稀疏语言与r-析取语言的连接（英文）

The concatenation of thin languages and r-disjunctive languages——several studies on combinatorial semigroups (Ⅰ)

综合了文献[1]与郭聿琦①等的另一篇文章中的几个事实,得到了命题1:若L1L∈Df(Dt,Dr),则L∈Df(Dt,Dr),其中L1,L为字母表A上语言且L1有限。关于命题1中的Dr情形,给出了一个新的简单证明。还证明了:关于D和Di,命题1也成立。进一步将命题1中L1从“有限的”改扩成“稀疏的”后,关于D,Df和Dt命题仍然成立;又用例子指出关于Di和Dr命题并不成立。

The background of this paper is from [1]and another paper① by Guo et al.,we merge some results in above two papers as Proposition 1: L1 L∈Df ( Dt,Dr ) implies L∈Df ( Dt,Dr ),where L1,L are languages over alphabet A and L1 is finite. In this paper,a new and simple proof of Proposition 1 is given for Dr . It is proved that Proposition 1 is also true for D and Di . Replacing “finite”with“thin”,Proposition 1 is true for D,Df and Dt;and some examples are given which show that Proposition 1 is not true for Di and Dr .