Ternary Walsh Transform and Its Operations for Completely and Incompletely Specified Boolean Functions

Author

Falkowski, Bogdan J. ; Yan, Shixing

Author_Institution

Nanyang Technol. Univ.

Volume

54

Issue

8

fYear

2007

Firstpage

1750

Lastpage

1764

Abstract

The new ternary Walsh transform is considered in this paper. Such a ternary Walsh transform can be used in a similar manner as the standard Walsh transform for binary logic functions as shown here. It is based on the Kronecker product as well as the Galois field and new ternary operations. The same hardware implementation can be used for both forward and inverse ternary Walsh transforms based on its fast algorithms and properties. The ternary Walsh transform is suitable for processing both completely and incompletely specified Boolean functions. Its properties for the decomposition and symmetry detections of the Boolean functions are shown.

Keywords

Galois fields; VLSI; Walsh functions; logic circuits; transforms; Boolean functions; Galois field; Kronecker product; VLSI circuits; binary logic functions; ternary Walsh transform; Boolean algebra; Boolean functions; Circuit synthesis; Circuit testing; Discrete transforms; Galois fields; Logic functions; Logic testing; Network synthesis; Very large scale integration; Boolean functions; Galois field (3) [GF(3)]; Walsh transforms; fast transforms; mathematical operations;

fLanguage

English

Journal_Title

Circuits and Systems I: Regular Papers, IEEE Transactions on

Publisher

ieee

ISSN

1549-8328

Type

jour

DOI

10.1109/TCSI.2007.902456

Filename

4282074