Efficient OBDD-Based Boolean Manipulation in CAD Beyond Current Limits

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 transformations, 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 HWBn which were proved to have only very large OBDD-representations, and - report some promising experimental results with some ISCAS benchmark circuits including the multiplier circuit C6288.