Analysis of Boolean Functions - Hardcover

O'Donnell, Ryan

Hardcover

ISBN 10: 1107038324 ISBN 13: 9781107038325

Publisher: Cambridge University Press, 2014

Synopsis

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.

About this title

Book Description

This graduate-level 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, the Goldreich-Levin algorithm, hardness of approximation, and "sharp threshold" theorems for random graphs.

About the Author

Ryan O'Donnell is an Associate Professor in the Computer Science Department at Carnegie Mellon University.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2014
• ISBN 10: 1107038324
• ISBN 13: 9781107038325
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 444