Closure of language classes under bounded duplication

Authors:
Masami Ito;Peter Leupold;Kayoko Shikishima-Tsuji
Affiliations:
Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Kyoto, Japan;Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, Catalunya, Spain;Tenri University, Tenri, Japan
Venue:
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Year:
2006

Citing 6
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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.