Representations Of Multiple Valued Logic Functions
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| Author | : Radomir S. Stankovic |
| Publisher | : Springer Nature |
| Total Pages | : 154 |
| Release | : 2022-06-01 |
| Genre | : Technology & Engineering |
| ISBN | : 303179852X |
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 | : Svetlana N. Yanushkevich |
| Publisher | : CRC Press |
| Total Pages | : 960 |
| Release | : 2018-10-03 |
| Genre | : Technology & Engineering |
| ISBN | : 1351836382 |
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.
| Author | : D. Michael Miller |
| Publisher | : Springer Nature |
| Total Pages | : 135 |
| Release | : 2022-05-31 |
| Genre | : Technology & Engineering |
| ISBN | : 3031797795 |
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 | : David C. Rine |
| Publisher | : Elsevier |
| Total Pages | : 563 |
| Release | : 2014-05-12 |
| Genre | : Technology & Engineering |
| ISBN | : 1483257924 |
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.
| Author | : M. Dunn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 341 |
| Release | : 2012-12-06 |
| Genre | : Philosophy |
| ISBN | : 9401011613 |
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.
| Author | : International Symposium on Multiple Valued Logic (34, 2004, Toronto) |
| Publisher | : Institute of Electrical & Electronics Engineers(IEEE) |
| Total Pages | : 378 |
| Release | : 2004 |
| Genre | : Computers |
| ISBN | : 9780769521305 |
| Author | : |
| Publisher | : |
| Total Pages | : 308 |
| Release | : 1997 |
| Genre | : Logic circuits |
| ISBN | : |
| Author | : Stephan Olariu |
| Publisher | : CRC Press |
| Total Pages | : 684 |
| Release | : 2005-09-29 |
| Genre | : Computers |
| ISBN | : 1420035061 |
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
| Author | : |
| Publisher | : |
| Total Pages | : 312 |
| Release | : 1978 |
| Genre | : Many-valued logic |
| ISBN | : |
| Author | : Tsutomu Sasao |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 1996-04-30 |
| Genre | : Technology & Engineering |
| ISBN | : 9780792397205 |
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.
