Abstract
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.
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