Title :
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
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;
Conference_Titel :
Multiple-Valued Logic, 2002. ISMVL 2002. Proceedings 32nd IEEE International Symposium on
Conference_Location :
Boston, MA
Print_ISBN :
0-7695-1462-6
DOI :
10.1109/ISMVL.2002.1011074
