The research of this thesis focuses on the analysis of polynomial classes and their practical exploitation for solving constraint satisfaction problems (CSPs) with finite domains. In particular, I worked on bridging the gap between theoretical works and practical results in constraint solvers. Specifically, the goal of this thesis is to find explanation for the effectiveness of solvers, and also to show that studied tractable classes are not artificial since several real-problems among the ones used in the CSP 2008 Competition belong to them.Our work is organized into three main parts. In the first part, we proposed several types of microstructures for CSPs of arbitrary arity which are based on some knwon binary encoding of non-binary CSPs like, dual encoding, hidden-variable transformation and mixed (or double) encoding. These theoretical tools are designed to facilitate the study of tractable classes, sets of CSP instances which can be solved in polytime, when the constraints are non-binary. After that, we propose a new tractable classes of CSPs whose the highlighting should allow on the one hand to explain the effectiveness of solvers of the state of the art namely FC, MAC, RFL and on the second hand to provide the opportunities for easy integration in these solvers. These would include the definition of new tractable classes without using of an ad hoc algorithms as in the traditional case. These new tractable classes are related to the number of maximal cliques in the microstructure of binary or non-binary CSP. In the last part, we focus on the presence of instances belonging to polynomial classes in classical benchmarks used by the CP community. We study in particular the Broken-Triangle Property (BTP) and its extension DBTP to CSP of arbitrary arity. Next, we prove that BTP can also be used to reduce the size of the search space by merging pairs of values on which no broken triangle exists. Finally, we introduce a formal framework, called transformation, and we develop the concept of hidden tractable class that we exploit from an experimental point of view.

中文翻译：

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任意随机应变CSP的可实践类：从理论到实践

本文的研究集中在多项式类的分析及其对有限域约束满足问题的实际利用上。特别是，我致力于缩小约束求解器中理论工作与实际结果之间的差距。具体而言，本论文的目的是寻找求解器有效性的解释，并表明研究的易处理类不是人为的，因为CSP 2008竞赛中使用的一些易解决的问题属于其中。分为三个主要部分。在第一部分中，我们基于非二进制CSP的一些已知二进制编码，例如双重编码，隐藏变量转换和混合（或双重）编码，提出了几种任意类型的CSP的微结构类型。这些理论工具旨在帮助研究易处理的类，CSP实例集，当约束是非二进制的时，可以在多时求解。此后，我们提出了一种新的易于处理的CSP类，其突出显示一方面应能解释最先进的求解器（即FC，MAC，RFL）的有效性，另一方面可为轻松集成提供机会在这些求解器中。这些将包括对新的易处理类的定义，而无需像传统情况那样使用临时算法。这些新的易处理类别与二元或非二元CSP的微观结构中的最大集团数量有关。在最后一部分中，我们重点关注CP社区使用的经典基准中属于多项式类的实例。我们特别研究了破碎三角形属性（BTP）及其将DBTP扩展为任意Arbiter的CSP。接下来，我们证明BTP还可用于通过合并不存在断三角形的值对来减小搜索空间的大小。最后，我们介绍了一个称为转换的正式框架，并开发了我们从实验角度出发利用的隐蔽易处理类的概念。