Using lower bounds during dynamic BDD minimization

Ordered binary decision diagrams (BDDs) are a data structure for the representation and manipulation of Boolean functions, often applied in very large scale integration (VLSI) computer-aided design (CAD). The choice of variable ordering largely influences the size of the BDD; its size may vary from linear to exponential. The most successful methods to find good orderings are based on dynamic variable reordering, i.e., exchanging neighboring variables. This basic operation has been used in various variants, like sifting and window permutation. In this paper, we show that lower bounds computed during the minimization process can speed up the computation significantly. First, lower bounds are studied from a theoretical point of view. Then these techniques are incorporated in dynamic minimization algorithms. By the computation of good lower bounds, large parts of the search space can be pruned, resulting in very fast computations. Experimental results are given to demonstrate the efficiency of the approach.