On OBDDs for CNFs of Bounded Treewidth

In this paper we show that a CNF cannot be compiled into an Ordered Binary Decision Diagram (OBDD) of fixed-parameter size parameterized by the primal graph tree width of the CNF. Thus we provide a parameterized separation between OBDDs and Sentential Decision Diagrams for which such fixed-parameter compilation is possible. We also show that the best existing parameterized upper bound for OBDDs in fact holds for incidence graph tree width parameterization.