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Bounded Independence Fools Degree-2 Threshold Functions

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3 Author(s)
Diakonikolas, I. ; Dept. of Comput. Sci., Columbia Univ., New York, NY, USA ; Kane, D.M. ; Nelson, J.

For an n-variate degree-2 real polynomial p, we prove that Ex~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(1/ε). This gives a broad class of explicit pseudorandom generators against degree-2 boolean threshold functions, and answers an open question of Diakonikolas et al. (FOCS 2009).

Published in:

Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on

Date of Conference:

23-26 Oct. 2010