Complexity Theoretical Aspects of OFDDs

We extend the list of complexity results for OFDDs on problems arising in practical applications. We show that it is NP-hard to decide whether a function represented by some OFDD can be represented by an OFDD of size s using another variable ordering. Given an OFDD representation for an incompletely defined function, it is NP-hard to compute an optimal OFDD cover for this function respecting the same variable ordering. The replacement of variables by constants may cause an exponential blow-up of the OFDD size. Finally, it is investigated how a local change of the variable ordering may change the OFDD size. This leads to simulated annealing algorithms to improve variable orderings.