Download PDF by Ryan O'Donnell: Analysis of Boolean Functions

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By Ryan O'Donnell

ISBN-10: 1107038324

ISBN-13: 9781107038325

Boolean capabilities are maybe the main simple gadgets of analysis in theoretical computing device technology. additionally they come up in different components of arithmetic, together with combinatorics, statistical physics, and mathematical social selection. the sphere of research of Boolean features seeks to appreciate them through their Fourier remodel and different analytic equipment. this article provides an intensive evaluation of the sector, starting with the main easy definitions and continuing to complicated issues akin to hypercontractivity and isoperimetry. each one bankruptcy encompasses a 'highlight program' equivalent to Arrow's theorem from economics, the Goldreich–Levin set of rules from cryptography/learning concept, Håstad's NP-hardness of approximation effects, and 'sharp threshold' theorems for random graph homes. The e-book contains approximately 450 workouts and will be used because the foundation of a one-semester graduate direction. it's going to attract complicated undergraduates, graduate scholars and researchers in machine technological know-how conception and comparable mathematical fields.

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Analysis of Boolean Functions by Ryan O'Donnell

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