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Multiple Valued Logic [electronic resource]: Concepts and Representations

D. Michael Miller, Mitchell A. Thornton
Format
EBook; Book; Online
Published
San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2008.
Language
English
Related Title
Synthesis digital library of engineering and computer science.
Series
Synthesis Lectures on Digital Circuits and Systems
Synthesis Lectures on Digital Circuits and Systems (Online)
ISBN
1598291912 (electronic bk.), 9781598291919 (electronic bk.), 1598291904 (pbk.), 9781598291902 (pbk.)
Summary
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-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.
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
  • 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.
Description
Mode of access: World wide Web.
Notes
  • Part of: Synthesis digital library of engineering and computer science.
  • Title from PDF t.p. (viewed on October 11, 2008).
  • Series from website.
  • Includes bibliographical references (p. 127-134) and index.
Series Statement
Synthesis lectures on digital circuits and systems, 1932-3174 ; #12
Synthesis lectures on digital circuits and systems (Online) ; #12
Copyright Not EvaluatedCopyright Not Evaluated
Technical Details
  • Access in Virgo Classic
  • Staff View

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    a| 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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    a| 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-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.
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