The correlation between parity and quadratic polynomials mod 3
Journal of Computer and System Sciences - Special issue on computational complexity 2002
On the Power of Small-Depth Computation
Foundations and Trends® in Theoretical Computer Science
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We highlight the challenge of proving correlation bounds between boolean functions and real-valued polynomials, where any non-boolean output counts against correlation. We prove that real-valued polynomials of degree 1 2 lg2 lg2 n have correlation with parity at most zero. Such a result is false for modular and threshold polynomials. Its proof is based on a variant of an anti-concentration result by Costello et al. [2006].