An implicit formulation for exact BDD minimization of incompletely specified functions

Abstract

This paper addresses the problem of binary decision diagram (BDD) minimization in the presence of don’t care sets. Specifically, given an incompletely specified function g and a fixed ordering of the variables, we propose an exact algorithm for selecting f such that f is a cover for g and the binary decision diagram for f is of minimum size. We proved that this problem is NP-complete. Here we show that the BDD minimization problem can be formulated as a binate covering problem and solved using implicit enumeration techniques similar to the ones used in the reduction of incompletely specified finite state machines.