Duplication Roots

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 contextfree language are closed under general duplication root. 1 Duplication A mutation, which occurs in DNA strands, is the duplication of a factor inside a strand. The interpretation of this as an operation on a string has inspired much recent work in Formal Languages, most prominently the duplication closure. The duplication closure of a word was introduced by Dassow et al. [6], who sho...

• Type: Conference
• Year: 2007
• Where: DLT
• Authors: Peter Leupold
• Keywords: DLT 2007, Duplication Closure, Duplication Root, Theoretical Computer Science, finite Duplication Root