Techniques for Smaller Intermediary BDDs

Binary decision diagrams (BDDs) have proven to be a powerful technique for combating the state explosion problem. Their application to verification is usually centered around the computation of the transitive closure of some binary relation. The closure is usually computed with a fixed point algorithm that expands some set until it stops growing. Unfortunately, the BDDs that arise during the computation are often much larger than the final BDD. The computation may thus fail because of lack of memory, even if the final BDD would be small. To alleviate this problem, this paper proposes four variations of the fixed point algorithm. They reduce the sizes of the intermediary BDDs by “rounding down” the sets they represent in such a way that the final BDD does not change. Consequently, more iterations may be required to compute the fixed point, but the intermediary BDDs computed during the run are smaller. The performance of the new algorithms is illustrated with a large number of experiments.