• DocumentCode
    1701606
  • 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
  • fYear
    2010
  • Firstpage
    11
  • Lastpage
    20
  • 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;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Foundations of Computer Science (FOCS), 2010 51st Annual IEEE Symposium on
  • Conference_Location
    Las Vegas, NV
  • ISSN
    0272-5428
  • Print_ISBN
    978-1-4244-8525-3
  • Type

    conf

  • DOI
    10.1109/FOCS.2010.8
  • Filename
    5670951
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1701606