Bi-decomposition of large Boolean functions using blocking edge graphs

Bi-decomposition techniques have been known to significantly reduce area, delay, and power during logic synthesis since they can explore multi-level and, or, and xor decompositions in a scalable technology-independent manner. The complexity of bi-decomposition techniques is in achieving a good variable partition for the given logic function. State-of-the-art techniques use heuristics and/or brute-force enumeration for variable partitioning, which results in sub-optimal results and/or poor scalability with function complexity. This paper describes a fast, scalable algorithm for obtaining provably optimum variable partitions for bi-decomposition of Boolean functions by constructing an undirected graph called the blocking edge graph (BEG). To the best of our knowledge, this is the first algorithm that demonstrates a systematic approach to derive disjoint and overlapping variable partitions for bi-decomposition. Since a BEG has only one vertex per input, our technique scales to Boolean functions with hundreds of inputs. Results indicate that on average, BEG-based bi-decomposition reduces the number of logic levels (mapped delay) of 16 benchmark circuits by 60%, 34%, 45%, and 30% (20%, 19%, 16% and 20%) over the best results of state-of-the-art tools FBDD, SIS, ABC, and an industry-standard synthesizer, respectively.