Multiple-valued logical functions derived from two-valued input multiple-valued output functions

A derivation rule for deriving p-valued logical functions from two-valued input p-valued output functions ((2, p)-functions) is provided. It is proved that by this rule, one p-valued function is derived from one (2, p)-function uniquely. The relationship between some classes of (2, p) functions and the classes of p-valued functions derived from them is clarified. Especially important is the result that all the p-valued unate functions are derived from monotonic (2, p)-functions, all the p-valued majority functions are derived from (2, p)-threshold functions, and all the p-valued functions derived from nonmonotonic (2, p)-functions can be expressed by logical formulae using only AND, OR, constants, and certain variables.<>