ENGLISH

Analysis of Boolean Functions

By Ryan O'Donnell

Book information

Publisher
Cambridge University Press
Year
2014
ISBN
1107038324, 9781107038325
Language
english
Format
PDF
Filesize
3 MB (3072347 bytes)
Pages
444\444
Orientation
portrait
Paginated
yes
Scanned
no
Time added
2014-07-24 19:36:18
Математика;Дискретная математика

Description

Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a "highlight application" such as Arrow's theorem from economics, the Goldreich-Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and "sharp threshold" theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students, and researchers in computer science theory and related mathematical fields.

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