Abstract
Free binary decision diagrams (FBDDs) are an extension of ordered BDDs (OBDDs) that allow different variable orders along each path. FBDDs are a more efficient representation, while (nearly) all of the properties of OBDDs are kept. In some cases, even an exponential reduction can be observed. In this paper we first present an exact algorithm to find a minimal FBDD representation for a given Boolean function. To reduce the huge search space, a pruning technique is used. Since the exact algorithm is only applicable to small functions, also two heuristic algorithms for FBDD minimization are described. The first one can be seen as a modification of the exact algorithm which constructs the FBDD starting from the root nodes. The second one is based on an evolutionary algorithm. Experimental results show that in many cases significant improvements can be obtained, compared to the best known OBDD and FBDD sizes.
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