稠密正规语言的S．Y猜想的一些等价刻划

一个语言称为正规的如果它可被一台有限自动机识别，一个语言称为稠密的如果每个字都是该语言中某个字的一个小字，一个非空字称为本原的，如果此字不是其他任一字的幂，否则称此非空字为非本原字，Shyr和Yu在[3]中给出如下猜想：每个稠密正规语言都包含一个非本原字，如果能给出S．Y猜想在半群理论及码论中的等价陈述，则可把稠密正规语言的问题归结为半群理论及码论中的问题，从而为解决S．Y猜想提供了更多的途径。

Some Equivalent Statements of the S.Y Conjecture about Dense Regular Languages

A Language is regular if it can be recognized by a finite automaton. A language is dense if every word is a subword of some word in the language. A non empty word is primitive if it is not a power of any other word, otherwise it is an imprimitive word. Shyr and Yu conjectured that every dense regular language contains an imprimitive word in [3]. Some equivalent statements in semigroup theory and code theory of the S.Y conjecture is given in this note, and thus the S.Y conjecture about dense regular languages is transformed to the problems in semigroup theory and in code theory.