Efficient manipulation algorithms for linearly transformed BDDs

Binary decision diagrams (BDDs) are the state-of-the-art data structure in VLSI CAD, but, due to their ordering restriction, only exponential-sized BDDs exist for many functions of practical relevance. Linear transformations (LTs) have been proposed as a new concept to minimize the size of BDDs, and it is known that, in some cases, even an exponential reduction can be obtained. In addition to a small representation, the efficient manipulation of a data structure is also important. In this paper, we present polynomial-time manipulation algorithms that can be used for linearly transformed BDDs (LT-BDDs) analogously to BDDs. For some operations, like synthesis algorithms based on ITE (if-then-else), it turns out that the techniques known from BDDs can be directly transferred, while for other operations, like quantification and cofactor computation, completely different algorithms have to be used. Experimental results are given to show the efficiency of the approach.