Multiple-valued combinational circuits with feedback

We consider the use of feedback loops in the realization of multiple-valued combinational circuits. We show that the number of purely combinational configurations in an r-valued system is 1/r of the total number. Thus, as the radix increases, the fraction of combinational configurations decreases. We also show that, for every radix value r, there is a circuit with feedback realizing a combinational logic function that has fewer gates than any feedback-free circuit