Author: Radomir S. Stankovic
Publisher: Springer Nature
ISBN: 303179852X
Category : Technology & Engineering
Languages : en
Pages : 154
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Book Description
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
Author: D. Michael Miller
Publisher: Springer Nature
ISBN: 3031797795
Category : Technology & Engineering
Languages : en
Pages : 135
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Book Description
Multiple Valued Logic: Concepts and Representations begins with a survey of the use ofmultiple-valued logic in several modern application areas including electronic design automation algorithms and circuit design. The mathematical basis and concepts of various algebras and systems of multiple valued logic are provided including comparisons among various systems and examples of their application. The book also provides an examination of alternative representations of multiple-valued logic suitable for implementation as data structures in automated computer applications. Decision diagram structures for multiple valued applications are described in detail with particular emphasis on the recently developed quantum multiple valued decision diagram. Table of Contents: Multiple Valued Logic Applications / MVL Concepts and Algebra / Functional Representations / Reversible andQuantum Circuits / Quantum Multiple-Valued Decision Diagrams / Summary / Bibliography
Author: Vasile Patrascu
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 10
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Book Description
The paper presents some steps for multi-valued representation of neutrosophic information. These steps are provided in the framework of multivalued logics using the following logical value: true, false, neutral, unknown and saturated. Also, this approach provides some calculus formulae for the following neutrosophic features: truth, falsity, neutrality, ignorance, underdefinedness, over-definedness, saturation and entropy. In addition, it was defined net truth, definedness and neutrosophic score.
Author: Tsutomu Sasao
Publisher: Springer Science & Business Media
ISBN: 1461313856
Category : Technology & Engineering
Languages : en
Pages : 344
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Book Description
Representations of Discrete Functions is an edited volume containing 13 chapter contributions from leading researchers with a focus on the latest research results. The first three chapters are introductions and contain many illustrations to clarify concepts presented in the text. It is recommended that these chapters are read first. The book then deals with the following topics: binary decision diagrams (BDDs), multi-terminal binary decision diagrams (MTBDDs), edge-valued binary decision diagrams (EVBDDs), functional decision diagrams (FDDs), Kronecker decision diagrams (KDDs), binary moment diagrams (BMDs), spectral transform decision diagrams (STDDs), ternary decision diagrams (TDDs), spectral transformation of logic functions, other transformations oflogic functions, EXOR-based two-level expressions, FPRM minimization with TDDs and MTBDDs, complexity theories on FDDs, multi-level logic synthesis, and complexity of three-level logic networks. Representations of Discrete Functions is designed for CAD researchers and engineers and will also be of interest to computer scientists who are interested in combinatorial problems. Exercises prepared by the editors help make this book useful as a graduate level textbook.
Author: Stankovic
Publisher:
ISBN: 9781608459087
Category :
Languages : en
Pages :
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Book Description
Author: Dmitriĭ Petrovich Zhelobenko
Publisher: American Mathematical Soc.
ISBN: 9780821886649
Category : Mathematics
Languages : en
Pages : 464
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Book Description
Author: Wu-Ki Tung
Publisher: World Scientific Publishing Company
ISBN: 981310404X
Category : Representations of groups
Languages : en
Pages : 336
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Book Description
An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet. Request Inspection Copy
Author: Philipp Niemann
Publisher: Springer
ISBN: 331963724X
Category : Computers
Languages : en
Pages : 126
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Book Description
This book discusses modern approaches and challenges of computer-aided design (CAD) of quantum circuits with a view to providing compact representations of quantum functionality. Focusing on the issue of quantum functionality, it presents Quantum Multiple-Valued Decision Diagrams (QMDDs – a means of compactly and efficiently representing and manipulating quantum logic. For future quantum computers, going well beyond the size of present-day prototypes, the manual design of quantum circuits that realize a given (quantum) functionality on these devices is no longer an option. In order to keep up with the technological advances, methods need to be provided which, similar to the design and synthesis of conventional circuits, automatically generate a circuit description of the desired functionality. To this end, an efficient representation of the desired quantum functionality is of the essence. While straightforward representations are restricted due to their (exponentially) large matrix descriptions and other decision diagram-like structures for quantum logic suffer from not comprehensively supporting typical characteristics, QMDDs employ a decomposition scheme that more naturally models quantum systems. As a result, QMDDs explicitly support quantum-mechanical effects like phase shifts and are able to take more advantage of corresponding redundancies, thereby allowing a very compact representation of relevant quantum functionality composed of dozens of qubits. This provides the basis for the development of sophisticated design methods as shown for quantum circuit synthesis and verification.
Author: John K. Gilbert
Publisher: Springer Science & Business Media
ISBN: 1402052677
Category : Education
Languages : en
Pages : 326
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Book Description
External representations (pictures, diagrams, graphs, concrete models) have always been valuable tools for the science teacher. This book brings together the insights of practicing scientists, science education researchers, computer specialists, and cognitive scientists, to produce a coherent overview. It links presentations about cognitive theory, its implications for science curriculum design, and for learning and teaching in classrooms and laboratories.
Author: Peggy Van Meter
Publisher: Routledge
ISBN: 0429813651
Category : Education
Languages : en
Pages : 696
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Book Description
In and out of formal schooling, online and off, today’s learners must consume and integrate a level of information that is exponentially larger and delivered through a wider range of formats and viewpoints than ever before. The Handbook of Learning from Multiple Representations and Perspectives provides a path for understanding the cognitive, motivational, and socioemotional processes and skills necessary for learners across educational contexts to make sense of and use information sourced from varying inputs. Uniting research and theory from education, psychology, literacy, library sciences, media and technology, and more, this forward-thinking volume explores the common concerns, shared challenges, and thematic patterns in our capacity to make meaning in an information-rich society. Chapter 16 of this book is freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license available at http://www.taylorfrancis.com/books/e/9780429443961.
