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Most Pseudo-copy Languages Are Not Context-Free

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Book cover Computing and Combinatorics (COCOON 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13025))

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Abstract

It is well known that the copy language \(L = \{ww \mid w \in \varSigma ^*\}\) is not context-free despite its simplicity. We study pseudo-copy languages that are defined to be sets of catenations of two similar strings, and prove non-context-freeness of these languages. We consider the Hamming distance and the edit-distance for the error measure of the two similar strings in pseudo-copy languages. When the error has an upper bound or a fixed value, we show that the pseudo-copy languages are not context-free. Similarly, if the error has a lower bound of at least four, then such languages are not context-free, either. Finally, we prove that all these pseudo-copy languages are context-sensitive.

H. Cheon and J. Hahn—The first two authors contributed equally to this work.

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Notes

  1. 1.

    We only consider even-length strings for the Hamming distance between two halves.

  2. 2.

    https://cs.stackexchange.com/q/11585.

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Acknowledgments

We wish to thank the referees for valuable suggestions that improve the presentation of the paper.

This research was supported by the NRF grant funded by MIST (NRF-2020R1A4A3079947, NRF-2018R1D1A1A09084107).

Author information

Authors and Affiliations

  1. Yonsei University, Seoul, Republic of Korea

    Hyunjoon Cheon, Joonghyuk Hahn & Yo-Sub Han

  2. Kangwon National University, Gangwon-Do, Republic of Korea

    Sang-Ki Ko

Authors
  1. Hyunjoon Cheon
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  2. Joonghyuk Hahn
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  3. Yo-Sub Han
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  4. Sang-Ki Ko
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Corresponding author

Correspondence to Yo-Sub Han .

Editor information

Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Chi-Yeh Chen

  2. National Tsing Hua University, Hsinchu, Taiwan

    Wing-Kai Hon

  3. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

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Cheon, H., Hahn, J., Han, YS., Ko, SK. (2021). Most Pseudo-copy Languages Are Not Context-Free. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_16

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  • DOI: https://doi.org/10.1007/978-3-030-89543-3_16

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  • Online ISBN: 978-3-030-89543-3

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