Representations of Multiple-Valued Logic Functions

Representations of Multiple-Valued Logic Functions PDF

Author: Radomir S. Stankovic

Publisher: Springer Nature

Published: 2022-06-01

Total Pages: 154

ISBN-13: 303179852X

DOWNLOAD EBOOK →

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

Representation of Multiple-valued Logic Functions

Representation of Multiple-valued Logic Functions PDF

Author: Radomir S. Stanković

Publisher: Morgan & Claypool Publishers

Published: 2012

Total Pages: 171

ISBN-13: 160845942X

DOWNLOAD EBOOK →

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

Multiple-Valued Logic PDF

Author: D. Michael Miller

Publisher: Springer Nature

Published: 2022-05-31

Total Pages: 135

ISBN-13: 3031797795

DOWNLOAD EBOOK →

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

Computer Science and Multiple-Valued Logic PDF

Author: David C. Rine

Publisher: Elsevier

Published: 2014-05-12

Total Pages: 563

ISBN-13: 1483257924

DOWNLOAD EBOOK →

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

Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook PDF

Author: Svetlana N. Yanushkevich

Publisher: CRC Press

Published: 2018-10-03

Total Pages: 960

ISBN-13: 1351836382

DOWNLOAD EBOOK →

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

Modern Uses of Multiple-Valued Logic PDF

Author: M. Dunn

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 341

ISBN-13: 9401011613

DOWNLOAD EBOOK →

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

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

Author: Rudolf Seising

Publisher: Springer

Published: 2016-10-20

Total Pages: 382

ISBN-13: 331948317X

DOWNLOAD EBOOK →

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

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

Author: Dai-Zhan Cheng

Publisher: World Scientific

Published: 2012

Total Pages: 610

ISBN-13: 9814374695

DOWNLOAD EBOOK →

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

Complex-Valued Neural Networks with Multi-Valued Neurons PDF

Author: Igor Aizenberg

Publisher: Springer Science & Business Media

Published: 2011-06-24

Total Pages: 273

ISBN-13: 3642203523

DOWNLOAD EBOOK →

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.

Lanterna Rally - Theme by Grace Themes