Enumeration of Ternary Threshold Functions of Three Variables

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.