caa a22 4500 445869542 CHVBK 20180317145507.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00236-010-0127-2 doi (NATIONALLICENCE)springer-10.1007/s00236-010-0127-2 Some properties of the disjunctive languages contained in Q [Elektronische Daten] [Zheng-Zhu Li, Y. Tsai] The set of all primitive words Q over an alphabet X was first defined and studied by Shyr and Thierrin (Proceedings of the 1977 Inter. FCT-Conference, Poznan, Poland, Lecture Notes in Computer Science 56. pp. 171-176 (1977)). It showed that for the case |X| ≥ 2, the set along with $${Q^{(i)} = \{f^i\,|\,f \in Q\}, i\geq 2}$$ are all disjunctive. Since then these disjunctive sets are often be quoted. Following Shyr and Thierrin showed that the half sets $${Q_{ev} = \{f \in Q\,|\,|f| = {\rm even}\}}$$ and Q od = Q \ Q ev of Q are disjunctive, Chien proved that each of the set $${Q_{p,r}= \{u\in Q\,|\,|u|\equiv r\,(mod\,p) \},\,0\leq r < p}$$ is disjunctive, where p is a prime number. In this paper, we generalize this property to that all the languages $${Q_{n,r}= \{u\in Q\,|\,|u|\equiv r\,(mod\,n) \},\, 0\leq r < n}$$ are disjunctive languages, where n is any positive integer. We proved that for any n≥ 1, k≥ 2, (Q n,0)k are all regular languages. Some algebraic properties related to the family of languages {Q n,r | n ≥ 2, 0 ≤ r < n } are investigated. Springer-Verlag, 2010 Li Zheng-Zhu Center of General Education, Aletheia University on Motou Campus, 721, Matou, Tainan, Taiwan aut Tsai Y. Department of Applied Mathematics, Chung-Yuan Christian University, 320, Chung-Li, Taiwan aut Acta Informatica Springer-Verlag 48/1(2011-02-01), 1-18 0001-5903 48:1<1 2011 48 236 https://doi.org/10.1007/s00236-010-0127-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00236-010-0127-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Zheng-Zhu Center of General Education, Aletheia University on Motou Campus, 721, Matou, Tainan, Taiwan aut NATIONALLICENCE 700 1- Tsai Y. Department of Applied Mathematics, Chung-Yuan Christian University, 320, Chung-Li, Taiwan aut NATIONALLICENCE 773 0- Acta Informatica Springer-Verlag 48/1(2011-02-01), 1-18 0001-5903 48:1<1 2011 48 236 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer