AI 中文总结
重新审视Scheder对3-SAT的PPSZ算法分析，保持正则和非正则估计不变，仅替换最终重组方式，给出新旧运行时间界限，未修改算法及定理，得到目前通用3-SAT最佳最坏情况随机运行时间界限。
AI 中文摘要
我们重新审视了Scheder对原始PPSZ算法的分析。保持其正则和非正则估计不变，在通用结构坐标中表达它们，仅用显式线性规划对偶证书替换其最终重组。给出了新旧运行时间界限。通用情况界限通过对相应的唯一3-SAT分析应用相同的现有Scheder - Steinberger唯一到通用提升定理得到。据我们所知，$O^*(1.307031578^n)$是目前已知的通用3-SAT的最佳最坏情况随机运行时间界限。既未修改PPSZ也未修改提升定理，数值不等式通过精确有理区间计算验证。
英文摘要
We revisit Scheder's analysis of the original PPSZ algorithm. Keeping his regular and irregular estimates unchanged, we express them in common structural coordinates and replace only their final recombination by an explicit linear-programming dual certificate. The old and new running-time bounds are \[ \begin{array}{c|cc} & \text{Unique-$3$-SAT} & \text{general $3$-SAT} \\ \hline \text{Scheder's analysis} & O^*(1.306972377^n) & O^*(1.307031594^n) \\ \text{this work} & O^*(1.306969598^n) & O^*(1.307031578^n). \end{array} \] In both rows, the general-case bound is obtained by applying the same existing Scheder--Steinberger unique-to-general lifting theorem to the corresponding Unique-$3$-SAT analysis. To the best of our knowledge, $O^*(1.307031578^n)$ is the best currently known worst-case randomized running-time bound for general $3$-SAT. Neither PPSZ nor the lifting theorem is modified. The numerical inequalities are certified by exact rational interval computation.
