Computer Science and Multiple-Valued Logic

Computer Science and Multiple-Valued Logic

Theory and Applications

1st Edition - January 1, 1977

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  • Editor: David C. Rine
  • eBook ISBN: 9781483257921

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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

Product details

  • No. of pages: 562
  • Language: English
  • Copyright: © North Holland 1977
  • Published: January 1, 1977
  • Imprint: North Holland
  • eBook ISBN: 9781483257921

About the Editor

David C. Rine

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