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• W2952338768 abstract "We study the relationship between two measures of Boolean functions; emph{algebraic thickness} and emph{normality}. For a function $f$, the algebraic thickness is a variant of the emph{sparsity}, the number of nonzero coefficients in the unique GF(2) polynomial representing $f$, and the normality is the largest dimension of an affine subspace on which $f$ is constant. We show that for $0 < epsilon<2$, any function with algebraic thickness $n^{3-epsilon}$ is constant on some affine subspace of dimension $Omegaleft(n^{frac{epsilon}{2}}right)$. Furthermore, we give an algorithm for finding such a subspace. We show that this is at most a factor of $Theta(sqrt{n})$ from the best guaranteed, and when restricted to the technique used, is at most a factor of $Theta(sqrt{log n})$ from the best guaranteed. We also show that a concrete function, majority, has algebraic thickness $Omegaleft(2^{n^{1/6}}right)$." @default.
• W2952338768 created "2019-06-27" @default.
• W2952338768 creator A5068354624 @default.
• W2952338768 date "2014-10-06" @default.
• W2952338768 modified "2023-09-27" @default.
• W2952338768 title "Constructive Relationships Between Algebraic Thickness and Normality" @default.
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• W2952338768 hasPublicationYear "2014" @default.
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