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Enumeration of Ternary Threshold Functions of Three Variables | IEEE Journals & Magazine | IEEE Xplore

Enumeration of Ternary Threshold Functions of Three Variables


Abstract:

This note discusses the generation of ternary threshold functions of three variables. Merrill's generation method to generate ternary threshold functions is modified. The...Show More

Abstract:

This note discusses the generation of ternary threshold functions of three variables. Merrill's generation method to generate ternary threshold functions is modified. The number of ternary threshold functions of three variables is counted by a computer, the number is 85629. Tables of characterizing parameters of canonical ternary threshold functions of two and three variables are presented. A table-lookup method to realize ternary threshold functions is given. It is verified that the complete monotonicity (three-value extension of the complete monotonicity in two-valued logic) is a sufficient condition for a ternary three-variable switching function to be a ternary threshold function.
Published in: IEEE Transactions on Computers ( Volume: C-21, Issue: 4, April 1972)
Page(s): 402 - 407
Date of Publication: 29 May 2009

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