Word Operation Closure and Primitivity of Languages

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.