Analysis of boolean functions [EBook] / Ryan O'Donnell, Carnegie Mellon University, Pittsburgh, Pennsylvania.
Analysis of boolean functions [EBook] / Ryan O'Donnell, Carnegie Mellon University, Pittsburgh, Pennsylvania.
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 Fo...
Personal Name(s):  O'Donnell, Ryan, (author) 

Imprint: 
Cambridge :
Cambridge University Press,
2014

Physical Description: 
1 online resource (xx, 423 pages) 
Note: 
englisch 
ISBN: 
9781107038325 9781139814782 9781107471542 
Subject (LOC):  
Full Text 
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 GoldreichLevin algorithm from cryptography/learning theory, Håstad's NPhardness 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 onesemester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mathematical fields. 