%A LIU Zu-hua, GUO Yu-qi
%T The concatenation of thin languages and r-disjunctive languages ——several studies on combinatorial semigroups(Ⅰ)
%0 Journal Article
%D 2019
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2019.172
%P 2-7
%V 54
%N 6
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3086.shtml}
%8
%X The background of this paper is from [1] and another paper(1) by Guo et al., we merge some results in above two papers as Proposition 1: L1L∈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.