Minimization of free BDDs

Free BDDs (FBDDs) are an extension of ordered BDDs (OBDDs). FBDDs may have different orderings along each path. They allow a more efficient representation, while keeping (nearly) all of the properties of OBDDs. In some cases even an exponential reduction can be observed. In this paper we present for the first time an exact algorithm for finding a minimal FBDD representation for a given Boolean function. To reduce the huge search space, it makes use of a pruning technique. The algorithm also considers symmetries of the function. Since the algorithm is only applicable to small functions, we also present a heuristic for FBDD minimization starting from an OBDD. Our experiments show that in many cases significant improvements can be obtained.