Testing Equivalence Probabilistically

Although the equivalence of two Ordered Binary Decision Diagrams (OBDDs) can be decided in polynomial time, the equivalence of two Free Binary Decision Diagrams (FBDDs) is only known to be probabilistically decidable in polynomial time. FBDDs are a strict superset of OBDDs, and are more succinct than OBDDs, which explains the interest in testing their equivalence. We show that the probabilistic equivalence test for FBDDs holds for the class of deterministic, decomposable negation normal forms (d-DNNFs), which forms a strict superset of FBDDs and is more succinct than FBDDs. Our theoretical results are backed up by experiments on a suite of combinational circuits.