License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2023.21
URN: urn:nbn:de:0030-drops-182919
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Chen, Xi ; Li, Yuhao ; Yannakakis, Mihalis

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

LIPIcs-CCC-2023-21.pdf (2 MB)


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.

BibTeX - Entry

  author =	{Chen, Xi and Li, Yuhao and Yannakakis, Mihalis},
  title =	{{Reducing Tarski to Unique Tarski (In the Black-Box Model)}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-182919},
  doi =		{10.4230/LIPIcs.CCC.2023.21},
  annote =	{Keywords: Tarski fixed point, Query complexity, TFNP}

Keywords: Tarski fixed point, Query complexity, TFNP
Collection: 38th Computational Complexity Conference (CCC 2023)
Issue Date: 2023
Date of publication: 10.07.2023

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