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.ITCS.2022.84
URN: urn:nbn:de:0030-drops-156803
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15680/
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Hirahara, Shuichi ; Santhanam, Rahul

Errorless Versus Error-Prone Average-Case Complexity

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LIPIcs-ITCS-2022-84.pdf (0.8 MB)

Abstract

We consider the question of whether errorless and error-prone notions of average-case hardness are equivalent, and make several contributions.
First, we study this question in the context of hardness for NP, and connect it to the long-standing open question of whether there are instance checkers for NP. We show that there is an efficient non-uniform non-adaptive reduction from errorless to error-prone heuristics for NP if and only if there is an efficient non-uniform average-case non-adaptive instance-checker for NP. We also suggest an approach to proving equivalence of the two notions of average-case hardness for PH.
Second, we show unconditionally that error-prone average-case hardness is equivalent to errorless average-case hardness for P against NC¹ and for UP ∩ coUP against P.
Third, we apply our results about errorless and error-prone average-case hardness to get new equivalences between hitting set generators and pseudo-random generators.

BibTeX - Entry

@InProceedings{hirahara_et_al:LIPIcs.ITCS.2022.84,
  author =	{Hirahara, Shuichi and Santhanam, Rahul},
  title =	{{Errorless Versus Error-Prone Average-Case Complexity}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{84:1--84:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15680},
  URN =		{urn:nbn:de:0030-drops-156803},
  doi =		{10.4230/LIPIcs.ITCS.2022.84},
  annote =	{Keywords: average-case complexity, instance checker, pseudorandomness}
}

Keywords: average-case complexity, instance checker, pseudorandomness
Collection: 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Issue Date: 2022
Date of publication: 25.01.2022

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