On the Use of Partially Ordered Decision Graphs for Knowledge Compilation and Quantified Boolean Formulae∗

Decomposable Negation Normal Form formulae (DNNFs) form an interesting propositional fragment, both for efficiency and succinctness reasons. A famous subclass of the DNNF fragment is the OBDD fragment which offers many polytime queries and transformations, including quantifier eliminations (under some ordering restrictions). Nevertheless, the decomposable AND nodes at work in OBDDs enable only sequential decisions: clusters of variables are never assigned “in parallel” like in full DNNFs. This is an serious drawback since succinctness for the full DNNF fragment relies on such a “parallelization property”. This is why we suggest to go a step further, from (sequentially) ordered decision diagrams to (partially) ordered, decomposable decision graphs, in which any decomposable AND node is allowed, and not only assignment ones. We show that, like the OBDD fragment, such a new class offers many tractable queries and transformations, including quantifier eliminations under some ordering restrictions. Furthermore, we show that this class is strictly more succinct than OBDD.