Index Generation Functions: Minimization Methods

Incompletely specified index generation functions can often be represented with fewer variables than original functions by appropriately assigning values to don't cares. The number of variables can be further reduced by using a linear transformation to the input variables. Minimization of variables under such conditions was considered to be a very hard problem. This paper surveys minimization methods for index generation functions. Major topics include 1) An upper bound on the number of variables to represent index generation functions,2) A heuristic minimization method using an ambiguity measure,3) A heuristic minimization method using remainders of a polynomial on GF(2),4) An exact minimization method using a SAT solver, and 5) Comparison of minimization methods.