Bounded Prefix-Suffix Duplication: Language Theoretic and Algorithmic Results

Abstract

We consider a restricted variant of the prefix-suffix duplication operation, called bounded prefix-suffix duplication. It consists in the iterative duplication of a length-bounded prefix or suffix of a given word. We give a sufficient condition for the closure of a class of languages under bounded prefix-suffix duplication. Consequently, we get that the class of regular languages is closed under bounded prefix-suffix duplication; furthermore, we propose an algorithm which decides whether a regular language is a finite k-prefix-suffix duplication language. An efficient algorithm solving the membership problem for the k-prefix-suffix duplication of a language is also presented. Finally, we define the k-prefix-suffix duplication distance between two words, extend it to languages and show how it can be computed for regular languages.