Analysis of Boolean Functions: List of Notation
Ryan O'Donnell
- 01 Jan 2014
775
TL;DR: Boolean functions are perhaps the most basic objects of study in theoretical computer science.
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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, Hstad'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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Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen
TL;DR: In el marco del Proyecto subvencionado by the Fundación Antorchas (FAN) as discussed by the authors, el material was digitalizado, e.g., en la Biblioteca del Departamento de Fisica de la Facultad de Ciencias Exactas de la Universidad Nacional de La Plata.
The Byzantine Generals Problem
TL;DR: The Albanian Generals Problem as mentioned in this paper is a generalization of Dijkstra's dining philosophers problem, where two generals have to come to a common agreement on whether to attack or retreat, but can communicate only by sending messengers who might never arrive.
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Luigi Ambrosio,Diego Pallara,Nicola Fusco +2 more
- 01 Jan 2000
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