等长部分字的非空集
Unavoidable Sets of Partial Words of Uniform Length
摘要：
有限字母表A上的部分字集合X称为不可避免的，如果A上的每个双边无限字都有一个因子与X的一个元素相容。与一组没有洞的词的情况不同，决定一个给定的k字母表上的n个部分词的有限集合是否是可避免的问题是NP难的，即使我们限制为一组均匀长度的部分词。因此，将这样的集合（参数为k和n）分类为可避免的或不可避免的就成了一个有趣的问题。在本文中，我们的工作对这个分类问题的调查孔的最大数量，我们可以填补在不可避免的集合的部分字的长度均匀的任何固定大小的字母表，同时保持可扩展性属性。
英文摘要：
A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X. Unlike the case of a set of words without holes, the problem of deciding whether or not a given finite set of n partial words over a k-letter alphabet is avoidable is NP-hard, even when we restrict to a set of partial words of uniform length. So classifying such sets, with parameters k and n, as avoidable or unavoidable becomes an interesting problem. In this paper, we work towards this classification problem by investigating the maximum number of holes we can fill in unavoidable sets of partial words of uniform length over an alphabet of any fixed size, while maintaining the unavoidability property.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
