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
