String-rewriting systems
On the regularity of languages on a binary alphabet generated by copying systems
Information Processing Letters
Deleting string rewriting systems preserve regularity
Theoretical Computer Science - Developments in language theory
Uniformly bounded duplication languages
Discrete Applied Mathematics
Closure of language classes under bounded duplication
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
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Recently the duplication closure of words and languages has received much interest. We investigate a reversal of it: the duplication root reduces a word to a square-free one. After stating a few elementary properties of this type of root, we explore the question whether or not a language has finite duplication root. For regular languages and uniformly bounded duplication root this is decidable. The main result then concerns the closure of regular and context-free languages under duplication. Regular languages are closed under bounded and uniformly bounded duplication root, while neither regular nor context-free language are closed under general duplication root.