Analysis of Boolean Functions ODonnell Ryan Carnegie Mellon University Pennsylvania
Boolean functions are perhaps the most basic objects of study in theoretical computer science. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. They also arise in other areas of mathematics, including comb… Celý popis ↓
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Popis Analysis of Boolean Functions ODonnell Ryan Carnegie Mellon University Pennsylvania
Analysis of Boolean Functions ODonnell Ryan Carnegie Mellon University Pennsylvania
Boolean functions are perhaps the most basic objects of study in theoretical computer science. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice.
Each chapter includes a highlight application such as Arrow's theorem from economics, the Goldreich-Levin algorithm from cryptography/learning theory, Hastad's NP-hardness of approximation results, and sharp threshold theorems for random graph properties. 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. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course.
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