Improving the efficiency of circuit-to-BDD conversion by gate and input ordering

Abstract

Boolean functions are fundamental to synthesis and verification of digital logic, and compact representations of Boolean functions have great practical significance. Popular representations, such as CNF, DNF, circuits and ROBDDs [4], offer different advantages and are preferred for different tasks. Conversion between those representations is common, especially when one is used to represent the input and another speeds up relevant algorithms. Our work addresses the construction of ROBDDs that represent outputs of a given Boolean circuit. It is used in synthesis and verification. Earlier works (Fujita, Fujisawa, and Kawato, 1988. Malik et al., 1988.) proposed ordering circuit inputs and gates by graph traversals. We contribute orderings based on circuit partitioning and placement, leveraging the progress in recursive bisection and multi-level min-cut partitioning achieved in late 1990s. Our empirical results show that the proposed orderings based on circuit partitioning and placement are more successful than straightforward DFS and BFS, as well as related heuristics.