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arXiv 2202.01030cs.AI
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信息太多:为什么CDCL求解器需要忘记已学习的子句

Too much information: why CDCL solvers need to forget learned clauses

Universität Ulm(乌尔姆大学)

Tom Krüger, Jan-Hendrik Lorenz, Florian Wörz

摘要:

摘要驱动小句学习是解决命题逻辑可满足性问题的一个非常成功的范例。与简单的深度优先回溯方法不同,这种求解器以附加子句的形式学习发生冲突背后的原因。然而,尽管CDCL解算器取得了巨大的成功,但人们对什么以何种方式影响这些解算器的性能仍然只有有限的了解。考虑到不同的措施,本文证明,相当令人惊讶的是,子句学习(无法摆脱一些子句)不仅可以帮助求解器,但往往可以显着恶化的解决方案的过程。通过大量的实证分析,我们进一步发现CDCL求解器的运行时间分布是多峰的。这种多模态可以被看作是上述恶化现象的原因。同时,它也给出了一个指示,为什么小句学习结合小句删除几乎是事实标准的SAT解决,尽管这一现象。作为最后的贡献,我们表明,威布尔混合分布可以准确地描述多峰分布。因此,向基实例添加新子句具有使运行时长尾化的固有效果。这种见解提供了一个解释,为什么遗忘子句的技术是有用的CDCL求解器除了优化单位传播速度。

英文摘要:

Conflict-driven clause learning (CDCL) is a remarkably successful paradigm for solving the satisfiability problem of propositional logic. Instead of a simple depth-first backtracking approach, this kind of solver learns the reason behind occurring conflicts in the form of additional clauses. However, despite the enormous success of CDCL solvers, there is still only a limited understanding of what influences the performance of these solvers in what way. Considering different measures, this paper demonstrates, quite surprisingly, that clause learning (without being able to get rid of some clauses) can not only help the solver but can oftentimes deteriorate the solution process dramatically. By conducting extensive empirical analysis, we furthermore find that the runtime distributions of CDCL solvers are multimodal. This multimodality can be seen as a reason for the deterioration phenomenon described above. Simultaneously, it also gives an indication of why clause learning in combination with clause deletion is virtually the de facto standard of SAT solving, in spite of this phenomenon. As a final contribution, we show that Weibull mixture distributions can accurately describe the multimodal distributions. Thus, adding new clauses to a base instance has an inherent effect of making runtimes long-tailed. This insight provides an explanation as to why the technique of forgetting clauses is useful in CDCL solvers apart from the optimization of unit propagation speed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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