A tighter bound on the number of relevant variables in a bounded degree Boolean function

03/19/2019

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by   Jake Wellens, et al.

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A classical theorem of Nisan and Szegedy says that a boolean function with degree d as a real polynomial depends on at most d2^d-1 of its variables. In recent work by Chiarelli, Hatami and Saks, this upper bound was improved to C · 2^d, where C = 6.614. Here we refine their argument to show that one may take C = 4.416.