Representation of Incompletely Specified Binary and Multiple-Valued Logic Functions by Compact Decision Diagrams

We present a new technique for defining, analysing, and simplifying digital functions, through hand-calculations, easily demonstrable therefore in the classrooms. It can be extended to represent discrete systems beyond the Boolean logic. The method is graphical in nature and provides complete ‘‘implementation-free” description of the logical functions, similar to binary decision diagrams (BDDs) and Karnaugh-maps (K-maps). Transforming a function into the proposed representations (also the inverse) is a very intuitive process, easy enough that a person can hand-calculate these transformations. The algorithmic nature allows for its computing-based implementations. Because the proposed technique effectively transforms a function into a scatter plot, it is possible to represent multiple functions simultaneously. Usability of the method, therefore, is constrained neither by the number of inputs of the function nor by its outputs in theory. This, being a new paradigm, offers a lot of scope for further research. Here, we put forward a few of the strategies invented so far for using the proposed representation for simplifying the logic functions. Finally, we present extensions of the method: one that extends its applicability to multivalued discrete systems beyond Boolean functions and the other that represents the variants in terms of the coordinate system in use.

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Development of Programmable Logic Array for Multiple-Valued Logic Functions

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems ◽

10.1109/tcad.2020.2966676 ◽

2020 ◽

pp. 1-1 ◽

Cited By ~ 1

Author(s):

Vitaly Levashenko ◽

Igor Lukyanchuk ◽

Elena Zaitseva ◽

Miroslav Kvassay ◽

Jan Rabcan ◽

...

Keyword(s):

Programmable Logic ◽

Multiple Valued Logic ◽

Programmable Logic Array ◽

Logic Functions ◽

Logic Array

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On complexity of representation of multiple-valued logic functions as polarised polynomials

Discrete Mathematics and Applications ◽

10.1515/dma-2002-0304 ◽

2002 ◽

Vol 12 (3) ◽

Cited By ~ 4

Author(s):

S.N. Selezneva

Keyword(s):

Polynomial Form ◽

Multiple Valued Logic ◽

Logic Functions

AbstractThe notion of a polarised polynomial form is extended to the case of multiple-valued logic functions. We introduce the Shannon functions of weight and length of polarised polynomial forms of multiple-valued logic functions and give some bounds for them.

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