TESTING AND REALIZATION OF TERNARY THRESHOLD FUNCTIONS.

For realization of multivalued threshold functions (including binary threshold functions) it is important to test a given logical function to decide whether it is a threshold function. At the present time, however, no effective methods for testing have been found. Thus, as an alternative solution to the problem of the realization, we consider the minimization of the set of input vectors required to conduct the test and the realization. In this paper the existing concepts of the vectors of connecting edges and boundary vectors for binary logical functions are extended to ternary logical functions, and the relations between the two extended concepts and ternary threshold functions are investigated. The extension of the concepts from binary logical functions to ternary can be the basis for further extension to n-ary logical functions with n greater than 3. Using the relations between vectors of connecting edges and boundary vectors of ternary functions, a method for constructing the set of semi-boundary vectors of a ternary threshold function from the connection tables is formulated. Properties of solution vectors for a ternary threshold function are investigated and a method for testing and realizing a ternary threshold function by using semi-boundary vectors is presented. This method can be directly extended so as to yield a method for testing and realization of any multivalued threshold function.