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摘要翻译：
对称性可以用来帮助解决许多问题。例如，爱因斯坦1905年的著名论文（“关于运动物体的电动力学”）使用对称性来帮助推导狭义相对论定律。在人工智能中，对称性在问题表示和推理中都发挥了重要作用。我描述了最近关于使用对称性来帮助解决约束满足问题的工作。对称性既存在于问题的个别解内，也存在于同一问题的不同解之间。对称性也可以应用于一个问题中的约束，给出新的对称约束。关于对称性的推理可以加快问题的解决，并导致在图论和数论中发现新的结果。
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英文标题：
《Symmetry within and between solutions》
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作者：
Toby Walsh
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最新提交年份：
2010
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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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英文摘要：
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has played an important role in both problem representation and reasoning. I describe recent work on using symmetry to help solve constraint satisfaction problems. Symmetries occur within individual solutions of problems as well as between different solutions of the same problem. Symmetry can also be applied to the constraints in a problem to give new symmetric constraints. Reasoning about symmetry can speed up problem solving, and has led to the discovery of new results in both graph and number theory.
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PDF链接：
https://arxiv.org/pdf/1007.0604
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