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URN: urn:nbn:de:0030-drops-50534
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A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting

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Abstract

We construct and analyze a new pseudorandom generator for degree 2 polynomial threshold functions with respect to the Gaussian measure. In particular, we obtain one whose seed length is polylogarithmic in both the dimension and the desired error, a substantial improvement over existing constructions. Our generator is obtained as an appropriate weighted average of pseudorandom generators against read once branching programs. The analysis requires a number of ideas including a hybrid argument and a structural result that allows us to treat our degree 2 threshold function as a function of a number of linear polynomials and one approximately linear polynomial.

BibTeX - Entry

@InProceedings{kane:LIPIcs:2015:5053,
  author =	{Daniel M. Kane},
  title =	{{A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{567--581},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{David Zuckerman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5053},
  URN =		{urn:nbn:de:0030-drops-50534},
  doi =		{10.4230/LIPIcs.CCC.2015.567},
  annote =	{Keywords: polynomial threshold function, pseudorandom generator, Gaussian distribution}
}

Keywords: polynomial threshold function, pseudorandom generator, Gaussian distribution
Seminar: 30th Conference on Computational Complexity (CCC 2015)
Issue date: 2015
Date of publication: 2015


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