Abstract A typical Branch and Bound algorithm for Max-SAT computes the lower bound by estimating the number of disjoint Inconsistent Subsets (IS) of the formula. The IS detection is ensured by Simulated Unit Propagation (SUP). Then, the inference rule for Max-SAT, Max-SAT resolution, is applied to ensure that the detected IS is counted only once. Learning Max-SAT resolution transformations can be detrimental to the algorithm performance, so they are usually selectively learned if they match certain patterns. In this paper, we study the impact of the transformations by Max-SAT resolution on the SUP mechanism, indispensable for IS detection. We introduce the notion of UP-resilience of a transformation which quantifies this impact and provides, from a theoretical point of view, an explanation to the empirical efficiency of the learning schemes developed in the last ten years. We also focus on recently introduced patterns called Unit Clause Subsets (UCSs). We characterize the transformations of certain UCSs using UP-resilience and we explain how our result can help extend the current patterns. Finally, we present empirical observations that support the relevance of the UP-resilience property and further consolidate our theoretical results.

中文翻译：

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通过 UP-Resilience 了解 Max-SAT 分辨率的威力

摘要 Max-SAT 的典型分支定界算法通过估计公式中不相交的不一致子集 (IS) 的数量来计算下界。IS 检测由模拟单元传播 (SUP) 确保。然后，应用 Max-SAT 的推理规则，即 Max-SAT 分辨率，以确保检测到的 IS 仅计数一次。学习 Max-SAT 分辨率转换可能不利于算法性能，因此如果它们匹配某些模式，通常会选择性地学习它们。在本文中，我们研究了 Max-SAT 分辨率转换对 SUP 机制的影响，这对于 IS 检测是必不可少的。我们引入了转型的 UP 弹性概念，该概念量化了这种影响，并从理论角度提供了：对过去十年开发的学习计划的经验效率的解释。我们还关注最近引入的称为单元子句子集 (UCS) 的模式。我们使用 UP 弹性来表征某些 UCS 的转换，并解释我们的结果如何帮助扩展当前模式。最后，我们提出了支持 UP 弹性属性相关性的实证观察，并进一步巩固了我们的理论结果。