Closure of language classes under bounded duplication

Abstract

Duplication is an operation generating a language from a single word by iterated application of rewriting rules u → uu on factors. We extend this operation to entire languages and investigate, whether the classes of the Chomsky hierarchy are closed under duplication. Here we treat mainly bounded duplication, where the factors duplicated cannot exceed a given length. While over two letters the regular languages are closed under bounded duplication, over three or more letters they are not, if the length bound is 4 or greater. For 2 they are closed under duplication, the case of 3 remains open. Finally, the class of context-free languages is closed under duplication over alphabets of any size. © Springer-Verlag Berlin Heidelberg 2006.