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| Author | : Ryan O'Donnell |
| Publisher | : Cambridge University Press |
| Total Pages | : 445 |
| Release | : 2014-06-05 |
| Genre | : Computers |
| ISBN | : 1107038324 |
This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.
| Author | : Ryan O'Donnell |
| Publisher | : Cambridge University Press |
| Total Pages | : 445 |
| Release | : 2014-06-05 |
| Genre | : Computers |
| ISBN | : 1139952501 |
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.
| Author | : Ryan O'Donnell |
| Publisher | : |
| Total Pages | : 444 |
| Release | : 2014 |
| Genre | : Algebra, Boolean |
| ISBN | : 9781107471542 |
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.
| Author | : Thomas W. Cusick |
| Publisher | : Academic Press |
| Total Pages | : 288 |
| Release | : 2017-03-31 |
| Genre | : Mathematics |
| ISBN | : 0128111305 |
Cryptographic Boolean Functions and Applications, Second Edition is designed to be a comprehensive reference for the use of Boolean functions in modern cryptography. While the vast majority of research on cryptographic Boolean functions has been achieved since the 1970s, when cryptography began to be widely used in everyday transactions, in particular banking, relevant material is scattered over hundreds of journal articles, conference proceedings, books, reports and notes, some of them only available online. This book follows the previous edition in sifting through this compendium and gathering the most significant information in one concise reference book. The work therefore encompasses over 600 citations, covering every aspect of the applications of cryptographic Boolean functions. Since 2008, the subject has seen a very large number of new results, and in response, the authors have prepared a new chapter on special functions. The new edition brings 100 completely new references and an expansion of 50 new pages, along with heavy revision throughout the text. Presents a foundational approach, beginning with the basics of the necessary theory, then progressing to more complex content Includes major concepts that are presented with complete proofs, with an emphasis on how they can be applied Includes an extensive list of references, including 100 new to this edition that were chosen to highlight relevant topics Contains a section on special functions and all-new numerical examples
| Author | : Yves Crama |
| Publisher | : Cambridge University Press |
| Total Pages | : 711 |
| Release | : 2011-05-16 |
| Genre | : Mathematics |
| ISBN | : 1139498630 |
Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.
| Author | : A.G. Kusraev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 345 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401144435 |
Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.
| Author | : Christophe Garban |
| Publisher | : Cambridge University Press |
| Total Pages | : 223 |
| Release | : 2015 |
| Genre | : Computers |
| ISBN | : 1107076439 |
This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.
| Author | : Chuan-Kun Wu |
| Publisher | : Springer |
| Total Pages | : 256 |
| Release | : 2016-02-23 |
| Genre | : Computers |
| ISBN | : 3662488655 |
This book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties. More specifically, Walsh spectrum description of the traditional cryptographic properties of Boolean functions, including linear structure, propagation criterion, nonlinearity, and correlation immunity are presented. Constructions of symmetric Boolean functions and of Boolean permutations with good cryptographic properties are specifically studied. This book is not meant to be comprehensive, but with its own focus on some original research of the authors in the past. To be self content, some basic concepts and properties are introduced. This book can serve as a reference for cryptographic algorithm designers, particularly the designers of stream ciphers and of block ciphers, and for academics with interest in the cryptographic properties of Boolean functions.
| Author | : Stasys Jukna |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 618 |
| Release | : 2012-01-06 |
| Genre | : Mathematics |
| ISBN | : 3642245080 |
Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.
| Author | : Claude Carlet |
| Publisher | : Cambridge University Press |
| Total Pages | : 577 |
| Release | : 2021-01-07 |
| Genre | : Computers |
| ISBN | : 1108634664 |
Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results. A useful resource for researchers and graduate students, the book balances detailed discussions of properties and parameters with examples of various types of cryptographic attacks that motivate the consideration of these parameters. It provides all the necessary background on mathematics, cryptography, and coding, and an overview on recent applications, such as side channel attacks on smart cards, cloud computing through fully homomorphic encryption, and local pseudo-random generators. The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications.
