The CNF formula satisfiability problem (CNF-SAT) has been reduced to many fundamental problems in P to prove tight lower bounds under the Strong Exponential Time Hypothesis (SETH). Recently, the works of Abboud, Hansen, Vassilevska W. and Williams (STOC 16), and later, Abboud and Bringmann (ICALP 18) have proposed basing lower bounds on the hardness of general boolean formula satisfiability (Formula-SAT). Reductions from Formula-SAT have two advantages over the usual reductions from CNF-SAT: (1) conjectures on the hardness of Formula-SAT are arguably much more plausible than those of CNF-SAT, and (2) these reductions give consequences even for logarithmic improvements in a problems upper bounds. Here we give tight reductions from Formula-SAT to two more problems: pattern matching on labeled graphs (PMLG) and subtree isomorphism. Previous reductions from Formula-SAT were to sequence alignment problems such as Edit Distance, LCS, and Frechet Distance and required some technical work. This paper uses ideas similar to those used previously, but in a decidedly simpler setting, helping to illustrate the most salient features of the underlying techniques.

中文翻译：

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从公式 SAT 到标记图和子树同构的模式匹配的简单归约

CNF 公式可满足性问题 (CNF-SAT) 已简化为 P 中的许多基本问题，以证明强指数时间假设 (SETH) 下的紧下界。最近，Abboud、Hansen、Vassilevska W. 和 Williams (STOC 16) 以及后来的 Abboud 和Bringmann (ICALP 18) 提出了基于一般布尔公式可满足性 (Formula-SAT) 硬度的下界。与 CNF-SAT 的通常减少相比，Formula-SAT 的减少有两个优点：(1) 对 Formula-SAT 硬度的猜想可以说比 CNF-SAT 的那些更合理，并且 (2) 这些减少给出了结果，即使对于问题上限的对数改进。在这里，我们将 Formula-SAT 严格归结为另外两个问题：标记图上的模式匹配 (PMLG) 和子树同构。之前从 Formula-SAT 中减少的是序列比对问题，例如编辑距离、LCS 和 Frechet 距离，并且需要一些技术工作。本文使用的思想与以前使用的思想相似，但在一个明显更简单的设置中，有助于说明底层技术的最显着特征。