论文标题

信息太多:为什么CDCL求解器需要忘记学习的条款

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

论文作者

Krüger, Tom, Lorenz, Jan-Hendrik, Wörz, Florian

论文摘要

冲突驱动的子句学习(CDCL)是解决命题逻辑令人满意问题的非常成功的范式。这种求解器不是简单的深度优先回溯方法,而是以其他条款的形式学习了发生冲突的原因。但是,尽管CDCL求解器取得了巨大的成功,但仍然对以什么方式影响这些求解器的性能有限。 考虑到不同的措施,本文非常令人惊讶地证明,条款的学习(无需摆脱某些条款)不仅可以帮助求解器,而且可能会大大恶化解决方案过程。通过进行广泛的经验分析,我们还发现CDCL求解器的运行时分布是多模式的。这种多模式可以看作是上述劣化现象的原因。同时,这也表明了为什么该子句与子句删除相结合,尽管这一现象是事实上,但实际上是SAT解决的事实标准。作为最终贡献,我们表明Weibull混合物分布可以准确地描述多模式分布。因此,在基本实例中添加新的子句具有长期运行时间的固有效果。该见解提供了一个解释,即为什么忘记子句的技术在CDCL求解器中有用,除了单位传播速度的优化。

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.

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