A practical comparison of methods to assess sum-of-products

Many methods have been proposed in the literature to assess the probability of a sum-of-products. This problem has been shown computationally hard (namely #P-hard). Therefore, algorithms can be compared only from a practical point of view. In this article, we propose first an efficient implementation of the pivotal decomposition method. This kind of algorithms is widely used in the Artificial Intelligence framework. It is unfortunately almost never considered in the reliability engineering framework, but as a pedagogical tool. We report experimental results that show that this method is in general much more efficient than classical methods that rewrite the sum-of-products under study into an equivalent sum of disjoint products. Then, we derive from our method a factorization algorithm to be used as a preprocessing method for binary decision diagrams. We show by means of experimental results that this latter approach outperforms the formers.