Lower Bounds for Approximations by Low Degree Polynomials Over Zm

@inproceedings{Alon2001LowerBF,
  title={Lower Bounds for Approximations by Low Degree Polynomials Over Zm},
  author={Noga Alon and Richard Beigel},
  booktitle={IEEE Conference on Computational Complexity},
  year={2001}
}
We use a Ramsey-theoretic argument to obtain the first lower bounds for approximations over Zm by nonlinear polynomials: A degree2 polynomial over Zm (m odd) must differ from the parity function on at least a 1=2 1=2(logn) (1) fraction of all points in the Booleann-cube. A degreeO(1) polynomial overZm (m odd) must differ from the parity function on at least a 1=2 o(1) fraction of all points in the Boolean-cube. These nonapproximability results imply the first known lower bounds on the top fanin… CONTINUE READING