Current PB solvers implement many techniques inspired by the CDCL architecture of modern SAT solvers, so as to benefit from its practical efficiency. However, they also need to deal with the fact that many of the properties leveraged by this architecture are no longer true when considering PB constraints. In this paper, we focus on one of these properties, namely the optimality of the so-called first unique implication point (1-UIP). While it is well known that learning the first assertive clause produced during conflict analysis ensures to perform the highest possible backjump in a SAT solver, we show that there is no such guarantee in the presence of PB constraints. We also introduce and evaluate different approaches designed to improve the backjump level identified during conflict analysis by allowing to continue the analysis after reaching the 1-UIP. Our experiments show that sub-optimal backjumps are fairly common in PB solvers, even though their impact on the solver is not clear.

中文翻译：

---

提高PB求解器的回跳水平

当前的 PB 求解器实施了许多受现代 SAT 求解器 CDCL 架构启发的技术，以便从其实际效率中受益。然而，他们还需要处理这样一个事实，即在考虑 PB 约束时，该架构利用的许多属性不再正确。在本文中，我们关注其中一个属性，即所谓的第一个唯一蕴涵点（1-UIP）的最优性。众所周知，学习冲突分析期间产生的第一个断言子句可确保在 SAT 求解器中执行尽可能高的回跳，但我们表明，在存在 PB 约束的情况下没有这样的保证。我们还介绍和评估了不同的方法，这些方法旨在通过允许在达到 1-UIP 后继续分析来提高冲突分析期间确定的回跳水平。我们的实验表明，次优回跳在 PB 求解器中相当普遍，尽管它们对求解器的影响尚不清楚。