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
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18291/
Chen, Xi ;
Li, Yuhao ;
Yannakakis, Mihalis
Reducing Tarski to Unique Tarski (In the Black-Box Model)
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.
BibTeX - Entry
@InProceedings{chen_et_al:LIPIcs.CCC.2023.21,
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 = {https://drops.dagstuhl.de/opus/volltexte/2023/18291},
URN = {urn:nbn:de:0030-drops-182919},
doi = {10.4230/LIPIcs.CCC.2023.21},
annote = {Keywords: Tarski fixed point, Query complexity, TFNP}
}
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Keywords: |
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Tarski fixed point, Query complexity, TFNP |
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Collection: |
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38th Computational Complexity Conference (CCC 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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10.07.2023 |
