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.2022.85
URN: urn:nbn:de:0030-drops-156819
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15681/
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Hirahara, Shuichi ; Santhanam, Rahul

Excluding PH Pessiland

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LIPIcs-ITCS-2022-85.pdf (0.8 MB)

Abstract

Heuristica and Pessiland are "worlds" of average-case complexity [Impagliazzo95] that are considered unlikely but that current techniques are unable to rule out. Recently, [Hirahara20] considered a PH (Polynomial Hierarchy) analogue of Heuristica, and showed that to rule it out, it would be sufficient to prove the NP-completeness of the problem GapMINKT^PH of estimating the PH-oracle time-bounded Kolmogorov complexity of a string.
In this work, we analogously define "PH Pessiland" to be a world where PH is hard on average but PH-computable pseudo-random generators do not exist. We unconditionally rule out PH-Pessiland in both non-uniform and uniform settings, by showing that the distributional problem of computing PH-oracle time-bounded Kolmogorov complexity of a string over the uniform distribution is complete for an (error-prone) average-case analogue of PH. Moreover, we show the equivalence between error-prone average-case hardness of PH and the existence of PH-computable pseudorandom generators.

BibTeX - Entry

@InProceedings{hirahara_et_al:LIPIcs.ITCS.2022.85,
  author =	{Hirahara, Shuichi and Santhanam, Rahul},
  title =	{{Excluding PH Pessiland}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{85:1--85:25},
  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/2022/15681},
  URN =		{urn:nbn:de:0030-drops-156819},
  doi =		{10.4230/LIPIcs.ITCS.2022.85},
  annote =	{Keywords: average-case complexity, pseudorandomness, meta-complexity}
}

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

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