Problems And New Solutions In The Boolean Domain
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Problems And New Solutions In The Boolean Domain
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Author : Bernd Steinbach
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2016-04-26
Problems And New Solutions In The Boolean Domain written by Bernd Steinbach and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-26 with Algebra, Boolean categories.
The Internet of Things is a great new challenge for the development of digital systems. In addition to the increasing number of classical unconnected digital systems, more people are regularly using new electronic devices and software that are controllable and usable by means of the internet. All such systems utilize the elementariness of Boolean values. A Boolean variable can carry only two different Boolean values: FALSE or TRUE (0 or 1), and has the best interference resistance in technical systems. However, a Boolean function exponentially depends on the number of its variables. This exponential complexity is the cause of major problems in the process of design and realization of circuits. According to Moore’s Law, the complexity of digital systems approximately doubles every 18 months. This requires comprehensive knowledge and techniques to solve complex Boolean problems. This book summarizes both new problems and solutions in the Boolean domain in solving such issues. Part 1 describes powerful new approaches in solving exceptionally complex Boolean problems. Efficient methods contribute to solving problems of extreme complexity. New algorithms and programs utilize the huge number of computing cores of the Graphical Processing Unit and improve the performance of calculations by several orders of magnitude. Part 2 represents several applications of digital systems. Due to the crucial role of the internet, both solutions and open problems regarding the security of these systems are discussed. The exploration of certain properties of such systems leads to a number of efficient solutions, which can be reused in a wide field of applications. Part 3 discusses the scientific basis of future circuit technologies, investigating the need for completely new design methods for the atomic level of quantum computers. This part also concerns itself with reversible circuits as the basis for quantum circuits and specifies important issues regarding future improvements.
Boolean Differential Calculus
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Author : Bernd Steinbach
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Boolean Differential Calculus 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 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.
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.
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.
Synthesis Of Quantum Circuits Vs Synthesis Of Classical Reversible Circuits
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Author : Alexis De Vos
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Synthesis Of Quantum Circuits Vs Synthesis Of Classical Reversible Circuits written by Alexis De Vos 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.
At first sight, quantum computing is completely different from classical computing. Nevertheless, a link is provided by reversible computation. Whereas an arbitrary quantum circuit, acting on ?? qubits, is described by an ?? × ?? unitary matrix with ??=2??, a reversible classical circuit, acting on ?? bits, is described by a 2?? × 2?? permutation matrix. The permutation matrices are studied in group theory of finite groups (in particular the symmetric group ????); the unitary matrices are discussed in group theory of continuous groups (a.k.a. Lie groups, in particular the unitary group U(??)). Both the synthesis of a reversible logic circuit and the synthesis of a quantum logic circuit take advantage of the decomposition of a matrix: the former of a permutation matrix, the latter of a unitary matrix. In both cases the decomposition is into three matrices. In both cases the decomposition is not unique.
Claudio Moraga A Passion For Multi Valued Logic And Soft Computing
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Author : Rudolf Seising
language : en
Publisher: Springer
Release Date : 2016-10-20
Claudio Moraga A Passion For Multi Valued Logic And Soft Computing written by Rudolf Seising and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Computers categories.
The book is an authoritative collection of contributions by leading experts on the topics of fuzzy logic, multi-valued logic and neural network. Originally written as an homage to Claudio Moraga, seen by his colleagues as an example of concentration, discipline and passion for science, the book also represents a timely reference guide for advance students and researchers in the field of soft computing, and multiple-valued logic.
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Author :
language : en
Publisher: IOS Press
Release Date :
written by and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Algebraic Techniques For Satisfiability Problems
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Author : Henning Schnoor
language : en
Publisher: Cuvillier Verlag
Release Date : 2007
Algebraic Techniques For Satisfiability Problems written by Henning Schnoor and has been published by Cuvillier Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Data Mining For Association Rules And Sequential Patterns
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Author : Jean-Marc Adamo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Data Mining For Association Rules And Sequential Patterns written by Jean-Marc Adamo 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 Computers categories.
Data mining includes a wide range of activities such as classification, clustering, similarity analysis, summarization, association rule and sequential pattern discovery, and so forth. The book focuses on the last two previously listed activities. It provides a unified presentation of algorithms for association rule and sequential pattern discovery. For both mining problems, the presentation relies on the lattice structure of the search space. All algorithms are built as processes running on this structure. Proving their properties takes advantage of the mathematical properties of the structure. Part of the motivation for writing this book was postgraduate teaching. One of the main intentions was to make the book a suitable support for the clear exposition of problems and algorithms as well as a sound base for further discussion and investigation. Since the book only assumes elementary mathematical knowledge in the domains of lattices, combinatorial optimization, probability calculus, and statistics, it is fit for use by undergraduate students as well. The algorithms are described in a C-like pseudo programming language. The computations are shown in great detail. This makes the book also fit for use by implementers: computer scientists in many domains as well as industry engineers.
Theory And Practice Of Natural Computing
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Author : Claus Aranha
language : en
Publisher: Springer Nature
Release Date : 2021-11-03
Theory And Practice Of Natural Computing written by Claus Aranha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-03 with Computers categories.
This book constitutes the refereed proceedings of the 10th International Conference on Theory and Practice of Natural Computing, TPNC 2021, held virtually, in December 2021. The 9 full papers presented together with 3 invited talks, in this book were carefully reviewed and selected from 14 submissions. The papers are organized in topical sections named Applications of Natural Computing, Deep Learning and Transfer Learning, Evolutionary and Swarm Algorithms.