Exact Minimization of Boolean Decision Diagrams Using ImplicitTechniquesAbstractThis

This paper addresses the problem of Boolean decision diagram (BDD) minimization in the presence of don't care sets. Speciically, given an incompletely speciied function g and a xed ordering of the variables, we propose an exact algorithm for selecting f such that f is a cover for g and the Boolean decision diagram for f is of minimum size. The approach described is the only known exact algorithm for this problem not based on explicit enumeration of all possible assignments for the points in the don't care set. We show that the BDD minimization problem can be formulated as a binate covering problem and solved using implicit enumeration techniques. In particular, we show that the minimum-sized Boolean decision diagram compatible with the speciication can be found by solving a problem that is very similar to the problem of reducing incompletely speciied nite state machines. We report experiments of an implicit implementation of our algorithm, by means of which a class of interesting examples was solved exactly.