Multiple-Valued Input Index Generation Functions: Optimization by Linear Transformation

In an incompletely specified function f, don´t care values can be chosen to minimize the number of variables to represent f. We consider incompletely specified multiple-valued input index generation functions f : D → {1, 2,...,k}, where D ⊆ Pⁿ and P={0, 1, 2, ..., p-1}. We show that most functions can be represented with 2[log_p (k+1) ]$ or fewer variables, where k denotes the number of elements in D. Also, we introduce linear transformations to further reduce the number of variables. Experimental results support these observations.