Restarts are a widely-used class of techniques integral to the efficiency of Conflict-Driven Clause Learning (CDCL) Boolean SAT solvers. While the utility of such policies has been well-established empirically, a theoretical explanation of whether restarts are indeed crucial to the power of CDCL solvers is lacking. In this paper, we prove a series of theoretical results that characterize the power of restarts for various models of SAT solvers. More precisely, we make the following contributions. First, we prove an exponential separation between a {\it drunk} randomized CDCL solver model with restarts and the same model without restarts using a family of satisfiable instances. Second, we show that the configuration of CDCL solver with VSIDS branching and restarts (with activities erased after restarts) is exponentially more powerful than the same configuration without restarts for a family of unsatisfiable instances. To the best of our knowledge, these are the first separation results involving restarts in the context of SAT solvers. Third, we show that restarts do not add any proof complexity-theoretic power vis-a-vis a number of models of CDCL and DPLL solvers with non-deterministic static variable and value selection.

中文翻译：

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对 SAT 求解器重启的复杂性理论理解

重新启动是一类广泛使用的技术，它是冲突驱动子句学习 (CDCL) 布尔 SAT 求解器效率不可或缺的一部分。虽然这些政策的效用已经根据经验得到了很好的证实，但缺乏关于重启是否确实对 CDCL 求解器的能力至关重要的理论解释。在本文中，我们证明了一系列理论结果，这些结果表征了各种 SAT 求解器模型的重启能力。更准确地说，我们做出了以下贡献。首先，我们证明了具有重新启动的 {\it lucky} 随机 CDCL 求解器模型与使用一系列可满足实例的未重新启动的相同模型之间的指数分离。第二，我们表明，对于一系列不可满足的实例，具有 VSIDS 分支和重新启动（重新启动后删除活动）的 CDCL 求解器的配置比没有重新启动的相同配置更强大。据我们所知，这些是涉及 SAT 求解器上下文中重新启动的第一个分离结果。第三，我们表明，与具有非确定性静态变量和值选择的 CDCL 和 DPLL 求解器的许多模型相比，重新启动不会增加任何证明复杂性的理论能力。