Analysis of Boolean Functions PDF Download

Author: Ryan O'Donnell
Publisher: Cambridge University Press
ISBN: 1107038324
Category : Computers
Languages : en
Pages : 445

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Book Description
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: Thomas W. Cusick
Publisher: Academic Press
ISBN: 0080952224
Category : Mathematics
Languages : en
Pages : 245

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Book Description
Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce).Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research. Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions Provides engineers and scientists with a needed reference for the use of Boolean functions in cryptography Addresses the issues of cryptographic Boolean functions theory and applications in one concentrated resource Organized logically to help the reader easily understand the topic

Author: Yves Crama
Publisher: Cambridge University Press
ISBN: 1139498630
Category : Mathematics
Languages : en
Pages : 711

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Book Description
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
ISBN: 9401144435
Category : Mathematics
Languages : en
Pages : 345

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Book Description
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
ISBN: 1107076439
Category : Computers
Languages : en
Pages : 223

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Book Description
This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.

Author: Claude Carlet
Publisher: Cambridge University Press
ISBN: 1108634664
Category : Computers
Languages : en
Pages : 577

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Book Description
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.

Author: Stasys Jukna
Publisher: Springer Science & Business Media
ISBN: 3642245080
Category : Mathematics
Languages : en
Pages : 618

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Book Description
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: Tharrmashastha SAPV
Publisher: Springer Nature
ISBN: 9811630615
Category : Computers
Languages : en
Pages : 128

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Book Description
This book is a timely report of the state-of-the-art analytical techniques in the domain of quantum algorithms related to Boolean functions. It bridges the gap between recent developments in the area and the hands-on analysis of the spectral properties of Boolean functions from a cryptologic viewpoint. Topics covered in the book include Qubit, Deutsch–Jozsa and Walsh spectrum, Grover’s algorithm, Simon’s algorithm and autocorrelation spectrum. The book aims at encouraging readers to design and implement practical algorithms related to Boolean functions. Apart from combinatorial techniques, this book considers implementing related programs in a quantum computer. Researchers, practitioners and educators will find this book valuable.

Author: Serban E. Vlad
Publisher: John Wiley & Sons
ISBN: 1119517478
Category : Mathematics
Languages : en
Pages : 198

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Book Description
The essential guide showing how the unbounded delay model of computation of the Boolean functions may be used in the analysis of the Boolean networks Boolean Functions: Topics in Asynchronicity contains the most current research in several issues of asynchronous Boolean systems. In this framework, asynchronicity means that the functions which model the digital circuits from electronics iterate their coordinates independently on each other and the author—a noted expert in the field—includes a formal mathematical description of these systems. Filled with helpful definitions and illustrative examples, the book covers a range of topics such as morphisms, antimorphisms, invariant sets, path connected sets, attractors. Further, it studies race freedom, called here the technical condition of proper operation, together with some of its generalized and strengthened versions, and also time reversal, borrowed from physics and also from dynamical systems, together with the symmetry that it generates. This book: Presents up-to-date research in the field of Boolean networks, Includes the information needed to understand the construction of an asynchronous Boolean systems theory and contains proofs, Employs use of the language of algebraic topology and homological algebra. Written formathematicians and computer scientists interested in the theory and applications of Boolean functions, dynamical systems, and circuits, Boolean Functions: Topics in Asynchronicity is an authoritative guide indicating a way of using the unbounded delay model of computation of the Boolean functions in the analysis of the Boolean networks.

Author: Daizhan Cheng
Publisher: Springer Science & Business Media
ISBN: 0857290975
Category : Science
Languages : en
Pages : 474

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Book Description
Analysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology – fixed points, cycles, transient times and basins of attractors – can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling etc.