期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2016
卷号：2016
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：In this paper, we apply tools from algebraic geometry to prove new results concerning extractors for algebraic sets, the recursive Fourier sampling problem, and VC dimension. We present a new construction of an extractor which works for algebraic sets defined by polynomials over F 2 of substantially higher degree than the current state-of-the-art construction. We also exactly determine the F 2 -polynomial degree of the recursive Fourier sampling problem and use this to provide new partial results towards a circuit lower bound for this problem. Finally, we answer a question posed in \cite{moran} concerning VC dimension, interpolation degree and the Hilbert function.
