Title Representation of multiple-valued logic functions / Radomir S. Stanković, Jaakko T. Astola, Claudio Moraga

Published Cham, Switzerland : Springer, ©2012

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Description 1 online resource (xiii, 154 pages) : illustrations illustration Series Synthesis lectures on digital circuits and systems, 1932-3174 ; #37 Synthesis lectures on digital circuits and systems ; #37. 1932-3174 Contents Acknowledgments -- 1. Multiple-valued logic functions -- 1.1 Tabular representations -- 1.2 Cubes -- 1.3 Encoding of variables -- 1.4 Other representations -- 1.5 Algebraic structures for multiple-valued functions -- 1.6 Functions with various properties 2. Functional expressions for multiple-valued functions -- 2.1 Functional expressions -- 2.2 Generalizations to multiple-valued functions -- 2.3 Sum-of-product expressions -- 2.4 Galois field expressions -- 2.5 Fixed-polarity GF-expressions -- 2.6 Efficiency of representations -- 2.7 Arithmetic expressions for multiple-valued functions -- 2.8 Haar-like expressions for multiple-valued functions -- 2.9 Sparse representations from covering codes 3. Spectral representations of multiple-valued functions -- 3.1 Fourier representations of logic functions -- 3.2 Construction of group characters -- 3.3 Haar series for multiple-valued logic functions 4. Decision diagrams for multiple-valued functions -- 4.1 Decision trees and decision diagrams -- 4.2 Reduction rules -- 4.3 Multiple-place decision diagrams -- 4.4 Reduction of decision trees -- 4.5 Functional decision diagrams for MV functions -- 4.6 Reed-Muller-Fourier decision diagrams -- 4.7 Vilenkin-Chrestenson decision diagrams -- 4.8 Haar spectral transform decision diagrams -- 4.9 Edge-valued decision diagrams -- 4.10 Construction of EVDDs -- 4.11 Construction of transforms from decision diagrams 5. Fast calculation algorithms -- 5.1 Illustrative examples of FFT-like algorithms -- Bibliography -- Authors' biographies -- Index Summary 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 Analysis multiple-valued logic functions Reed-Muller expressions Reed-Muller-Fourier expressions Galois field expressions spectral expressions decision diagrams Notes Part of: Synthesis digital library of engineering and computer science Bibliography Includes bibliographical references (pages 127-150) and index Notes Online resource; title from PDF title page (Morgan & Claypool, viewed Sept. 27, 2012) Subject Many-valued logic -- Mathematical models Signal processing -- Digital techniques -- Mathematical models Logic design. MATHEMATICS -- Infinity. MATHEMATICS -- Logic. Logic design Signal processing -- Digital techniques -- Mathematical models Form Electronic book Author Astola, Jaakko. Moraga, Claudio. ISBN 9781608459438 1608459438 9783031798528 303179852X

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