Combining Top-down and Bottom-up approaches for ROBDD Construction

ROBDDs have traditionally been built in a bottom-up fashion, through the recursive use of Bryant's apply procedure [6], or the ITE [4] procedure. With these methods, the peak memory utilization is often larger than the nal ROBDD size. Though methods like Dynamic Variable Reordering [21] have been proposed to reduce the memory utilization, such schemes have an associated time penalty. In this paper, we show that for a large number of applications, it is more e cient to construct the ROBDD by a suitable combination of top-down (decomposition based) and bottom-up (composition based) approaches. We suitably select decomposition points during the construction of the ROBDD, and follow it by a symbolic composition to get the nal ROBDD. We propose two heuristic algorithms for decomposition. One is based on a topological analysis of a given combinational netlist, while the other is purely functional, making no assumptions about the underlying topology of the circuit. We demonstrate the utility of our scheme on the standard benchmark circuits. Our results show that for a given variable ordering, our method usually has signi cantly better time as well as memory characteristics than existing techniques. Our methods are easily extended to many variants of ROBDDs, and in that sense are powerful in their scope. 2