### 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 |
---|---|

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.

}

*International Journal of Unconventional Computing*, vol. 12, no. 2-3, pp. 145-167.

**Duplications and pseudo-duplications.** / Cho, Da Jung; Han, Yo Sub; Kim, Hwee; Palioudakis, Alexandros; Salomaa, Kai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Duplications and pseudo-duplications

AU - Cho, Da Jung

AU - Han, Yo Sub

AU - Kim, Hwee

AU - Palioudakis, Alexandros

AU - Salomaa, Kai

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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 = x1x2x3, a duplication of w is x1x2x2x3. 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.

AB - 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 = x1x2x3, a duplication of w is x1x2x2x3. 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.

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M3 - Article

VL - 12

SP - 145

EP - 167

JO - International Journal of Unconventional Computing

JF - International Journal of Unconventional Computing

SN - 1548-7199

IS - 2-3

ER -