Boolean Differential Equations
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Boolean Differential Equations
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Author : Bernd Steinbach
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2013-06-01
Boolean Differential Equations written by Bernd Steinbach 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 2013-06-01 with Technology & Engineering categories.
The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean Algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean Algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can be applied to any task described by logic functions and equations together with the Boolean Algebra. The BDC can be widely used for the analysis, synthesis, and testing of digital circuits. Generally speaking, a Boolean differential equation (BDE) is an equation in which elements of the BDC appear. It includes variables, functions, and derivative operations of these functions. The solution of such a BDE is a set of Boolean functions. This is a significant extension of Boolean equations, which have sets of Boolean vectors as solutions. In the simplest BDE a derivative operation of the BDC on the left-hand side is equal to a logic function on the right-hand side. The solution of such a simple BDE means to execute an operation which is inverse to the given derivative. BDEs can be applied in the same fields as the BDC, however, their possibility to express sets of Boolean functions extends the application field significantly.
Boolean Differential Calculus
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Author : Bernd Steinbach
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-06-07
Boolean Differential Calculus written by Bernd Steinbach 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 2017-06-07 with Mathematics categories.
The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly. Its applications are based on Boolean spaces ?? and ??n, Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolean equations, Boolean inequalities, incompletely specified Boolean functions, and Boolean lattices of Boolean functions. These basics, sometimes also called switching theory, are widely used in many modern information processing applications. The BDC extends the known concepts and allows the consideration of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. The BDC defines a small number of derivative and differential operations. Many existing theorems are very welcome and allow new insights due to possible transformations of problems. The available operations of the BDC have been efficiently implemented in several software packages. The common use of the basic concepts and the BDC opens a very wide field of applications. The roots of the BDC go back to the practical problem of testing digital circuits. The BDC deals with changes of signals which are very important in applications of the analysis and the synthesis of digital circuits. The comprehensive evaluation and utilization of properties of Boolean functions allow, for instance, to decompose Boolean functions very efficiently; this can be applied not only in circuit design, but also in data mining. Other examples for the use of the BDC are the detection of hazards or cryptography. The knowledge of the BDC gives the scientists and engineers an extended insight into Boolean problems leading to new applications, e.g., the use of Boolean lattices of Boolean functions.
Lattice Functions And Equations
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Author : Sergiu Rudeanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lattice Functions And Equations written by Sergiu Rudeanu 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 Mathematics categories.
One of the chief aims of this self-contained monograph is to survey recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices. Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. Special attention is also paid to consistency conditions and reproductive general solutions. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others. Lattice Functions and Equations updates and extends the author's previous monograph - Boolean Functions and Equations.
Logic Functions And Equations
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Author : Christian Posthoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Logic Functions And Equations written by Christian Posthoff 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 2013-03-19 with Mathematics categories.
Logic functions and equations are (some of) the most important concepts of Computer Science with many applications such as Binary Arithmetics, Coding, Complexity, Logic Design, Programming, Computer Architecture and Artificial Intelligence. They are very often studied in a minimum way prior to or together with their respective applications. Based on our long-time teaching experience, a comprehensive presentation of these concepts is given, especially emphasising a thorough understanding as well as numerical and computer-based solution methods. Any applications and examples from all the respective areas are given that can be dealt with in a unified way. They offer a broad understanding of the recent developments in Computer Science and are directly applicable in professional life. Logic Functions and Equations is highly recommended for a one- or two-semester course in many Computer Science or computer Science-oriented programmes. It allows students an easy high-level access to these methods and enables sophisticated applications in many different areas. It elegantly bridges the gap between Mathematics and the required theoretical foundations of Computer Science.
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.
Boolean Differential Equations
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Author : Bernd Steinbach
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Boolean Differential 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 2022-05-31 with Technology & Engineering categories.
The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean Algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean Algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can be applied to any task described by logic functions and equations together with the Boolean Algebra. The BDC can be widely used for the analysis, synthesis, and testing of digital circuits. Generally speaking, a Boolean differential equation (BDE) is an equation in which elements of the BDC appear. It includes variables, functions, and derivative operations of these functions. The solution of such a BDE is a set of Boolean functions. This is a significant extension of Boolean equations, which have sets of Boolean vectors as solutions. In the simplest BDE a derivative operation of the BDC on the left-hand side is equal to a logic function on the right-hand side. The solution of such a simple BDE means to execute an operation which is inverse to the given derivative. BDEs can be applied in the same fields as the BDC, however, their possibility to express sets of Boolean functions extends the application field significantly.
A Treatise On Differential Equations
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Author : George Boole
language : en
Publisher:
Release Date : 1877
A Treatise On Differential Equations written by George Boole and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1877 with Mathematics categories.
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.
A Treatise On Differential Equations
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Author : George Boole
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-03-14
A Treatise On Differential Equations written by George Boole and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-14 with Fiction categories.
Reprint of the original, first published in 1865.
Boolean Valued Analysis
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Author : A.G. Kusraev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Boolean Valued Analysis written by A.G. Kusraev 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 Mathematics categories.
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.