Ordered Binary Decision Diagrams (BDDs) are a data structure for efficient representation and manipulation of Boolean functions. They are frequently used in logic synthesis and formal verification. The size of BDDs depends on a chosen variable ordering, i.e. the size may vary from linear to exponential, and the problem of improving the variable ordering is known to be NP-complete.

In this paper we present a new exact branch & bound technique for determining an optimal variable order. In contrast to all previous approaches, that only considered one lower bound, our method makes use of a combination of three bounds and by this avoids unnecessary computations. The lower bounds are derived by generalization of a lower bound known from VLSI design. They allow to build the BDD either top down or bottom up. Experimental results are given to show the efficiency of our approach.