文章基本信息

标题：A Polylogarithmic PRG for Degree 2 Threshold Functions in the Gaussian Setting
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作者：Daniel M. Kane
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：33
页码：567-581
DOI：10.4230/LIPIcs.CCC.2015.567
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：polynomial threshold function; pseudorandom generator; Gaussian distribution