An Asymptotically Tight Bound on the Number of Relevant Variables in a Bounded Degree Boolean Function

John Chiarelli
John Chiarelli
Michael Saks
Michael Saks

arXiv: Combinatorics, 2018.

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Abstract:

We prove that there is a constant $Cleq 6.614$ such that every Boolean function of degree at most $d$ (as a polynomial over $mathbb{R}$) is a $Ccdot 2^d$-junta, i.e. it depends on at most $Ccdot 2^d$ variables. This improves the $dcdot 2^{d-1}$ upper bound of Nisan and Szegedy [Computational Complexity 4 (1994)]. Our proof uses a new weig...More

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