Representations of Multiple-Valued Logic Functions

Representations of Multiple-Valued Logic Functions

Radomir S. Stankovic, Jaakko Astola, Claudio Moraga
ISBN: 9781608459421 | PDF ISBN: 9781608459438
Copyright © 2012 | 168 Pages | Publication Date: 01/01/2012

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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. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools.

This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions.

Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them.

Table of Contents

Multiple-Valued Logic Functions
Functional Expressions for Multiple-Valued Functions
Spectral Representations of Multiple-Valued Functions
Decision Diagrams for Multiple-Valued Functions
Fast Calculation Algorithms

About the Author(s)

Radomir S. Stankovic, University of Nis, Serbia
Radomir S. Stankovic received a B.Sc. degree in Electronic Engineering from the faculty of Electronics, University of Nis, Serbia, in 1976, and M.Sc. and Ph.D. degrees in Applied Mathematics from the Faculty of Electrical Engineering, University of Belgrade, Serbia, in 1984 and 1986, respectively. Currently, he is a Professor at the Department of Computer Science, Faculty of Electronics, University of Nis, Serbia. In 1997, he was awarded by the Kyushu Institute of Technology Fellowship and worked as a visiting researcher at the Department of Computer Science and Electronics, Kyushu Institute of Technology, Iizuka, Fukuoka, Japan. In 2000 he was awarded by the Nokia Visiting Researcher Fellowship by Nokia, Finland. Since 1999, he has worked in part at the Tampere International Center for Signal Processing, Department of Signal Processing, Faculty of Computing and Electrical Engineering, Tampere University of Technology, Tampere, Finland, where he is currently an adjunct professor. His research interests include switching theory, multiple-valued logic, spectral techniques, and signal processing

Jaakko Astola, Tampere University of Technology, Finland
Jaakko T. Astola received B.Sc., M.Sc., Licenciate, and Ph.D. degrees in Mathematics (specializing in error-correcting codes) from Turku University, Finland in 1972, 1973, 1975, and 1978, respectively. From 1976-1977 he was with the Research Institute for Mathematical Sciences of Kyoto University, Kyoto, Japan. Between 1979 and 1987 he was with the Department of Information Technology, Lappeenranta University of Technology, Lappeenranta, Finland, holding various teaching positions in Mathematics, Applied Mathematics, and Computer Science. In 1984, he worked as a visiting scientist at Eindhoven University of Technology, The Netherlands. From 1987-1992 he was an Associate Professor in Applied Mathematics at Tampere University, Tampere, Finland. Since 1993, he has been a Professor of Signal Processing and the Director of Tampere International Center for Signal Processing, leading a group of about 60 scientists and was nominated Academy Professor by Academy of Finland (2001-2006). Currently, he is Director of the Centre of Excellence of the Academy of Finland in Signal Processing. His research interests include signal processing, coding theory, spectral techniques, and statistics. He is a Fellow of IEEE.

Claudio Moraga, European Centre for Soft Computing, Spain and Technical University of Dortmund, Germany
Claudio Moraga received a B.Sc. in Electrical Engineering from the Catholic University of Valparaiso (UCV), Chile, in 1961 and a M.Sc. in Electrical Engineering from the Massachusetts Institute of Technology (MIT), in 1962, and a Ph.D. in Electrical Engineering (Summa cum Laude) from the Technical University "Federico Santa Maria" (UTFSM), Valparaiso, Chile, in 1972. From 1963-1970 he was a lecturer at the Deptartment of Electrical Engineering, UCV, where he served as the head of the department from 1964-1970. From 1970-1973 he worked at the Technical University "Federico Santa Maria" (UTFSM), as an Associate Professor of Electrical Engineering, and was promoted to a Professor of Computer Science in 1973. Also during that time, from 1972-1973, he also served as the Academic Vice President of the Technical University "Frederico Santa Maria" (UTFSM). From November 1974-August 1976, he was awarded the Alexander von Humboldt Research Fellowship at the Department of Computer Science, University of Dortmund, FRG. He continued working at the same University as a lecturer from September 1976-March 1985. From April 1985-September 1986, he was a Professor of Computer Science, in the area of Computer Architecture, at the Department of Mathematics and Computer Science, University of Bremen, FRG. From October 1986-February 2002, he was a Professor of Computer Science, in the area Theory of Automata at the Department of Computer Science, University of Dortmund, FRG. Since March 2002, Claudio Moraga is a Professor Emeritus at the Department of Computer Science, University of Dortmund, FRG. Since March 2006, he has been a Researcher Emeritus at the European Centre for Soft Computing, Mieres, Asturias, Spain. Claudio Moraga is a member of the IEEE Technical Committee on Multiple-valued Logic (USA), and a member of the editorial board of several international journals,as well as holding several awards,including the "Long Service Award for outstanding contributions to Multiple-valued Logic since 1971" from the IEEE TC on Multiple-valued Logic, received in May 2004, and the best paper award in Multiple-valued Logic at the ISMVL 2010. In 2005, Claudio Moraga was awarded the title of the Doctor Honoris Causa of the University of Nis, Serbia.

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