Reducing variable dependency in combinational circuits

The problem of encoding inputs to an n-input, 2-output combinational circuit so as to reduce the number of variables upon which the two output functions depend is considered in this paper. It is assumed that the number of input conditions (n-vectors) which must produce each output state is given. It is clear that for each mapping of n-vectors into output status a different pair of output functions will be specified. The objective of this work is to find that pair of output functions which is independent of as many of the input variables as possible. The problem is first considered for the case where all 2n input conditions are specified. The solution obtained here is later generalized to allow for don´t care conditions. The generalization of the problem to m output functions is also discussed.