An Efficient Two-phase Method for Prime Compilation of Non-clausal Boolean Formulae

Abstract

Prime compilation aims to generate all prime implicates/implicants of a Boolean formula. Recently, prime compilation of non-clausal formulae has received great attention. Since it is hard for $\Sigma_{2}^{P}$, existing methods have performance issues. We argue that the main performance bottleneck stems from enlarging the search space using dual rail (DR) encoding, and computing a minimal clausal formula as a by-product. To deal with the issue, we propose a two-phase approach, namely CoAPI, for prime compilation of non-clausal formulae. Thanks to the two-phase framework, we construct a clausal formula without using DR encoding. In addition, to improve performance, the key in our work is a novel bounded prime extraction (BPE) method that, interleaving extracting prime implicates with extracting small implicates, enables constructing a succinct clausal formula rather than a minimal one. Following the assessment way of the state-of-the-art (SOTA) work, we show that CoAPI achieves SOTA performance. Particularly, for generating all prime implicates, CoAPI is up to about one order of magnitude faster. Moreover, we evaluate CoAPI on a benchmark sourcing from real-world industries. The results also confirm the outperformance of CoAPI11Our code and benchmarks are publicly available at https://github.com/LuoWeiLinWillam/CoAPI.