An implicit formulation for exact BDD minimization

This paper addresses the problem of binary decision diagram (BDD) minimization in the presence of don’t caresets. Specifically, given an incompletely specified function g and a fixed ordering of the variables, we propose anexact algorithm for selectingf such that f is a cover for g and the binary decision diagram for f is of minimumsize. The approach described is the only known exact algorithm for this problem not based on the enumeration of allpossible assignments to the points in the don’t care set. We also present a proof that this problem is NP-complete, aresult that was also recently obtained in an independent way by other authors.We show that the BDD minimization problem can be formulated as a binate covering problem and solved usingimplicit enumeration techniques. In particular, we show that the minimum-sized binary decision diagram compatiblewith the specification can be found by solving a problem that is very similar to the problem of reducing incompletelyspecified finite state machines. We report experiments of an implicit implementation of our algorithm, by meansof which a class of interesting examples was solved exactly. We compare it with existing heuristic algorithms, tomeasure the quality of the latter.