略论隐现词
Remarks on Privileged Words
摘要：
我们讨论的特权词的概念，最近介绍了Peltomaki。一个单词w是特权的，如果它的长度<=1，或者有一个特权边界在w中正好出现两次。我们证明了以下结果：（1）如果w^k对某些k >=1是特权的，那么w^j对所有j >= 0是特权的;（2）特权字的语言既不是正则的也不是上下文无关的;（3）存在一个线性时间算法来检查给定的字是否是特权的;（4）至少有2^{n-5}/n^2个长度为n的特权二进制字。
英文摘要：
We discuss the notion of privileged word, recently introduced by Peltomaki. A word w is privileged if it is of length <=1, or has a privileged border that occurs exactly twice in w. We prove the following results: (1) if w^k is privileged for some k >=1, then w^j is privileged for all j >= 0; (2) the language of privileged words is neither regular nor context-free; (3) there is a linear-time algorithm to check if a given word is privileged; and (4) there are at least 2^{n-5}/n^2 privileged binary words of length n.
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