Tight Bound on the Number of Relevant Variables in a Bounded degree Boolean function

John Chiarelli
John Chiarelli
Michael Saks
Michael Saks

arXiv: Combinatorics, Volume abs/1801.08564, 2018.

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Abstract:

In this paper, we prove that a degree $d$ Boolean function depends on at most $Ccdot 2^d$ variables for some $Cu003c22$, i.e. it is a $Ccdot 2^d$-junta. This improves the $dcdot 2^{d-1}$ upper bound of Nisan and Szegedy [NS94]. Our proof uses a new weighting scheme where we assign weights to variables based on the highest degree monomial ...More

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