Can we trust module-respect heuristics?

Abstract

BDD (Binary Decision Diagrams) have proven to be a very efficient tool to assess Fault Trees. However, the size of BDD, and therefore the efficiency of the whole methodology, depends dramatically on the choice of variable ordering. The determination of the best variable ordering is intractable. Therefore, heuristics have been designed to select reasonably good variable orderings. One very important common feature for good static heuristics is to respect modules. In this paper, the notion of module-respect is studied in a systematic way. It is proved that under certain condition there always exists an optimal ordering that respects modules. This condition is that for each module there is always a smallest module BDD and each included module variable appears only once. On the other hand, it is shown that for the trees not satisfying the above sufficient condition the optimal orderings may not be able to be directly generated using module-respect heuristics, even when the shuffling strategy is used.