英文标题：
《Impossibility Theorems and the Universal Algebraic Toolkit》
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作者：
Mario Szegedy and Yixin Xu
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最新提交年份：
2015
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英文摘要：
We elucidate a close connection between the Theory of Judgment Aggregation (more generally, Evaluation Aggregation), and a relatively young but rapidly growing field of universal algebra, that was primarily developed to investigate constraint satisfaction problems. Our connection yields a full classification of non-binary evaluations into possibility and impossibility domains both under the idempotent and the supportive conditions. Prior to the current result E. Dokow and R. Holzman nearly classified non-binary evaluations in the supportive case, by combinatorial means. The algebraic approach gives us new insights to the easier binary case as well, which had been fully classified by the above authors. Our algebraic view lets us put forth a suggestion about a strengthening of the Non-dictatorship criterion, that helps us avoid \"outliers\" like the affine subspace. Finally, we give upper bounds on the complexity of computing if a domain is impossible or not (to our best knowledge no finite time bounds were given earlier).
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中文摘要：
我们阐明了判断聚合理论（更一般地说，评估聚合）与一个相对年轻但发展迅速的普适代数领域之间的密切联系，该领域主要是为了研究约束满足问题而开发的。在幂等元和支持条件下，我们的联系将非二元求值分为可能域和不可能域。在目前的结果之前，E.Dokow和R.Holzman几乎通过组合方法将支持性案例中的非二元评估进行了分类。代数方法也为我们提供了对更简单的二元情况的新见解，这已被上述作者完全分类。我们的代数观点让我们提出了一个关于加强非独裁标准的建议，这有助于我们避免像仿射子空间这样的“异常值”。最后，我们给出了计算复杂度的上界，如果一个域是不可能的（据我们所知，之前没有给出有限时间界限）。
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分类信息：

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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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：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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