Ryan O'DonnellCambridge University Press, 6/5/2014EAN 9781107038325, ISBN10: 1107038324Hardcover, 444 pages, 22.8 x 15.2 x 2.5 cmLanguage: EnglishBoolean 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.1. Boolean functions and the Fourier expansion2. Basic concepts and social choice3. Spectral structure and learning4. DNF formulas and small-depth circuits5. Majority and threshold functions6. Pseudorandomness and F2-polynomials7. Property testing, PCPPs, and CSPs8. Generalized domains9. Basics of hypercontractivity10. Advanced hypercontractivity11. Gaussian space and invariance principles.
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