Preprocessing Boolean Formulae for BDDs in a Probabilistic Context

Inference in many probabilistic logic systems is based on representing the proofs of a query as a DNF Boolean formula. Assessing the probability of such a formula is known as a #P-hard task. In practice, a large DNF is given to a BDD software package to construct the corresponding BDD. The DNF has to be transformed into the input format of the package. This is the preprocessing step. In this paper we investigate and compare different preprocessing methods, including our new trie based approach. Our experiments within the ProbLog system show that the behaviour of the methods changes according to the amount of sharing in the original DNF. The decomposition method is preferred when there is not much sharing in the DNF, whereas DNFs with sharing benefit from our trie based method. While our methods are motivated and applied in the ProbLog context, our results are interesting for other applications that manipulate DNF Boolean formulae.