On the complexity of enumerations for multiple-valued Kleenean functions and unate functions

Abstract

Multiple-valued Kleenean functions are represented by multiple-valued AND, OR, NOT, variables and constants. In their previous work (see proc. of 20th Int. Symp. Multiple Valued Logic, IEEE, p.410-17, 1990), the authors pointed out that both mapping from Kleenean functions to some (3,p)-functions and mapping from unate functions to some (2,p)-functions are bijections. In this paper, by using the above relations, 3-up-to-7 valued Kleenean functions of 3-or-less variables are enumerated on a computer. Their exact numbers are tabulated. The results show that as p becomes larger, the number of p-valued Kleenean functions increases stepwise, and that of p-valued unate functions increases smoothly.<>