Some relationships between multiple-valued Kleenean functions and ternary input multiple-valued output functions

Abstract

The multiple-valued Kleenean functions discussed are multiple-valued-logic functions represented by multiple-valued AND, OR, NOT, constants, and variables. First, when p=odd, ternary input p-valued output functions (or (3, p)-functions for short) are defined, and when p=even, ternary input (p+1)-valued output functions ((3, p+1)-functions for short) are defined by adding the value (p-1)/2. A derivation rule is proposed as a link between (3, p)-functions (or (3, p+1)-functions and p-valued (or (p+1)-valued) Kleenean functions. For p=odd, the mapping from monotonic (3,p)-functions to p-valued Kleenean functions is a bijection. For p=even, since the mapping from monotonic (3, p+1)-functions to p-valued Kleenean functions is not a bijection, a condition which makes the mapping a bijection is developed. Moreover, Kleenean functions with no constants are derived from B-ternary logic functions by the rule; then the mapping is a bijection. >