity. Our reduction is based on a novel notion of partial-information functions which we use to fool algorithms for the unique Tarski problem as if they were working on a monotone function with a unique fixed point.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Exact and approximate computation of equilibria
Keywords
  • Tarski fixed point
  • Query complexity
  • TFNP

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References

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