109 urn:lsid:arphahub.com:pub:3dc5f44e-8666-58db-bc76-a455210e8891 JUCS - Journal of Universal Computer Science jucs 0948-695X 0948-6968 Journal of Universal Computer Science 10.3217/jucs-008-02-0243 27855 Research Article F.4.3 - Formal Languages Word Operation Closure and Primitivity of Languages Hsiao H. K. hkhsiao@mail.dyu.edu.tw 1 Huang C. C. 1 Yu S. S. 2 Department of General Education, Chung-Shan Medical University, Taichung, Taiwan Department of General Education, Chung-Shan Medical University Taichung Taiwan Department of Applied Mathematics, National Chung-Hsing University,, Taichung, Taiwan Department of Applied Mathematics, National Chung-Hsing University, Taichung Taiwan

Corresponding author: H. K. Hsiao (hkhsiao@mail.dyu.edu.tw).

Academic editor:

2002 28 02 2002 8 2 243 256 8E95D2F4-7BBE-5351-A511-EF079B5E6CBE 6996121 H. K. Hsiao, C. C. Huang, S. S. Yu This article is freely available under the J.UCS Open Content License.

Based on the general operation of words, called bw_operation, the notions of primitive words, closed languages, bases of languages and operation_left_quotient_closed languages are defined and investigated. These notions turn out to be generalizations of the classical notions of primitive words, plus_closed (star_closed) languages, minimal generating sets and deletion_closed languages. Properties of the set of all primitive words, the bases of non_empty languages, right residuals and operation_left_quotient closed languages are studied under the general concept of word operation. Properties of bi_catenation and related languages are discussed as examples and also by their own interests. 1.) C. S. Calude, K. Salomaa, S. Yu (eds.). Advances and Trends in Automata and Formal Languages. A Collection of Papers in Honour of the 60th Birthday of Helmut Jürgensen.