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Enumeration of Ternary Threshold Functions of Three Variables
April 1972 (vol. 21 no. 4)
pp. 402-407
Tsunehiro Aibara, Department of Electrical Engineering, Ehime University, Matsuyama, Japan.
Michihiro Akagi, Electrical Communication Laboratory, Nippon Telegraph and Telephone Corporation, Musashino, Tokyo, Japan.
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.
Citation:
Tsunehiro Aibara, Michihiro Akagi, "Enumeration of Ternary Threshold Functions of Three Variables," IEEE Transactions on Computers, vol. 21, no. 4, pp. 402-407, April 1972, doi:10.1109/TC.1972.5008986
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