JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 2-7.doi: 10.6040/j.issn.1671-9352.0.2019.172


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

LIU Zu-hua1,2, GUO Yu-qi1*   

  1. 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, China;
    2. School of Mathematics, Kunming University, Kunming 650214, Yunan, China
  • Published:2019-06-05

Abstract: 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.

Key words: syntactic congruence, thin language, regular(disjunctive)language, r-regular(disjunctive)language

CLC Number: 

  • O157.4
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