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.CCC.2015.567
URN: urn:nbn:de:0030-drops-50534
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5053/
Kane, Daniel M.
A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting
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 |
|
Collection: |
|
30th Conference on Computational Complexity (CCC 2015) |
|
Issue Date: |
|
2015 |
|
Date of publication: |
|
06.06.2015 |
