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Multiple valued logic concepts and representations /

Multiple-Valued Logic: Concepts and Representations begins with a survey of the use of multiple-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-value...

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Bibliographic Details
Main Author: Miller, D. Michael.
Other Authors: Thornton, Mitchell Aaron.
Format: Electronic
Language:English
Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2008.
Series:Synthesis lectures on digital circuits and systems (Online) ; #12.
Subjects:
Many-valued logic.
Quantum logic.
Online Access:Abstract with links to full text
Table of Contents:
  • Multiple-valued logic applications
  • Introduction
  • MVL in EDA-CAD methods
  • Hardware description languages
  • Logic synthesis
  • Logic simulation
  • Digital hardware testing
  • Formal verification
  • MVL circuit design
  • Logic circuit design with MVL signals
  • Memory circuits
  • Computer arithmetic circuits
  • Programmable logic arrays (PLAs)
  • MVL circuits utilizing next-generation devices
  • Resonant tunneling diodes
  • Single electron transistors
  • MV quantum logic
  • Organization of the book
  • MVL concepts and algebra
  • Introduction
  • Sets and relations
  • Relations as graphs
  • Hasse diagrams
  • Finite lattices
  • Algebraic structures
  • Functions
  • Rings
  • Fields
  • Boolean algebra
  • Basic definition
  • Alternative definitions
  • Boolean normal forms
  • Logic systems and algebras
  • MVL operators
  • Functional completeness
  • Example MVL algebras based on non-modular operators
  • Lukasiewicz logic
  • Post logic and algebra
  • Bochvar logic
  • Kleene logic
  • Allen and Givone algebra
  • Vranesic, Lee and Smith algebra
  • Example MVL algebras based on modular operators
  • Cohn algebra
  • Pradhan algebra
  • Dubrova and Muzio algebra
  • Summary of MVL algebras
  • Functional representations
  • Logic tables
  • Hypercubes
  • Maps
  • Binary maps
  • Multiple-valued maps
  • Cube notation
  • Binary cubes
  • Multiple-valued cubes
  • Cube representation of functions
  • Operations on cubes
  • Function operations
  • Decision diagrams
  • Binary decision diagrams
  • Multiple-valued decision diagrams
  • MDD implementation techniques
  • Reversible and quantum circuits
  • Binary reversible gates and circuits
  • MVL reversible gates and circuits
  • Matrix representation of reversible gates and circuits
  • Quantum gates and circuits
  • Quantum multiple-valued decision diagrams
  • The QMDD structure
  • QMDD operations
  • QMDD gate matrix construction
  • Row and column vectors
  • Variable reordering for QMDD
  • QMDD implementation
  • Identity matrices
  • Edge weights
  • Complex number representation
  • Complex number computation tables
  • Unique and computed table hash functions
  • QMDD applications
  • Binary circuits
  • Ternary circuits
  • Circuit equivalence and verification
  • Summary
  • Bibliography.

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