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 computationaly hard (namely #Phard). Therefore, algorithms to solve it can be compare 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 shown that this method is in general much more efficient than classical methods that work by rewriting the sum of products under study into a sum of disjoint products. Then, we derive from our method a factorization algorithm to be used as a proprocessing method for Binary Decision Diagrams. We show by means of experimental results that this latter technology outperforms the formers. keywords: Sum-of-(Disjoints)-Products, Pivotal Decomposition, Binary Decision Diagrams.