Nowadays, many real-world problems are encoded into SAT instances and efficiently solved by modern SAT solvers. These solvers, usually known as Conflict-Driven Clause Learning (CDCL) SAT solvers, include a variety of sophisticated techniques, such as clause learning, lazy data structures, conflict-based adaptive branching heuristics, or random restarts, among others. However, the reasons of their efficiency in solving real-world, or industrial, SAT instances are still unknown. The common wisdom in the SAT community is that these technique exploit some hidden structure of real-world problems.In this thesis, we characterize some important features of the underlying structure of industrial SAT instances. Namely, they are the community structure and the self-similar structure. We observe that most industrial SAT formulas, viewed as graphs, have these two properties. This means that (i) in a graph with a clear community structure, i.e. having high modularity, we can find a partition of its nodes into communities such that most edges connect nodes of the same community; and (ii) in a graph with a self-similar pattern, i.e. being fractal, its shape is kept after re-scalings, i.e., grouping sets of nodes into a single node. We also analyze how these structures are affected by the effects of CDCL techniques during the search.Using the previous structural studies, we propose three applications. First, we face the problem of generating pseudo-industrial random SAT instances using the notion of modularity. Our model generates instances similar to (classical) random SAT formulas when the modularity is low, but when this value is high, our model is also adequate to model realistic pseudo-industrial problems. Second, we propose a method based on the community structure of the instance to detect relevant learnt clauses. Our technique augments the original instance with this set of relevant clauses, and this results into an overall improvement of the efficiency of several state-of-the-art CDCL SAT solvers. Finally, we analyze the classification of industrial SAT instances into families using the previously analyzed structure features, and we compare them to other classifiers commonly used in portfolio SAT approaches.In summary, this dissertation extends the understandings of the structure of SAT instances, with the aim of better explaining the success of CDCL techniques and possibly improve them, and propose a number of applications based on this analysis of the underlying structure of SAT formulas.

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超越SAT公式的结构

如今，许多现实世界中的问题都被编码为SAT实例，并由现代SAT解算器有效解决。这些求解器通常称为冲突驱动子句学习（CDCL）SAT求解器，其中包括多种复杂的技术，例如子句学习，惰性数据结构，基于冲突的自适应分支启发法或随机重启等。但是，它们解决实际或工业SAT实例效率高的原因仍然未知。SAT社区的共同智慧是，这些技术利用了一些隐藏的实际问题的结构。在本文中，我们描述了工业SAT实例底层结构的一些重要特征。即，它们是社区结构和自相似结构。我们观察到，大多数工业SAT公式（被视为图形）都具有这两个属性。这意味着（i）在具有清晰社区结构（即具有高度模块化）的图中，我们可以找到其节点划分为社区的划分，以使大多数边连接同一社区的节点；（ii）在具有自相似图案（即分形）的图形中，其形状在重新缩放后保持不变，即，将节点集分组为单个节点。我们还分析了搜索过程中CDCL技术对这些结构的影响。使用以前的结构研究，我们提出了三种应用。首先，我们面临使用模块化概念生成伪工业随机SAT实例的问题。当模块性较低时，我们的模型会生成类似于（经典）随机SAT公式的实例，但是当此值较高时，我们的模型也足以对现实的伪工业问题进行建模。其次，我们提出了一种基于实例的社区结构的方法来检测相关的学习子句。我们的技术使用这组相关的条款对原始实例进行了扩充，从而使整体上提高了几种最新CDCL SAT求解器的效率。最后，我们使用先前分析的结构特征来分析工业SAT实例的分类，并将它们与投资组合SAT方法中常用的其他分类器进行比较。总之，本文扩展了对SAT实例结构的理解，