Rees定理在稠密正规语言中的一个应用

An application of Rees theorem to dense regular languages

称可被有限自动机识别的语言为正规语言 .字母表 A上的语言 L称为稠密的 ,如果 A*中每个字都是 L中字的子字 .不能写为其他字的幂的非空字称为本原字 ,不是本原字的非空字称为非本原字 .Shyr等提出如下猜想 :每个稠密正规语言中含有非本原字 ,本文利用

A language is regular if it can be recognized by a finite automaton.A language is dense if every word in A  is a subword of some word in the language.A non-empty word is a primitive word if it is not a power of any other word,otherwise it is an imprimitive word,Shyr H J and Yu S S conjectured that every dense regular language contains an imprimitive word in .The conjecture is proved by using Rees theorem in this paper.