### Abstract

A duplication is one of the basic phenomena that occur in molecular evolution on a biological sequence. A duplication on a string is a process of copying a substring of the string—Given w = x_{1}x_{2}x_{3}, a duplication of w is x_{1}x_{2}x_{2}x_{3}. We define k-pseudo-duplication of a string w to be a set of all strings obtained from w by inserting after a substring u of w another substring uʹ such that the edit distance between u and uʹ is at most k. We consider duplication, k-pseudo-duplication and reverse duplication as operations on formal languages. First, we demonstrate that regular languages and context-free languages are not closed under the duplication, k-pseudo-duplication and reverse-duplication operations. Second, we show that context-sensitive languages are closed under duplication, pseudo-duplication and reverse-duplication. Last, we present the necessary and sufficient number of states that a nondeterministic finite automaton needs to recognize all duplications of a string with respect to the string length.

Original language | English |
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Pages (from-to) | 145-167 |

Number of pages | 23 |

Journal | International Journal of Unconventional Computing |

Volume | 12 |

Issue number | 2-3 |

Publication status | Published - 2016 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)

### Cite this

*International Journal of Unconventional Computing*,

*12*(2-3), 145-167.