Reed-Muller Canonical Forms in Multivalued Logic

Authors:
K. L. Kodandapani;R. V. Setlur
Affiliations:
Department of Electrical Engineering and Computer Science Program, Indian Institute of Technology;-
Venue:
IEEE Transactions on Computers
Year:
1975

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Abstract

Canonical forms for m-valued functions referred to as m-Reed-Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ?m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.