Summary: Lower Bounds for Approximations by Low Degree Polynomials Over
¢¡
Noga Alon£
Tel Aviv University
noga@math.tau.ac.il
Richard Beigel¤
Temple University
beigel@joda.cis.temple.edu
Abstract
We use a Ramsey-theoretic argument to obtain the first
lower bounds for approximations over ¥§¦ by nonlinear
polynomials:
¨ A degree-© polynomial over ¥ ¦ (
¡
odd) must
differ from the parity function on at least a
© ©!#"%$'&%()10 fraction of all points in the
Boolean 2 -cube.
¨ A degree-354 6 polynomial over ¥§¦ (
¡

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

Collections: Mathematics