Word Operation Closure and Primitivity of Languages

H. K. Hsiao (Department of General Education, Chung-Shan Medical University, Taiwan)

C. C. Huang (Department of General Education, Chung-Shan Medical University, Taiwan)

S. S. Yu (Department of Applied Mathematics, National Chung-Hsing University,, Taiwan)

Abstract: 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.

Keywords: Word operation, base, closure, dense, primitivity, right residual

Categories: F.4.3