Real Advantage

Abstract

We highlight the challenge of proving correlation bounds between boolean functions and integer-valued polynomials, where any non-boolean output counts against correlation. We prove that integer-valued polynomials of degree 1 2 lg2 lg2 n have zero correlation with parity. Such a result is false for modular and threshold polynomials. Its proof is based on a strengthening of an anti-concentration result by Costello, Tao, and Vu (Duke Math. J. 2006).

Similar works

This paper was published in CiteSeerX.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.