Representations of Multiple-Valued Logic Functions

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Publisher : Springer Nature
ISBN 13 : 303179852X
Total Pages : 154 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Representations of Multiple-Valued Logic Functions by : Radomir S. Stankovic

Download or read book Representations of Multiple-Valued Logic Functions written by Radomir S. Stankovic and published by Springer Nature. This book was released on 2022-06-01 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Representations of Multiple-Valued

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Author :
Publisher :
ISBN 13 : 9781608459087
Total Pages : pages
Book Rating : 4.4/5 (59 download)

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Book Synopsis Representations of Multiple-Valued by : Stankovic

Download or read book Representations of Multiple-Valued written by Stankovic and published by . This book was released on 2014-08-04 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Representation of Multiple-valued Logic Functions

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Author :
Publisher : Morgan & Claypool Publishers
ISBN 13 : 160845942X
Total Pages : 171 pages
Book Rating : 4.6/5 (84 download)

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Book Synopsis Representation of Multiple-valued Logic Functions by : Radomir S. Stanković

Download or read book Representation of Multiple-valued Logic Functions written by Radomir S. Stanković and published by Morgan & Claypool Publishers. This book was released on 2012 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multiple-Valued Logic

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Publisher : Springer Nature
ISBN 13 : 3031797795
Total Pages : 135 pages
Book Rating : 4.0/5 (317 download)

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Book Synopsis Multiple-Valued Logic by : D. Michael Miller

Download or read book Multiple-Valued Logic written by D. Michael Miller and published by Springer Nature. This book was released on 2022-05-31 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Computer Science and Multiple-Valued Logic

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Author :
Publisher : Elsevier
ISBN 13 : 1483257924
Total Pages : 563 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Computer Science and Multiple-Valued Logic by : David C. Rine

Download or read book Computer Science and Multiple-Valued Logic written by David C. Rine and published by Elsevier. This book was released on 2014-05-12 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science and Multiple-Valued Logic: Theory and Applications focuses on the processes, methodologies, and approaches involved in multiple-valued logic and its relationship to computer science. The selection first tackles an introduction to multiple-valued logic, lattice theory of post algebras, multiple-valued logic design and applications in binary computers, smallest many-valued logic for the treatment of complemented and uncomplemented error signals, and chain based lattices. Discussions focus on formulation, representation theory, theory and circuit design, logical tables, and unary operations. The text then examines multiple-valued signal processing with limiting, development of multiple-valued logic as related to computer science, p-algebras, and an algorithm for axiomatizing every finite logic. The book takes a look at completeness properties of multiple-valued logic algebras, computer simplification of multi-valued switching functions, and minimization of multivalued functions. Topics include generation of prime implicants, realizations, minimization algorithms, decomposition algorithm for multi-valued switching functions, and relation between the sum-of-products form and array of cubes. The selection is aimed at computer engineers, computer scientists, applied mathematicians, and physicists interested in multiple-valued logic as the discipline relates to computer engineering and computer science.

Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook

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Publisher : CRC Press
ISBN 13 : 1351836382
Total Pages : 960 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook by : Svetlana N. Yanushkevich

Download or read book Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook written by Svetlana N. Yanushkevich and published by CRC Press. This book was released on 2018-10-03 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decision diagram (DD) techniques are very popular in the electronic design automation (EDA) of integrated circuits, and for good reason. They can accurately simulate logic design, can show where to make reductions in complexity, and can be easily modified to model different scenarios. Presenting DD techniques from an applied perspective, Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook provides a comprehensive, up-to-date collection of DD techniques. Experts with more than forty years of combined experience in both industrial and academic settings demonstrate how to apply the techniques to full advantage with more than 400 examples and illustrations. Beginning with the fundamental theory, data structures, and logic underlying DD techniques, they explore a breadth of topics from arithmetic and word-level representations to spectral techniques and event-driven analysis. The book also includes abundant references to more detailed information and additional applications. Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook collects the theory, methods, and practical knowledge necessary to design more advanced circuits and places it at your fingertips in a single, concise reference.

Modern Uses of Multiple-Valued Logic

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Publisher : Springer Science & Business Media
ISBN 13 : 9401011613
Total Pages : 341 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Modern Uses of Multiple-Valued Logic by : M. Dunn

Download or read book Modern Uses of Multiple-Valued Logic written by M. Dunn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of invited papers from the 1975 International Sym posium on Multiple-valued Logic. Also included is an extensive bib liography of works in the field of multiple-valued logic prior to 1975 - this supplements and extends an earlier bibliography of works prior to 1965, by Nicholas Rescher in his book Many-Valued Logic, McGraw-Hill, 1969. There are a number of possible reasons for interest in the present volume. First, the range of various uses covered in this collection of papers may be taken as indicative of a breadth which occurs in the field of multiple-valued logic as a whole - the papers here can do no more than cover a small sample: question-answering systems, analysis of computer hazards, algebraic structures relating to multiple-valued logic, algebra of computer programs, fuzzy sets. Second, a large part of the interest in such uses and applications has occurred in the last twenty, even ten years. It would be too much to expect this to be reflected in Rescher's 1969 book. Third, in the 1970's a series of annual symposia have been held on multiple-valued logic, which have brought much of this into a sharp focus. * The 1971 and 1972 symposia were held at the SUNY at Buffalo, the 1973 symposium at the Uni versity of Toronto, and the 1974 symposium at West Virginia Uni versity. Papers from these symposia are included in the bibliography which may be found in an appendix of this book.

Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing

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Author :
Publisher : Springer
ISBN 13 : 331948317X
Total Pages : 382 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing by : Rudolf Seising

Download or read book Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing written by Rudolf Seising and published by Springer. This book was released on 2016-10-20 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Semi-tensor Product of Matrices and Its Applications

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Publisher : World Scientific
ISBN 13 : 9814374695
Total Pages : 610 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis An Introduction to Semi-tensor Product of Matrices and Its Applications by : Dai-Zhan Cheng

Download or read book An Introduction to Semi-tensor Product of Matrices and Its Applications written by Dai-Zhan Cheng and published by World Scientific. This book was released on 2012 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations.This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.

Complex-Valued Neural Networks with Multi-Valued Neurons

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Publisher : Springer Science & Business Media
ISBN 13 : 3642203523
Total Pages : 273 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Complex-Valued Neural Networks with Multi-Valued Neurons by : Igor Aizenberg

Download or read book Complex-Valued Neural Networks with Multi-Valued Neurons written by Igor Aizenberg and published by Springer Science & Business Media. This book was released on 2011-06-24 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex-Valued Neural Networks have higher functionality, learn faster and generalize better than their real-valued counterparts. This book is devoted to the Multi-Valued Neuron (MVN) and MVN-based neural networks. It contains a comprehensive observation of MVN theory, its learning, and applications. MVN is a complex-valued neuron whose inputs and output are located on the unit circle. Its activation function is a function only of argument (phase) of the weighted sum. MVN derivative-free learning is based on the error-correction rule. A single MVN can learn those input/output mappings that are non-linearly separable in the real domain. Such classical non-linearly separable problems as XOR and Parity n are the simplest that can be learned by a single MVN. Another important advantage of MVN is a proper treatment of the phase information. These properties of MVN become even more remarkable when this neuron is used as a basic one in neural networks. The Multilayer Neural Network based on Multi-Valued Neurons (MLMVN) is an MVN-based feedforward neural network. Its backpropagation learning algorithm is derivative-free and based on the error-correction rule. It does not suffer from the local minima phenomenon. MLMVN outperforms many other machine learning techniques in terms of learning speed, network complexity and generalization capability when solving both benchmark and real-world classification and prediction problems. Another interesting application of MVN is its use as a basic neuron in multi-state associative memories. The book is addressed to those readers who develop theoretical fundamentals of neural networks and use neural networks for solving various real-world problems. It should also be very suitable for Ph.D. and graduate students pursuing their degrees in computational intelligence.

Handbook of Bioinspired Algorithms and Applications

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Publisher : CRC Press
ISBN 13 : 1420035061
Total Pages : 684 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Bioinspired Algorithms and Applications by : Stephan Olariu

Download or read book Handbook of Bioinspired Algorithms and Applications written by Stephan Olariu and published by CRC Press. This book was released on 2005-09-29 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mystique of biologically inspired (or bioinspired) paradigms is their ability to describe and solve complex relationships from intrinsically very simple initial conditions and with little or no knowledge of the search space. Edited by two prominent, well-respected researchers, the Handbook of Bioinspired Algorithms and Applications reveals the

A Summary of Research 1995

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Publisher :
ISBN 13 :
Total Pages : 588 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis A Summary of Research 1995 by : United States. Naval Postgraduate School, Monterey, CA.

Download or read book A Summary of Research 1995 written by United States. Naval Postgraduate School, Monterey, CA. and published by . This book was released on 1995 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scientific and Technical Aerospace Reports

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Publisher :
ISBN 13 :
Total Pages : 558 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1984 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Eighth International Symposium on Multiple-Valued Logic

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Publisher :
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.X/5 ( download)

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Book Synopsis The Eighth International Symposium on Multiple-Valued Logic by :

Download or read book The Eighth International Symposium on Multiple-Valued Logic written by and published by . This book was released on 1978 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

ISMVL 2004

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Publisher : Institute of Electrical & Electronics Engineers(IEEE)
ISBN 13 : 9780769521305
Total Pages : 378 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis ISMVL 2004 by : International Symposium on Multiple Valued Logic (34, 2004, Toronto)

Download or read book ISMVL 2004 written by International Symposium on Multiple Valued Logic (34, 2004, Toronto) and published by Institute of Electrical & Electronics Engineers(IEEE). This book was released on 2004 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Treatise on Many-valued Logics

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Publisher :
ISBN 13 :
Total Pages : 624 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis A Treatise on Many-valued Logics by : Siegfried Gottwald

Download or read book A Treatise on Many-valued Logics written by Siegfried Gottwald and published by . This book was released on 2001 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: A growing interest in many-valued logic has developed which to a large extent is based on applications, intended as well as already realised ones. These applications range from the field of computer science, e.g. in the areas of automated theorem proving, approximate reasoning, multi-agent systems, switching theory, and program verification, through the field of pure mathematics, e.g. in independence of consistency proofs, in generalized set theories, or in the theory of particular algebraic structures, into the fields of humanities, linguistics and philosophy.

Automated Deduction in Multiple-valued Logics

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Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Automated Deduction in Multiple-valued Logics by : Reiner Hähnle

Download or read book Automated Deduction in Multiple-valued Logics written by Reiner Hähnle and published by . This book was released on 1993 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: A notation called sets-as-signs is developed, and then it is demonstrated how it can be used to modify any known inference method to handle many-valued logics. Applications are discussed, both in pure mathematics, and in hardware verification and interval arithmetic. Concludes with a historical overview of activities in many-valued theorem proving. Annotation copyright by Book News, Inc., Portland, OR