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.