Classification of Ternary Logic Functions by NPC Operations
Takako Soma and Takashi Soma
Classification of ternary logic functions by NPC group of operations is investigated using ternary parametron logic. Based on multiplexor (MUX) realization of a function, a self-dual function is constructed by introducing Goto’s self-dualizing variable which feeds constant signals to MUX circuit. Self-dualizing operation is an operation to transform from one function to another among functions realized by different values of self-dualizing variable. It is an element of NPC group which is a combination of permutation operation on values and positions of variables (Negation and Permutation), and that on values of function (Cyclic permutation). These operations can be formulated as an exponentiation group and the equivalence class count is obtained from the cycle index of the group.
Keywords: Phasor based ternary logic, ternary logic function, self-dualizing operation, exponentiation group, classification of functions.