Word Operation Closure and Primitivity of Languages

Abstract: Based on the general operation ◦ of words, called bw-operation, the notions of ◦-primitive words, ◦-closed languages, ◦-bases of languages and operationleft-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