Reed-Muller tree-based minimisation of fixed polarity Reed-Muller expansions

Author

Aborhey, S.

Author_Institution

Dept. of Technol., Univ. of South Pacific, Suva, Fiji

Volume

148

Issue

2

fYear

2001

fDate

3/1/2001 12:00:00 AM

Firstpage

63

Lastpage

70

Abstract

A heuristic method for the determination of optimum or near-optimum fixed polarity Reed-Muller (FPRM) representation of multiple output, completely specified Boolean systems is presented. The Reed-Muller (RM) tree representation forms the conceptual framework for the method, which involves manipulations of arrays of cubes. A coding method that is well adapted to RM tree representation is presented. The minimisation method takes as input a disjoint sum of cubes representation of the Boolean system. Using Karpovsky´s complexity estimates as the basis for polarity selection, the method obtains the FPRM expansion by generating in one run an optimum or near optimum Reed-Muller tree representation

Keywords

Boolean functions; Reed-Muller codes; computational complexity; encoding; minimisation; Boolean system; Karpovsky´s complexity estimates; Reed-Muller tree-based minimisation; coding method; completely specified Boolean systems; conceptual framework; disjoint sum; fixed polarity Reed-Muller expansions; heuristic method; minimisation method; polarity selection;

fLanguage

English

Journal_Title

Computers and Digital Techniques, IEE Proceedings -

Publisher

iet

ISSN

1350-2387

Type

jour

DOI

10.1049/ip-cdt:20010252

Filename

926401