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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2018.7
URN: urn:nbn:de:0030-drops-88824
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8882/
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Impagliazzo, Russell ; Kabanets, Valentine ; Volkovich, Ilya

The Power of Natural Properties as Oracles

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Abstract

We study the power of randomized complexity classes that are given oracle access to a natural property of Razborov and Rudich (JCSS, 1997) or its special case, the Minimal Circuit Size Problem (MCSP). We show that in a number of complexity-theoretic results that use the SAT oracle, one can use the MCSP oracle instead. For example, we show that ZPEXP^{MCSP} !subseteq P/poly, which should be contrasted with the previously known circuit lower bound ZPEXP^{NP} !subseteq P/poly. We also show that, assuming the existence of Indistinguishability Obfuscators (IO), SAT and MCSP are equivalent in the sense that one has a ZPP algorithm if and only the other one does. We interpret our results as providing some evidence that MCSP may be NP-hard under randomized polynomial-time reductions.

BibTeX - Entry

@InProceedings{impagliazzo_et_al:LIPIcs:2018:8882,
  author =	{Russell Impagliazzo and Valentine Kabanets and Ilya Volkovich},
  title =	{{The Power of Natural Properties as Oracles}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Rocco A. Servedio},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8882},
  URN =		{urn:nbn:de:0030-drops-88824},
  doi =		{10.4230/LIPIcs.CCC.2018.7},
  annote =	{Keywords: natural properties, Minimal Circuit Size Problem (MCSP), circuit lower bounds, hardness of MCSP, learning algorithms, obfuscation, Indistinguishabilit}
}

Keywords: natural properties, Minimal Circuit Size Problem (MCSP), circuit lower bounds, hardness of MCSP, learning algorithms, obfuscation, Indistinguishabilit
Seminar: 33rd Computational Complexity Conference (CCC 2018)
Issue Date: 2018
Date of publication: 01.06.2018


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