A Polylogarithmic PRG for Degree $2$ Threshold Functions in the Gaussian Setting

D. Kane
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引用次数: 7

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.
高斯设置下二阶阈值函数的多对数PRG
构造并分析了一种新的基于高斯测度的2次多项式阈值函数伪随机生成器。特别是,我们得到了一个种子长度在维数和期望误差上都是多对数的,比现有结构有了很大的改进。我们的生成器是针对只读一次分支程序的伪随机生成器的适当加权平均值。这个分析需要一些想法,包括一个混合论证和一个结构结果,它允许我们把我们的2度阈值函数当作一个线性多项式和一个近似线性多项式的函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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