摘要翻译：
泛代数方法已被证明是研究CSPS复杂性的有力工具。这种方法以前曾应用于有限或（无限）欧米伽范畴模板的CSPs研究，并依赖于两个事实。第一个是在有限或欧米茄范畴结构A中，一个关系是本原正定义的当且仅当它被A的多态性所保持。第二个是每一个有限或欧米茄范畴结构同态等价于一个核心结构。在本文中，我们将这些事实推广到不一定是欧米加范畴的无限结构。（由于arXiv的篇幅限制，本摘要被严重缩减--请阅读本文的完整摘要。）最后，我们给出了我们的一般结果在描述和分析CSPS复杂度方面的应用。特别地，我们给出了基于不存在依赖于一个以上参数的多态性的一般硬度准则，并对那些一阶可定义（因此可以在多项式时间内求解）的CSP给出了基于多态性的描述。
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英文标题：
《On the Scope of the Universal-Algebraic Approach to Constraint
  Satisfaction》
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作者：
Barnaby Martin (Durham University, UK.), Manuel Bodirsky (CNRS/LIX,
  Ecole Polytechnique, France), Martin Hils (Equipe de Logique Mathematique,
  Universite Paris Diderot - Paris 7, France)
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最新提交年份：
2013
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Logic in Computer Science        计算机科学中的逻辑
分类描述：Covers all aspects of logic in computer science, including finite model theory, logics of programs, modal logic, and program verification. Programming language semantics should have Programming Languages as the primary subject area. Roughly includes material in ACM Subject Classes D.2.4, F.3.1, F.4.0, F.4.1, and F.4.2; some material in F.4.3 (formal languages) may also be appropriate here, although Computational Complexity is typically the more appropriate subject area.
涵盖计算机科学中逻辑的所有方面，包括有限模型理论，程序逻辑，模态逻辑和程序验证。程序设计语言语义学应该把程序设计语言作为主要的学科领域。大致包括ACM学科类D.2.4、F.3.1、F.4.0、F.4.1和F.4.2中的材料；F.4.3（形式语言）中的一些材料在这里也可能是合适的，尽管计算复杂性通常是更合适的主题领域。
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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：
  The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two facts. The first is that in finite or omega-categorical structures A, a relation is primitive positive definable if and only if it is preserved by the polymorphisms of A. The second is that every finite or omega-categorical structure is homomorphically equivalent to a core structure. In this paper, we present generalizations of these facts to infinite structures that are not necessarily omega-categorical. (This abstract has been severely curtailed by the space constraints of arXiv -- please read the full abstract in the article.) Finally, we present applications of our general results to the description and analysis of the complexity of CSPs. In particular, we give general hardness criteria based on the absence of polymorphisms that depend on more than one argument, and we present a polymorphism-based description of those CSPs that are first-order definable (and therefore can be solved in polynomial time).
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PDF链接：
https://arxiv.org/pdf/0909.5097