Problems And New Solutions In The Boolean Domain

Author : Bernd Steinbach
Publisher : Cambridge Scholars Publishing
Page : 480 pages
File Size : 40,9 Mb
Release : 2016-04-26
Category : Algebra, Boolean
ISBN : 9781443892421

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Problems and New Solutions in the Boolean Domain by Bernd Steinbach Pdf

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.

Author : Bernd Steinbach
Publisher : Cambridge Scholars Publishing
Page : 536 pages
File Size : 55,5 Mb
Release : 2019-01-18
Category : Computers
ISBN : 9781527526389

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Further Improvements in the Boolean Domain by Bernd Steinbach Pdf

The amount of digital systems supporting our daily life is increasing continuously. Improved technical facilities for their production have led to growing challenges for engineers and scientists working in the Boolean domain. A Boolean variable can only carry 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 reason for 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 very complex Boolean problems. This volume represents the third book in a series that provides further insights into the Boolean domain. Part 1 explores powerful models, methods and techniques which improve the efficiency in solving Boolean problems of extreme complexity. The universality of Boolean equations as a model to solve Non-deterministic Polynomial-time (NP) hard problems, as well as special properties of index generation functions, spectral techniques, or relational approaches, is discussed here. Both hardware devices, such as Field Programmable Gate Arrays (FPGAs) or Graphics Processing Units (GPUs), and optimized algorithms realized in software contribute to the acceleration of Boolean calculations. Part 2 contributes to the synthesis and visualization of digital circuits, and provides interesting new solutions for several types of circuits. A comprehensive collection of benchmarks supports the evolution of both existing and new synthesis approaches. The continuous reduction of the size of the transistors increases the challenges with regard to the reliability of the circuits. Part 3 describes several new approaches for the synthesis of reversible circuits. These approaches, as well as a classification of reversible functions, extend the basis of future quantum computers.

Author : Bernd Steinbach
Publisher : Cambridge Scholars Publishing
Page : 254 pages
File Size : 42,5 Mb
Release : 2022-09-26
Category : Computers
ISBN : 9781527588738

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Advances in the Boolean Domain by Bernd Steinbach Pdf

This book gathers together the results of research on the Boolean domain related to important real-life applications that will support the reader in solving their scientific and practical tasks. It highlights that ongoing digitalization leads to increasing amounts of complex applications, the digits of which are usually encoded by Boolean variables due to their simplicity as only two values are used. However, as shown here, an exponentially growing number of vectors of Boolean variables can negate this simplicity, which leads to challenges in advancing progress in the Boolean domain and supporting a wide range of applications.

Author : Bernd Steinbach,Christian Posthoff
Publisher : Springer Nature
Page : 818 pages
File Size : 53,5 Mb
Release : 2022-06-06
Category : Technology & Engineering
ISBN : 9783030889456

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Logic Functions and Equations by Bernd Steinbach,Christian Posthoff Pdf

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.

Author : Bernd Steinbach
Publisher : Cambridge Scholars Publishing
Page : 455 pages
File Size : 43,8 Mb
Release : 2014-04-23
Category : Mathematics
ISBN : 9781443859677

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Recent Progress in the Boolean Domain by Bernd Steinbach Pdf

In today’s world, people are using more and more digital systems in daily life. 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 very complex Boolean problems. This book summarizes the recent progress in the Boolean domain in solving such issues. Part 1 describes the most powerful approaches in solving exceptionally complex Boolean problems. It is shown how an extremely rare solution could be found in a gigantic search space of more than 10^195 (this is a number of 196 decimal digits) different color patterns. Part 2 describes new research into digital circuits that realize Boolean functions. This part contains the chapters “Design” and “Test”, which present solutions to problems of power dissipation, and the testing of digital circuits using a special data structure, as well as further topics. Part 3 contributes to the scientific basis of future circuit technologies, investigating the need for completely new design methods for the atomic level of quantum computers. This section also concerns itself with circuit structures in reversible logic as the basis for quantum logic.

Author : Bernd Steinbach,Christian Posthoff
Publisher : Springer Nature
Page : 203 pages
File Size : 52,9 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031798924

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Boolean Differential Calculus by Bernd Steinbach,Christian Posthoff Pdf

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.

Author : Christian Posthoff,Bernd Steinbach
Publisher : Springer
Page : 511 pages
File Size : 48,8 Mb
Release : 2018-12-31
Category : Computers
ISBN : 9783030024208

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Logic Functions and Equations by Christian Posthoff,Bernd Steinbach Pdf

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.

Author : Rudolf Seising,Héctor Allende-Cid
Publisher : Springer
Page : 382 pages
File Size : 45,5 Mb
Release : 2016-10-20
Category : Computers
ISBN : 9783319483177

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Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing by Rudolf Seising,Héctor Allende-Cid Pdf

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.

Author : Rolf Drechsler,Daniel Große
Publisher : Springer Nature
Page : 198 pages
File Size : 41,6 Mb
Release : 2021-04-29
Category : Technology & Engineering
ISBN : 9783030680718

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Recent Findings in Boolean Techniques by Rolf Drechsler,Daniel Große Pdf

This book describes recent findings in the domain of Boolean logic and Boolean algebra, covering application domains in circuit and system design, but also basic research in mathematics and theoretical computer science. Content includes invited chapters and a selection of the best papers presented at the 14th annual International Workshop on Boolean Problems.

Author : Rolf Drechsler,Mathias Soeken
Publisher : Springer
Page : 265 pages
File Size : 43,9 Mb
Release : 2019-07-08
Category : Technology & Engineering
ISBN : 9783030203238

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Advanced Boolean Techniques by Rolf Drechsler,Mathias Soeken Pdf

This book describes recent findings in the domain of Boolean logic and Boolean algebra, covering application domains in circuit and system design, but also basic research in mathematics and theoretical computer science. Content includes invited chapters and a selection of the best papers presented at the 13th annual International Workshop on Boolean Problems. Provides a single-source reference to the state-of-the-art research in the field of logic synthesis and Boolean techniques; Includes a selection of the best papers presented at the 13th annual International Workshop on Boolean Problems; Covers Boolean algebras, Boolean logic, Boolean modeling, Combinatorial Search, Boolean and bitwise arithmetic, Software and tools for the solution of Boolean problems, Applications of Boolean logic and algebras, Applications to real-world problems, Boolean constraint solving, and Extensions of Boolean logic.

Author : Yuhui Shi,Kay Chen Tan,Mengjie Zhang,Ke Tang,Xiaodong Li,Qingfu Zhang,Ying Tan,Martin Middendorf,Yaochu Jin
Publisher : Springer
Page : 1041 pages
File Size : 41,9 Mb
Release : 2017-11-01
Category : Computers
ISBN : 9783319687599

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Simulated Evolution and Learning by Yuhui Shi,Kay Chen Tan,Mengjie Zhang,Ke Tang,Xiaodong Li,Qingfu Zhang,Ying Tan,Martin Middendorf,Yaochu Jin Pdf

This book constitutes the refereed proceedings of the 11th International Conference on Simulated Evolution and Learning, SEAL 2017, held in Shenzhen, China, in November 2017. The 85 papers presented in this volume were carefully reviewed and selected from 145 submissions. They were organized in topical sections named: evolutionary optimisation; evolutionary multiobjective optimisation; evolutionary machine learning; theoretical developments; feature selection and dimensionality reduction; dynamic and uncertain environments; real-world applications; adaptive systems; and swarm intelligence.

Author : Youssef Hamadi,Marc Schoenauer
Publisher : Springer
Page : 514 pages
File Size : 51,9 Mb
Release : 2012-10-01
Category : Computers
ISBN : 9783642344138

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Learning and Intelligent Optimization by Youssef Hamadi,Marc Schoenauer Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Learning and Intelligent Optimization, LION 6, held in Paris, France, in January 2012. The 23 long and 30 short revised papers were carefully reviewed and selected from a total of 99 submissions. The papers focus on the intersections and uncharted territories between machine learning, artificial intelligence, mathematical programming and algorithms for hard optimization problems. In addition to the paper contributions the conference also included 3 invited speakers, who presented forefront research results and frontiers, and 3 tutorial talks, which were crucial in bringing together the different components of LION community.

Author : Claus Aranha,Carlos Martín-Vide,Miguel A. Vega-Rodríguez
Publisher : Springer Nature
Page : 126 pages
File Size : 41,9 Mb
Release : 2021-11-03
Category : Computers
ISBN : 9783030904258

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Theory and Practice of Natural Computing by Claus Aranha,Carlos Martín-Vide,Miguel A. Vega-Rodríguez Pdf

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.

Author : Henning Schnoor
Publisher : Cuvillier Verlag
Page : 137 pages
File Size : 47,8 Mb
Release : 2007
Category : Electronic
ISBN : 9783867271769

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Algebraic Techniques for Satisfiability Problems by Henning Schnoor Pdf

Author : Tsutomu Sasao
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461531548

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Logic Synthesis and Optimization by Tsutomu Sasao Pdf

Logic Synthesis and Optimization presents up-to-date research information in a pedagogical form. The authors are recognized as the leading experts on the subject. The focus of the book is on logic minimization and includes such topics as two-level minimization, multi-level minimization, application of binary decision diagrams, delay optimization, asynchronous circuits, spectral method for logic design, field programmable gate array (FPGA) design, EXOR logic synthesis and technology mapping. Examples and illustrations are included so that each contribution can be read independently. Logic Synthesis and Optimization is an indispensable reference for academic researchers as well as professional CAD engineers.