OBDDs, SDDs, and circuits of bounded width: Completeness matters

Ordered Binary Decision Diagrams (OBDDs) are dynamic data structures with many application areas. The literature suggested that OBDDs of bounded width equate to Boolean circuits of bounded pathwidth. In this paper, we show that this relationship holds only for complete OBDDs. Additionally, we demonstrate that similar limitations affect the claimed equivalence between Sentential Decision Diagrams (SDDs) of bounded width and Boolean circuits of bounded treewidth.