A characterization of binary decision diagrams

Binary decision diagrams (BDDs) are a representation of Boolean functions. Its use in the synthesis, simulation, and testing of Boolean circuits has been proposed by various researchers. In all these applications of BDDs solutions to some fundamental computational problems are needed. A characterization of BDDs in terms of the complexity of these computational problems is presented. A tighter bound on the size of an ordered BDD that can be computed from a given Boolean circuit is presented. On the basis of the results, a case is made for exploring the use of repeated BDDs, with a small number of repeated variables, and free BDDs for some applications for which only ordered BDDs have been used so far.<>