
Program Analysis (an Appetizer)
This book is an introduction to program analysis that is meant to be con...
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Interactions of Computational Complexity Theory and Mathematics
[This paper is a (self contained) chapter in a new book, Mathematics an...
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Approximating minimum representations of key Horn functions
Horn functions form a subclass of Boolean functions and appear in many d...
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The Atlas for the Aspiring Network Scientist
Network science is the field dedicated to the investigation and analysis...
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Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge
This volume consists of papers presented at the Sixteenth Conference on ...
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Reliability of decisions based on tests: Fourier analysis of Boolean decision functions
Items in a test are often used as a basis for making decisions and such ...
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Notes on Category Theory with examples from basic mathematics
These notes were originally developed as lecture notes for a category th...
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Analysis of Boolean Functions
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions f : {0,1}^n →{0,1} via their Fourier expansion and other analytic means. Boolean functions are perhaps the most basic object of study in theoretical computer science, and Fourier analysis has become an indispensable tool in the field. The topic has also played a key role in several other areas of mathematics, from combinatorics, random graph theory, and statistical physics, to Gaussian geometry, metric/Banach spaces, and social choice theory. The intent of this book is both to develop the foundations of the field and to give a wide (though far from exhaustive) overview of its applications. Each chapter ends with a "highlight" showing the power of analysis of Boolean functions in different subject areas: property testing, social choice, cryptography, circuit complexity, learning theory, pseudorandomness, hardness of approximation, concrete complexity, and random graph theory. The book can be used as a reference for working researchers or as the basis of a onesemester graduatelevel course. The author has twice taught such a course at Carnegie Mellon University, attended mainly by graduate students in computer science and mathematics but also by advanced undergraduates, postdocs, and researchers in adjacent fields. In both years most of Chapters 15 and 7 were covered, along with parts of Chapters 6, 8, 9, and 11, and some additional material on additive combinatorics. Nearly 500 exercises are provided at the ends of the book's chapters.
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