Closure of Language Classes Under Bounded Duplication

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. 1 Duplication In a series of recent articles, languages generated from a single word by iteration of the duplication operation have been investigated. This operation was inspired by a behaviour observed in strands of DNA: certain factors of such sequences can be duplicated within their strand forming...

• Type: Conference
• Year: 2006
• Where: DLT
• Authors: Masami Ito, Peter Leupold, Kayoko Shikishima-Tsuji
• Keywords: DLT 2006, DLT 2007, Duplication Operation, Iterated Application, Single Words