Space- and time-efficient BDD construction via working set control

Abstract

Binary decision diagrams (BDDs) have been shown to be a powerful tool in formal verification. Efficient BDD construction techniques become more important as the complexity of protocol and circuit designs increases. This paper addresses this issue by introducing three techniques based on working set control. First, we introduce a novel BDD construction algorithm based on partial breadth-first expansion. This approach has the good memory locality of the breadth-first BDD construction while maintaining the low memory overhead of the depth-first approach. Second, we describe how memory management on a per-variable basis can improve spatial locality of BDD construction at all levels, including expansion, reduction, and rehashing. Finally, we introduce a memory compacting garbage collection algorithm to remove unreachable BDD nodes and minimize memory fragmentation. Experimental results show that when the applications fit in physical memory, our approach has speedups of up to 1.6 in comparison to both depth-first (CUDD) and breadth-first (GAL) packages. When the applications do not fit into physical memory, our approach outperforms both CUDD and CAL by up to an order of magnitude. Furthermore, the good memory locality and low memory overhead of this approach has enabled us to be the first to have successfully constructed the entire C6288 multiplication circuit from the ISCAS85 benchmark set using only conventional BDD representations.