Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01f4752k18d
 Title: Techniques for Analysis of Boolean Functions Authors: Reeves, Thomas Rowan Advisors: Marcus, Adam Contributors: Naor, Asaf Department: Mathematics Class Year: 2016 Abstract: We discuss techniques for Fourier analysis of Boolean functions. After an introduction to Boolean functions and their Fourier expansions, we discuss perhaps the simplest complexity measures of Boolean functions { sensitivity and influence. We turn to the question of nding restrictions on the Fourier coe cients of a Boolean function and derive an identity. Finally, we discuss the entropy-influence conjecture with a focus on useful generalizations of the problem, including generalizations of entropy and probability distribution. We propose a generalization of the Fourier basis using rotation matrices and derive an analogue of the Margulis-Russo Formula. Extent: 26 pages URI: http://arks.princeton.edu/ark:/88435/dsp01f4752k18d Type of Material: Princeton University Senior Theses Language: en_US Appears in Collections: Mathematics, 1934-2016

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