Analysis of Boolean Functions
eBook - PDF

Analysis of Boolean Functions

  1. 446 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Analysis of Boolean Functions

About this book

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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Table of contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. List of Notation
  9. 1 Boolean Functions and the Fourier Expansion
  10. 2 Basic Concepts and Social Choice
  11. 3 Spectral Structure and Learning
  12. 4 DNF Formulas and Small-Depth Circuits
  13. 5 Majority and Threshold Functions
  14. 6 Pseudorandomness and F[sub(2)]-Polynomials
  15. 7 Property Testing, PCPPs, and CSPs
  16. 8 Generalized Domains
  17. 9 Basics of Hypercontractivity
  18. 10 Advanced Hypercontractivity
  19. 11 Gaussian Space and Invariance Principles
  20. Some Tips
  21. Bibliography
  22. Index

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Yes, you can access Analysis of Boolean Functions by Ryan O'Donnell in PDF and/or ePUB format, as well as other popular books in Computer Science & Computer Science General. We have over one million books available in our catalogue for you to explore.