SDD: A New Canonical Representation of Propositional Knowledge Bases

We identify a new representation of propositional knowledge bases, the Sentential Decision Diagram (SDD), which is interesting for a number of reasons. First, it is canonical in the presence of additional properties that resemble reduction rules of OBDDs. Second, SDDs can be combined using any Boolean operator in polytime. Third, CNFs with n variables and treewidth w have canonical SDDs of size O(n2), which is tighter than the bound on OBDDs based on pathwidth. Finally, every OBDD is an SDD. Hence, working with the latter does not preclude the former.