License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2018.29
URN: urn:nbn:de:0030-drops-83300
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8330/
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Hatami, Pooya ; Tal, Avishay

Pseudorandom Generators for Low Sensitivity Functions

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LIPIcs-ITCS-2018-29.pdf (0.5 MB)

Abstract

A Boolean function is said to have maximal sensitivity s if s is the largest number of Hamming neighbors of a point which differ from it in function value. We initiate the study of pseudorandom generators fooling low-sensitivity functions as an intermediate step towards settling the sensitivity conjecture. We construct a pseudorandom generator with seed-length 2^{O(s^{1/2})} log(n) that fools Boolean functions on n variables with maximal sensitivity at most s. Prior to our work, the (implicitly) best pseudorandom generators for this class of functions required seed-length 2^{O(s)} log(n).

BibTeX - Entry

@InProceedings{hatami_et_al:LIPIcs:2018:8330,
  author =	{Pooya Hatami and Avishay Tal},
  title =	{{Pseudorandom Generators for Low Sensitivity Functions}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{29:1--29:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Anna R. Karlin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8330},
  URN =		{urn:nbn:de:0030-drops-83300},
  doi =		{10.4230/LIPIcs.ITCS.2018.29},
  annote =	{Keywords: Pseudorandom Generators, Sensitivity, Sensitivity Conjecture}
}

Keywords: Pseudorandom Generators, Sensitivity, Sensitivity Conjecture
Collection: 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Issue Date: 2018
Date of publication: 12.01.2018

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