由覆盖诱导的邻域等于 覆盖自身

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摘要翻译：
在什么条件下复盖诱导的邻域等于复盖本身是一个有意义的问题。一些学者为这一问题提供了一个充要条件。本文通过一个反例，首先指出该充要条件是假的。其次，我们给出了这个问题的一个充要条件。第三，研究了由覆盖计算邻域的逆问题，即给定任意覆盖，无论是否存在另一个覆盖，使得它所导出的邻域只是前一个覆盖。我们也给出了这个问题的一个充要条件。总之，通过对街区诱导的两个基本问题的研究，我们对街区与诱导街区的覆盖之间的关系有了更深刻的认识。
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英文标题：
《Condition for neighborhoods induced by a covering to be equal to the
  covering itself》
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作者：
Hua Yao and William Zhu
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最新提交年份：
2012
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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：
  It is a meaningful issue that under what condition neighborhoods induced by a covering are equal to the covering itself. A necessary and sufficient condition for this issue has been provided by some scholars. In this paper, through a counter-example, we firstly point out the necessary and sufficient condition is false. Second, we present a necessary and sufficient condition for this issue. Third, we concentrate on the inverse issue of computing neighborhoods by a covering, namely giving an arbitrary covering, whether or not there exists another covering such that the neighborhoods induced by it is just the former covering. We present a necessary and sufficient condition for this issue as well. In a word, through the study on the two fundamental issues induced by neighborhoods, we have gained a deeper understanding of the relationship between neighborhoods and the covering which induce the neighborhoods.
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PDF链接：
https://arxiv.org/pdf/1209.5484

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关键词：neighborhood Presentation relationship Intelligence Fundamental 学者 充要条件 等于 equal 存在