Reduced ordered binary decision diagrams (OBDD's) are nowadays the state-of-the-art representation scheme for Boolean functions in Boolean manipulation. Recent results have shown that it is possible to use the more general concept of free binary decision diagrams (FBDD's) without giving up most of the useful computational properties of OBDD's, but possibly reducing the space requirements considerably. The amount of space reduction depends essentially on the shape of so-called FBDD-types the Boolean manipulation in terms of FBDD's is based on. Here, we propose some heuristics for deriving tree-like FBDD-types from given circuit descriptions. The experimental results we obtained clearly demonstrate that the FBDD-approach is not only of theoretical interest, but also of practical usefulness even in the ease of using merely such simple-structured tree-based FBDD-types as produced by the investigated heuristics.

It is well-known that the size of an ordered binary decision diagram (OBDD) may depend crucially on the order in which the variables occur. In the paper, we describe an implementation of an output-efficient algorithm that transforms an OBDD P representing a Boolean function f with respect to one variable ordering /spl pi/ into an OBDD Q that represents f with respect to another variable ordering /spl sigma/. The algorithm runs in average time O(|P/spl par/Q|) and requires O(|P|+|Q|) space. The importance of the algorithm is demonstrated by means of experimental results on basically two different applications. In one of them, the algorithm is used merely once. Such transformations are needed to test equivalence or to perform synthesis on OBDD's in which variables appear in different orders. The other application shows a way how to decrease the size of intermediate OBDD representations of a given circuit in the course of its symbolic simulation. Here, the algorithm is used dynamically, whenever the size of the manipulated OBDD's becomes too large.

We present the concept of TBDD's which considerably enlarges the class of Boolean functions that can be efficiently manipulated in terms of OBDD's. It extends the idea of using domain trans-formations, which is well-known in many areas of mathematics, physics, and technical sciences, to the context of OBDD-based Boolean function manipulation in CAD: Instead of working with the OBDD-representation of a function f, TBDD's allow working with an OBDD-representation of a suited cube transformed version of f. Besides of giving some theoretical insights into the new concept, we investigate in some detail cube transformations which are based on complete types. We show that such TBDD-representations can be derived similarly as OBDD-representations, give evidence of the practical importance of such TBDD's by presenting very small-size TBDD-representations of the hidden weighted bit functions