Fast exact minimization of BDD's

We present a new exact algorithm for finding the optimal variable ordering for reduced ordered binary decision diagrams (BDD's). The algorithm makes use of a lower bound technique known from very large scale integration design. Up to now this technique has been used only for theoretical considerations and it is adapted here for this purpose. Furthermore, the algorithm supports symmetry aspects and uses a hashing based data structure. Experimental results are given to demonstrate the efficiency of our approach. We succeeded in minimizing several functions, including adders with up to 64 variables, for which all other previously presented approaches fail.