Comparison of different features of quaternary Reed-Muller canonical forms and some new statistical results

Author

Adams, K.J. ; McGregor, J.

Author_Institution

Fac. of Inf., Ulster Univ., Londonderry, UK

fYear

2002

fDate

2002

Firstpage

83

Lastpage

88

Abstract

An integrated set of utility programs in C is presented. These can be used to perform calculations in any quaternary Reed-Muller algebra by entering addition and multiplication tables, and the zero-polarity transform matrix. For every completely specified quaternary function, canonical forms are generated for any pre-selected set of polarities. A laboratory is used to generate statistics comparing the realisation efficiency of five different algebras. A number of optimisation statistics were generated and are discussed, and, based on our experiments, the number of non-zero coefficients in a representation seems to be a reasonable measure of complexity

Keywords

Reed-Muller codes; arithmetic; computational complexity; mathematics computing; matrix algebra; multivalued logic; optimisation; statistics; utility programs; C programs; Reed-Muller algebra; addition tables; completely specified quaternary functions; complexity measure; integrated utility programs; multiplication tables; nonzero coefficients; optimisation statistics; pre-selected polarities; quaternary Reed-Muller canonical forms; realisation efficiency; zero-polarity transform matrix; Algebra; Arithmetic; Educational institutions; Informatics; Laboratories; Logic functions; Logic testing; Minimization; Programmable logic arrays; Statistics;

fLanguage

English

Publisher

ieee

Conference_Titel

Multiple-Valued Logic, 2002. ISMVL 2002. Proceedings 32nd IEEE International Symposium on

Conference_Location

Boston, MA

Print_ISBN

0-7695-1462-6

Type

conf

DOI

10.1109/ISMVL.2002.1011074

Filename

1011074