Title :
Bounded Independence Fools Degree-2 Threshold Functions
Author :
Diakonikolas, Ilias ; Kane, Daniel M. ; Nelson, Jelani
Author_Institution :
Dept. of Comput. Sci., Columbia Univ., New York, NY, USA
Abstract :
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).
Keywords :
Boolean functions; polynomials; bounded independence fools degree-2; k-wise Independent distribution; pseudorandom generator; real polynomial; threshold function; Approximation methods; Convolution; Eigenvalues and eigenfunctions; Fourier transforms; Neodymium; Polynomials; Smoothing methods; $k$-wise independence; derandomization; polynomial threshold functions;
Conference_Titel :
Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on
Conference_Location :
Las Vegas, NV
Print_ISBN :
978-1-4244-8525-3
DOI :
10.1109/FOCS.2010.8
