Conjunctive normal forms (CNF) of structured satisfiability problems contain logic gate patterns. So Boolean circuits (BC) by and large can be obtained from them and thus structural information that is lost in the CNF can be recovered. However, it is not known which logic gates are useful for local search on BCs or which logic gates in particular help local search the most and why. In this article, we empirically show that exploitation of xor, xnor, eq, and not gates is a key factor behind the performance of local search algorithms using single variable flips when adapted to logic gate constraints. Moreover, controlled experiments and investigations into the variables selected for flipping further elucidates these findings. To achieve these conclusions, we have adapted the AdaptNovelty+ and CCANr algorithms to cope with logic gate-based constraint models. These are two prominent families of local search algorithms for satisfiability. We performed our experiments using a large set of benchmark instances from SATLib, SAT2014, and SAT2020. We have also presented techniques to eliminate cycles among logic gates that are detected from CNF and to propagate equivalence of variables statically through the logic gate dependency relationships.

结构化可满足性问题的联合范式 (CNF) 包含逻辑门模式。因此，大体上可以从中获得布尔电路（BC），从而可以恢复在 CNF 中丢失的结构信息。然而，不知道哪些逻辑门对 BC 的局部搜索有用，或者哪些逻辑门特别有助于局部搜索以及为什么。在本文中，我们凭经验表明，利用xor、xnor、eq，而不是当适应逻辑门约束时，门是使用单变量翻转的局部搜索算法性能背后的关键因素。此外，对选择用于翻转的变量的受控实验和调查进一步阐明了这些发现。为了获得这些结论，我们采用了AdaptNovelty+和CCANr算法来处理基于逻辑门的约束模型。这是满足可满足性的两个著名的局部搜索算法系列。我们使用来自 SATLib、SAT2014 和 SAT2020 的大量基准实例进行了实验。我们还介绍了消除从 CNF 检测到的逻辑门之间的循环的技术，并通过逻辑门依赖关系静态地传播变量的等效性。