Tableaux, Path Dissolution, and Decomposable Negation Normal Form for Knowledge Compilation

Decomposable negation normal form (DNNF) was developed primarily for knowledge compilation. Formulas in DNNF are linkless, in negation normal form (NNF), and have the property that atoms are not shared across conjunctions. Full dissolvents are linkless NNF formulas that do not in general have the latter property. However, many of the applications of DNNF can be obtained with full dissolvents. Two additional methods — regular tableaux and semantic factoring — are shown to produce equivalent DNNF. A class of formulas is presented on which earlier DNNF conversion techniques are necessarily exponential; path dissolution and semantic factoring handle these formulas in linear time.