bookCambridge University Press eBooksJun 5, 2014GREEN OA

Analysis of Boolean Functions

RORyan O’Donnell

Carnegie Mellon University

Indexed inarxivcrossrefdatacite

Abstract

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…

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Topics & keywords

Topics
Keywords
  • Boolean function
  • Field (mathematics)
  • Graduate students
  • Computer science
  • Cryptography
  • Theoretical computer science
  • Algebra over a field
  • Mathematics
UN Sustainable Development Goals
  • Reduced inequalities
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