Computer Science and Multiple-Valued Logic - 1st Edition - ISBN: 9780720404067, 9781483257921

Computer Science and Multiple-Valued Logic

1st Edition

Theory and Applications

Editors: David C. Rine
eBook ISBN: 9781483257921
Imprint: North Holland
Published Date: 1st January 1977
Page Count: 562
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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.

Table of Contents

List of Contributors


Chapter 1. Introduction, Foundations, History, Motivation

Part I. Algebraic Theory

Chapter 2. From Fixed to Mixed Radix

Chapter 3. Decisive Implication

Chapter 4. Post Algebras through P0 and P1 Lattices

Chapter 5. An Algorithm for Axiomatizing Every Finite Logic

Chapter 6. Completeness Properties of Multiple-Valued Logic Algebras

Part II. Logic Design and Switching Theory

Chapter 7. Computer Simplification of Multi-Valued Switching Functions

Chapter 8. Minimization of Multivalued Functions

Chapter 9. The Allen-Givone Implementation Oriented Algebra

Chapter 10. Multi-Valued Asynchronous Networks

Chapter 11. Vector Boolean Algebra and Vector Boolean Calculus; Theory and Applications

Chapter 12. Binary Network Hazard Elimination by Multi-Valued Gates; Techniques and Relative Costs

Part III. Threshold Logic Design

Chapter 13. A Monograph on Ternary Threshold Logic

Part IV. Physical Components and Implementations

Chapter 14. Electronic Circuits for Multi-Valued Digital Systems

Chapter 15. Multiple-Valued Negative Resistance Integrated Circuits

Part V. Applications

Chapter 16. Application of Multiple-Valued Logic: Possibilities and Problems

Chapter 17. Multi-Valued Logic in Arithmetic Units

Chapter 18. Variable-Valued Logic and its Applications to Pattern Recognition and Machine Learning

Chapter 19. Multiple-Real-Valued Walsh Functions


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© North Holland 1977
North Holland
eBook ISBN:

About the Editor

David C. Rine

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