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

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