The List-Decoding Size of Fourier-Sparse Boolean Functions

TOCT, Volume 8, Issue 3, 2016.

Cited by: 7|Bibtex|Views16|Links
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Keywords:
Fourier-sparse Boolean functionslearning theoryproperty testing

Abstract:

A function defined on the Boolean hypercube is k-Fourier-sparse if it has at most k nonzero Fourier coefficients. For a function f : Fn2 → R and parameters k and d, we prove a strong upper bound on the number of k -Fourier-sparse Boolean functions that disagree with f on at most d inputs. Our bound implies that the number of uniform and i...More

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