Representations Of Multiple Valued Logic Functions

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Representations of Multiple-Valued Logic Functions

Author : Radomir S. Stankovic
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

Author : Stankovic
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:

Multiple-Valued Logic

Author : D. Michael Miller
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

Representation of Multiple-valued Logic Functions

Author : Radomir S. Stanković
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.

Computer Science and Multiple-Valued Logic

Author : David C. Rine
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.

Modern Uses of Multiple-Valued Logic

Author : M. Dunn
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.

Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook

Author : Svetlana N. Yanushkevich
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.

Multiple-Valued Logic Design

Author : G Epstein
Publisher : Routledge
ISBN 13 : 1351429620
Total Pages : 383 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Multiple-Valued Logic Design by : G Epstein

Download or read book Multiple-Valued Logic Design written by G Epstein and published by Routledge. This book was released on 2017-09-29 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple-Valued Logic Design: An Introduction explains the theory and applications of this increasingly important subject. Written in a clear and understandable style, the author develops the material in a skillful way. Without using a huge mathematical apparatus, he introduces the subject in a general form that includes the well-known binary logic as a special case. The book is further enhanced by more 200 explanatory diagrams and circuits, hardware and software applications with supporting PASCAL programming, and comprehensive exercises with even-numbered answers for every chapter. Requiring introductory knowledge in Boolean algebra, 2-valued logic, or 2-valued switching theory, Multiple-Valued Logic Design: An Introduction is an ideal book for courses not only in logic design, but also in switching theory, nonclassical logic, and computer arithmetic. Computer scientists, mathematicians, and electronic engineers can also use the book as a basis for research into multiple-valued logic design.

Many-Valued Logics 2

Author : Leonard Bolc
Publisher : Springer Science & Business Media
ISBN 13 : 9783540645078
Total Pages : 328 pages
Book Rating : 4.6/5 (45 download)

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Book Synopsis Many-Valued Logics 2 by : Leonard Bolc

Download or read book Many-Valued Logics 2 written by Leonard Bolc and published by Springer Science & Business Media. This book was released on 2003-10-23 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many-valued logics are becoming increasingly important in all areas of computer science. This is the second volume of an authoritative two-volume handbook on many valued logics by two leading figures in the field. While the first volume was mainly concerned with theoretical foundations, this volume emphasizes automated reasoning, practical applications, and the latest developments in fuzzy logic and rough set theory. Among the applications presented are those in software specification and electronic circuit verification.

ISMVL 2004

Author : International Symposium on Multiple Valued Logic (34, 2004, Toronto)
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:

1997 27th International Symposium on Multiple-Valued Logic

Author :
Publisher :
ISBN 13 :
Total Pages : 308 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis 1997 27th International Symposium on Multiple-Valued Logic by :

Download or read book 1997 27th International Symposium on Multiple-Valued Logic written by and published by . This book was released on 1997 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Design of Multiple-valued Logic Systems

Author : Donald D. Givone
Publisher :
ISBN 13 :
Total Pages : 114 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis The Design of Multiple-valued Logic Systems by : Donald D. Givone

Download or read book The Design of Multiple-valued Logic Systems written by Donald D. Givone and published by . This book was released on 1968 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: A multiple-valued algebra is introduced as a mathematical model for the study of switching circuits having two or more logic values. A minimization criterion is given and various minimization techniques for manipulating functions expressed in this algebra. In particular, an algorithmic method is presented for deriving all minimal cost representations of the switching functions. (Author).

Handbook of Bioinspired Algorithms and Applications

Author : Stephan Olariu
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

The Eighth International Symposium on Multiple-Valued Logic

Author :
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:

Beyond Two: Theory and Applications of Multiple-Valued Logic

Author : Melvin Fitting
Publisher : Physica
ISBN 13 : 3790817694
Total Pages : 374 pages
Book Rating : 4.7/5 (98 download)

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Book Synopsis Beyond Two: Theory and Applications of Multiple-Valued Logic by : Melvin Fitting

Download or read book Beyond Two: Theory and Applications of Multiple-Valued Logic written by Melvin Fitting and published by Physica. This book was released on 2013-06-05 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.

A Treatise on Many-valued Logics

Author : Siegfried Gottwald
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.

Neutrality and Many-Valued Logics

Author : Andrew Schumann
Publisher : Infinite Study
ISBN 13 : 159973026X
Total Pages : 123 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Neutrality and Many-Valued Logics by : Andrew Schumann

Download or read book Neutrality and Many-Valued Logics written by Andrew Schumann and published by Infinite Study. This book was released on 2007 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen's style sequents that was introduced independently by Avron and Pottinger. In particular, we consider Hilbert's style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz's, Godel?s, and Product logics. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Godel?s, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. We consider two cases of non-Archimedean multi-valued logics: the first with many-validity in the interval [0,1] of hypernumbers and the second with many-validity in the ring of p-adic integers. Notice that in the second case we set discrete infinite-valued logics. Logics investigated: 1. hyperrational valued Lukasiewicz's, Godel?s, and Product logics, 2. hyperreal valued Lukasiewicz's, Godel?s, and Product logics, 3. p-adic valued Lukasiewicz's, Godel?s, and Post's logics.