Binary Functions And Their Applications
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Binary Functions And Their Applications
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Author : Horand Störmer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Binary Functions And Their Applications written by Horand Störmer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
In this book binary functions and their representation by implicants or implicates are described. In particular minimal representations by prime implicants or prime implicates are given. Such representations generalize the minimal representations of the usual Boolean functions. It is shown that implicants (implicates) of discrete functions may be constructed with the help of implicants (implicates) of binary functions. One substantial application is the description of the reliability structure of technical systems, another is the use of binary respectively discrete functions to classify objects which are described by the grades of certain attributes. Finally a class of Boolean algebras of practical importance (set algebras, indicator algebras, algebras of classes of propositions) are considered. The elements of such algebras have representations which are strongly connected with the representations of binary functions.
Logic Functions And Equations
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Author : Christian Posthoff
language : en
Publisher: Springer
Release Date : 2018-12-31
Logic Functions And Equations written by Christian Posthoff and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-31 with Computers categories.
The expanded and updated 2nd edition of this classic text offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science. The approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods. Updated throughout, some major additions for the 2nd edition include: - an expanded introductory section on logic equations; - a new chapter on sets, lattices, and classes of logic functions; - a new chapter about SAT-problems; - a new chapter about methods to solve extremely complex problems; and - an expanded section with new decomposition methods utilizing the Boolean Differential Calculus extended to lattices of logic functions. The book provides insight into applications across binary arithmetic, coding, complexity, logic design, programming, computer architecture, and artificial intelligence. Based on the extensive teaching experience of the authors, Logic Functions and Equations is highly recommended for a one- or two-semester course in computer science and related programs. It provides straightforward high-level access to these methods and enables sophisticated applications, elegantly bridging the gap between mathematics and the theoretical foundations of computer science.
Boolean Functions And Their Applications In Cryptography
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Author : Chuan-Kun Wu
language : en
Publisher: Springer
Release Date : 2016-02-23
Boolean Functions And Their Applications In Cryptography written by Chuan-Kun Wu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-23 with Computers categories.
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.
Hadamard Matrices And Their Applications
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Author : K. J. Horadam
language : en
Publisher: Princeton University Press
Release Date : 2007
Hadamard Matrices And Their Applications written by K. J. Horadam and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
In Hadamard Matrices and Their Applications, K. J. Horadam provides the first unified account of cocyclic Hadamard matrices and their applications in signal and data processing. This original work is based on the development of an algebraic link between Hadamard matrices and the cohomology of finite groups that was discovered fifteen years ago. The book translates physical applications into terms a pure mathematician will appreciate, and theoretical structures into ones an applied mathematician, computer scientist, or communications engineer can adapt and use. The first half of the book explains the state of our knowledge of Hadamard matrices and two important generalizations: matrices with group entries and multidimensional Hadamard arrays. It focuses on their applications in engineering and computer science, as signal transforms, spreading sequences, error-correcting codes, and cryptographic primitives. The book's second half presents the new results in cocyclic Hadamard matrices and their applications. Full expression of this theory has been realized only recently, in the Five-fold Constellation. This identifies cocyclic generalized Hadamard matrices with particular "stars" in four other areas of mathematics and engineering: group cohomology, incidence structures, combinatorics, and signal correlation. Pointing the way to possible new developments in a field ripe for further research, this book formulates and discusses ninety open questions.
Progress In Applications Of Boolean Functions
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Author : Tsutomu Sasao
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2010
Progress In Applications Of Boolean Functions written by Tsutomu Sasao and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Algebra, Boolean categories.
This book brings together five topics on the application of Boolean functions. They are 1. Equivalence classes of Boolean functions: The number of n-variable functions is large, even for values as small as n = 6, and there has been much research on classifying functions. There are many classifications, each with their own distinct merit. 2. Boolean functions for cryptography: The process of encrypting/decrypting plain text messages often depends on Boolean functions with specific properties. For example, highly nonlinear functions are valued because they are less susceptible to linear attacks. 3. Boolean differential calculus: An operation analogous to taking the derivative of a real-valued function offers important insight into the properties of Boolean functions. One can determine tests or susceptibility to hazards. 4. Reversible logic: Most logic functions are irreversible; it is impossible to reconstruct the input, given the output. However, Boolean functions that are reversible are necessary for quantum computing, and hold significant promise for low-power computing. 5. Data mining: The process of extracting subtle patterns from enormous amounts of data has benefited from the use of a graph-based representation of Boolean functions. This has use in surveillance, fraud detection, scientific discovery including bio-informatics, genetics, medicine, and education. Written by experts, these chapters present a tutorial view of new and emerging technologies in Boolean functions. Table of Contents: Equivalence Classes of Boolean Functions / Boolean Functions for Cryptography / Boolean Differential Calculus / Synthesis of Boolean Functions in Reversible Logic / Data Mining Using Binary Decision Diagrams
Progress In Applications Of Boolean Functions
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Author : Tsutomu Sasao
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Progress In Applications Of Boolean Functions written by Tsutomu Sasao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
This book brings together five topics on the application of Boolean functions. They are 1. Equivalence classes of Boolean functions: The number of n-variable functions is large, even for values as small as n = 6, and there has been much research on classifying functions. There are many classifications, each with their own distinct merit. 2. Boolean functions for cryptography: The process of encrypting/decrypting plaintext messages often depends on Boolean functions with specific properties. For example, highly nonlinear functions are valued because they are less susceptible to linear attacks. 3. Boolean differential calculus: An operation analogous to taking the derivative of a real-valued function offers important insight into the properties of Boolean functions. One can determine tests or susceptibility to hazards. 4. Reversible logic: Most logic functions are irreversible; it is impossible to reconstruct the input, given the output. However, Boolean functions that are reversible are necessary for quantum computing, and hold significant promise for low-power computing. 5. Data mining: The process of extracting subtle patterns from enormous amounts of data has benefited from the use of a graph-based representation of Boolean functions. This has use in surveillance, fraud detection, scientific discovery including bio-informatics, genetics, medicine, and education. Written by experts, these chapters present a tutorial view of new and emerging technologies in Boolean functions. Table of Contents: Equivalence Classes of Boolean Functions / Boolean Functions for Cryptography / Boolean Differential Calculus / Synthesis of Boolean Functions in Reversible Logic / Data Mining Using Binary Decision Diagrams
Logic Functions And Equations
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Author : Bernd Steinbach
language : en
Publisher: Springer Nature
Release Date : 2022-06-06
Logic Functions And Equations written by Bernd Steinbach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-06 with Technology & Engineering categories.
The greatly expanded and updated 3rd edition of this textbook offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science and engineering. The authors’ approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods. The book provides insight into applications across propositional logic, binary arithmetic, coding, cryptography, complexity, logic design, and artificial intelligence. Updated throughout, some major additions for the 3rd edition include: a new chapter about the concepts contributing to the power of XBOOLE; a new chapter that introduces into the application of the XBOOLE-Monitor XBM 2; many tasks that support the readers in amplifying the learned content at the end of the chapters; solutions of a large subset of these tasks to confirm learning success; challenging tasks that need the power of the XBOOLE software for their solution. The XBOOLE-monitor XBM 2 software is used to solve the exercises; in this way the time-consuming and error-prone manipulation on the bit level is moved to an ordinary PC, more realistic tasks can be solved, and the challenges of thinking about algorithms leads to a higher level of education.
Binary Polynomial Transforms And Non Linear Digital Filters
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Author : S. Agaian
language : en
Publisher: CRC Press
Release Date : 1995-04-27
Binary Polynomial Transforms And Non Linear Digital Filters written by S. Agaian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-27 with Technology & Engineering categories.
This work offers a unified presentation of the theory of binary polynomial transforms and details their numerous applications in nonlinear signal processing. The book also: introduces the Rademacher logical functions; considers fast algorithms for computing Rademacher and polynomial logical functions; focuses attention on general auto- and cross-correlation functions; and more.;The work is intended for applied mathematicians; electrical, electronics and other engineers; computer scientists; and upper-level undergraduate and graduate students in these disciplines.
Representations Of Multiple Valued Logic Functions
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Author : Radomir S. Stankovic
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Representations Of Multiple Valued Logic Functions written by Radomir S. Stankovic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Technology & Engineering categories.
Compared to binary switching functions, the multiple-valued functions (MV) offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools. This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions. Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them. Table of Contents: Multiple-Valued Logic Functions / Functional Expressions for Multiple-Valued Functions / Spectral Representations of Multiple-Valued Functions / Decision Diagrams for Multiple-Valued Functions / Fast Calculation Algorithms
Boolean Algebra And Its Applications
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Author : J. Eldon Whitesitt
language : en
Publisher: Courier Corporation
Release Date : 2012-05-24
Boolean Algebra And Its Applications written by J. Eldon Whitesitt and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.
