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Duplications and Pseudo-Duplications

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Unconventional Computation and Natural Computation (UCNC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9252))

Abstract

A duplication is basic phenomenon that occurs through molecular evolution on a biological sequence. A duplication on a string copies any substring of the string. We define k-pseudo-duplication of a string w that consists, roughly speaking, of all strings obtained from w by inserting after a substring u another substring obtained from u by at most k edit operations. We consider three variants of duplication operations, duplication, k-pseudo-duplication and reverse-duplication. First, we give the necessary and sufficient number of states that a nondeterministic finite automaton needs to recognize duplications on a string. Then, we show that regular languages and context-free languages are not closed under the duplication, k-pseudo-duplication and reverse-duplication operations. Furthermore, we show that the class of context-sensitive languages is closed under duplication, pseudo-duplication and reverse-duplication.

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Acknowledgements

We wish to thank the referees for valuable suggestions that improve proofs for several results.

This research was supported by the Basic Science Research Program through NRF funded by MEST (2012R1A1A2044562), the International Cooperation Program managed by NRF of Korea (2014K2A1A2048512), the Yonsei University Future-leading Research Initiative of 2014 and the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.

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Authors and Affiliations

  1. Department of Computer Science, Yonsei University, 50 Yonsei-Ro, Seodaemum-Gu, Seoul, 120–749, Republic of Korea

    Da-Jung Cho, Yo-Sub Han, Hwee Kim & Alexandros Palioudakis

  2. School of Computing, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Kai Salomaa

Authors
  1. Da-Jung Cho
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  2. Yo-Sub Han
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  3. Hwee Kim
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  4. Alexandros Palioudakis
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  5. Kai Salomaa
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Corresponding author

Correspondence to Yo-Sub Han .

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Editors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Cristian S. Calude

  2. University of Auckland, Auckland, New Zealand

    Michael J. Dinneen

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Cho, DJ., Han, YS., Kim, H., Palioudakis, A., Salomaa, K. (2015). Duplications and Pseudo-Duplications. In: Calude, C., Dinneen, M. (eds) Unconventional Computation and Natural Computation. UCNC 2015. Lecture Notes in Computer Science(), vol 9252. Springer, Cham. https://doi.org/10.1007/978-3-319-21819-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-21819-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21818-2

  • Online ISBN: 978-3-319-21819-9

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