Let x be a random vector coming from any k-wise independent distribution over {-1, 1}^ n.
For an n-variate degree-2 polynomial p, we prove that E [sgn (p (x))] is determined up to an …

For an n-variate degree-2 real polynomial p, we prove that E x~ D [sig (p (x))] Is determined
up to an additive ε as long as D is a k-wise Independent distribution over {-1, 1} n for k= poly …

We develop a pseudo-random generator to fool degree-$ d $ polynomial threshold functions
with respect to the Gaussian distribution. For $ c> 0$ any constant, we construct a pseudo …

We devise a new pseudorandom generator against degree 2 polynomial threshold functions
in the Gaussian setting. We manage to achieve $\epsilon $ error with seed length …

We show that any distribution on {-1,+1\}^n that is k-wise independent fools any halfspace
(or linear threshold function) h:{-1,+1\}^n→{-1,+1\}, ie, any function of the form …

arXiv:1012.1614v3 [cs.CC] 11 Nov 2011 Page 1 arXiv:1012.1614v3 [cs.CC] 11 Nov 2011 k-Independent
Gaussians Fool Polynomial Threshold Functions Daniel M. Kane November 9, 2018 1 …

There are only a few known general approaches for constructing explicit pseudorandom
generators (PRGs). The" iterated restrictions" approach, pioneered by Ajtai and Wigderson …

We construct explicit pseudorandom generators that fool $ n $-variate polynomials of degree
at most $ d $ over a finite field $\mathbb {F} _q $. The seed length of our generators is $ O …

We show that a very simple pseudorandom generator fools intersections of k linear
threshold functions (LTFs) and arbitrary functions of k LTFs over n-dimensional Gaussian …

Abstract Recentry, Viola (CCC'08) showed that the sum of d small-biased distributions fools
degree-d polynomial tests; that is, every polynomial expression of degree at most d in the …