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Logic Functions And Equations
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Book Synopsis Logic Functions and Equations by : Christian Posthoff
Download or read book Logic Functions and Equations written by Christian Posthoff and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Logic Functions and Equations by : Bernd Steinbach
Download or read book Logic Functions and Equations written by Bernd Steinbach and published by Springer Science & Business Media. This book was released on 2009-01-29 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tsutomu Sasao – Kyushu Institute of Technology, Japan The material covered in this book is quite unique especially for p- ple who are reading English, since such material is quite hard to ?nd in the U.S. literature. German and Russian people have independently developed their theories, but such work is not well known in the U.S. societies. On the other hand, the theories developed in the U.S. are not conveyed to the other places. Thus, the same theory is re-invented or re-discovered in various places. For example, the switching theory was developed independently in the U.S., Europe, and Japan, almost at the same time [4, 18, 19]. Thus, the same notions are represented by di?- ent terminologies. For example, the Shegalkin polynomial is often called complement-free ring-sum, Reed-Muller expression [10], or Positive - larityReed-Mullerexpression [19].Anyway,itisquitedesirablethatsuch a unique book like this is written in English, and many people can read it without any di?culties. The authors have developed a logic system called XBOOLE.Itp- forms logical operations on the given functions. With XBOOLE, the readers can solve the problems given in the book. Many examples and complete solutions to the problems are shown, so the readers can study at home. I believe that the book containing many exercises and their solutions [9] is quite useful not only for the students, but also the p- fessors.
Book Synopsis Logic Functions and Equations by : Bernd Steinbach
Download or read book Logic Functions and Equations written by Bernd Steinbach and published by Springer Nature. This book was released on 2022-06-06 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Logic Functions and Equations by : Christian Posthoff
Download or read book Logic Functions and Equations written by Christian Posthoff and published by Springer. This book was released on 2018-12-31 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Boolean Reasoning by : Frank Markham Brown
Download or read book Boolean Reasoning written by Frank Markham Brown and published by Courier Corporation. This book was released on 2012-02-10 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.
Book Synopsis Boolean Differential Equations by : Bernd Steinbach
Download or read book Boolean Differential Equations written by Bernd Steinbach and published by Morgan & Claypool Publishers. This book was released on 2013-06-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Boolean Differential Calculus by : Bernd Steinbach
Download or read book Boolean Differential Calculus written by Bernd Steinbach and published by Springer Nature. This book was released on 2022-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lattice Functions and Equations by : Sergiu Rudeanu
Download or read book Lattice Functions and Equations written by Sergiu Rudeanu and published by Springer Science & Business Media. This book was released on 2001-07-30 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Logic and Boolean Algebra by : Bradford Henry Arnold
Download or read book Logic and Boolean Algebra written by Bradford Henry Arnold and published by Courier Corporation. This book was released on 2011-01-01 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.
Book Synopsis Boolean Functions and Equations by : Sergiu Rudeanu
Download or read book Boolean Functions and Equations written by Sergiu Rudeanu and published by . This book was released on 1974 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boolean Reasoning by : Frank Markham Brown
Download or read book Boolean Reasoning written by Frank Markham Brown and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the logic of Boolean equations. Such equations were central in the "algebra of logic" created in 1847 by Boole [12, 13] and devel oped by others, notably Schroder [178], in the remainder of the nineteenth century. Boolean equations are also the language by which digital circuits are described today. Logicians in the twentieth century have abandoned Boole's equation based logic in favor of the more powerful predicate calculus. As a result, digital engineers-and others who use Boole's language routinely-remain largely unaware of its utility as a medium for reasoning. The aim of this book, accordingly, is to is to present a systematic outline of the logic of Boolean equations, in the hope that Boole's methods may prove useful in solving present-day problems. Two Logical Languages Logic seeks to reduce reasoning to calculation. Two main languages have been developed to achieve that object: Boole's "algebra of logic" and the predicate calculus. Boole's approach was to represent classes (e. g. , happy creatures, things productive of pleasure) by symbols and to represent logical statements as equations to be solved. His formulation proved inadequate, however, to represent ordinary discourse. A number of nineteenth-century logicians, including Jevons [94], Poretsky [159], Schroder [178], Venn [210], and Whitehead [212, 213], sought an improved formulation based on ex tensions or modifications of Boole's algebra. These efforts met with only limited success.
Download or read book Boolean Functions written by Yves Crama and published by Cambridge University Press. This book was released on 2011-05-16 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analysis of Boolean Functions by : Ryan O'Donnell
Download or read book Analysis of Boolean Functions written by Ryan O'Donnell and published by Cambridge University Press. This book was released on 2014-06-05 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of Logic and Mathematics by : Yves Nievergelt
Download or read book Foundations of Logic and Mathematics written by Yves Nievergelt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.
Book Synopsis Recursive Function Theory and Logic by : Ann Yasuhara
Download or read book Recursive Function Theory and Logic written by Ann Yasuhara and published by . This book was released on 1971 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Complexity of Boolean Functions by : Ingo Wegener
Download or read book The Complexity of Boolean Functions written by Ingo Wegener and published by . This book was released on 1987 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boolean Differential Equations by : Bernd Steinbach
Download or read book Boolean Differential Equations written by Bernd Steinbach and published by Springer Nature. This book was released on 2022-05-31 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
