全局约束推理的复杂性

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摘要翻译：
约束传播是约束规划成功的关键技术之一。为了减少搜索，与每个约束相关的快速算法对变量域进行剪枝。对于全局（或非二进制）约束，这种传播的代价可能比二进制约束的二次代价大得多。因此，我们研究了具有全局约束的推理的计算复杂性。我们首先描述了一些与约束传播有关的重要问题。我们证明了这些问题通常是难处理的，并确定了不同问题的可处理性和难处理性之间的依赖关系。然后，我们演示了计算复杂性的工具如何用于特定全局约束的设计和分析。特别地，我们说明了如何使用计算复杂性来确定何时应该强制执行较低水平的局部一致性，何时可以安全地推广约束，何时分解约束将减少剪枝量，以及何时组合约束是可处理的。
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英文标题：
《The Complexity of Reasoning with Global Constraints》
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作者：
Christian Bessiere and Emmanuel Hebrard and Brahim Hnich and Toby
  Walsh
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最新提交年份：
2009
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Computational Complexity        计算复杂度
分类描述：Covers models of computation, complexity classes, structural complexity, complexity tradeoffs, upper and lower bounds. Roughly includes material in ACM Subject Classes F.1 (computation by abstract devices), F.2.3 (tradeoffs among complexity measures), and F.4.3 (formal languages), although some material in formal languages may be more appropriate for Logic in Computer Science. Some material in F.2.1 and F.2.2, may also be appropriate here, but is more likely to have Data Structures and Algorithms as the primary subject area.
涵盖计算模型，复杂度类别，结构复杂度，复杂度折衷，上限和下限。大致包括ACM学科类F.1（抽象设备的计算）、F.2.3（复杂性度量之间的权衡）和F.4.3（形式语言）中的材料，尽管形式语言中的一些材料可能更适合于计算机科学中的逻辑。在F.2.1和F.2.2中的一些材料可能也适用于这里，但更有可能以数据结构和算法作为主要主题领域。
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英文摘要：
  Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the cost of such propagation may be much greater than the quadratic cost for binary constraints. We therefore study the computational complexity of reasoning with global constraints. We first characterise a number of important questions related to constraint propagation. We show that such questions are intractable in general, and identify dependencies between the tractability and intractability of the different questions. We then demonstrate how the tools of computational complexity can be used in the design and analysis of specific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be enforced, when constraints can be safely generalized, when decomposing constraints will reduce the amount of pruning, and when combining constraints is tractable.
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PDF链接：
https://arxiv.org/pdf/0903.1139

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关键词：复杂性 Presentation Intelligence Constraints Computation 传播 propagation complexity 应该 such