By Ryan O'Donnell

ISBN-10: 1107038324

ISBN-13: 9781107038325

Boolean features are probably the main simple gadgets of analysis in theoretical machine technology. in addition they come up in different components of arithmetic, together with combinatorics, statistical physics, and mathematical social selection. the sphere of research of Boolean services seeks to appreciate them through their Fourier remodel and different analytic equipment. this article offers an intensive evaluation of the sector, starting with the main easy definitions and continuing to complex themes akin to hypercontractivity and isoperimetry. every one bankruptcy features a 'highlight program' resembling Arrow's theorem from economics, the Goldreich–Levin set of rules from cryptography/learning conception, Håstad's NP-hardness of approximation effects, and 'sharp threshold' theorems for random graph homes. The e-book comprises approximately 450 workouts and will be used because the foundation of a one-semester graduate path. it may entice complicated undergraduates, graduate scholars and researchers in computing device technology conception and similar mathematical fields.

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Analysis of Boolean Functions by Ryan O'Donnell


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