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1-Normal DRA for Insertion Languages

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Theoretical Computer Science and Discrete Mathematics (ICTCSDM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10398))

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Abstract

Restarting automaton is a type of regulated rewriting system, introduced as a model for analysis by reduction. It is a linguistically motivated method for checking the correctness of a sentence. In this paper, we introduce a new definition of normal restarting automaton in which only one substring is removed using the DEL operation in a cycle. This DEL operation is applied to reverse the insertion operation in an insertion grammar. We use this 1-normal restarting automaton to solve the membership problem of insertion languages. Further, we introduce some interesting closure properties of 1-normal restarting automata.

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Notes

  1. 1.

    in our paper, we assume that after every DEL operation is immediately followed by RST, its forming DEL-RST.

References

  1. Jancar, P., Mraz, F., Platek, M., Prochazka, M., Vogel, J.: Deleting automata with a restart operation. In: Bozapalidis, S. (ed.) Proceedings of Developments in Language language theory III(97), Thessaloniki, pp. 191–202 (1998)

    Google Scholar 

  2. Jancar, P., Mraz, F., Platek, M., Prochazka, M., Vogel, J.: Restarting automata, marcus grammars and context-free languages. In: Dassow, J., Rozenberg, G., Salomaa, A. (eds.) Developments in Language Theory, pp. 102–111. World Scientific Publishing (1996)

    Google Scholar 

  3. Haussler, D.: Insertion and Iterated Insertion as Operations on Formal Languages. Ph.D. Thesis, University of Colorado, Boulder (1982)

    Google Scholar 

  4. Haussler, D.: Insertion languages. Inf. Sci. 131(1), 77–89 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  5. Galiukschov, B.S.: Semicontextual grammars (in Russian). MAT. Logica i Mat. Ling. 38–50 (1981)

    Google Scholar 

  6. Kari, L., Thierrin, G.: Contextual insertions/deletions and computability. Inf. Comput. 131(1), 47–61 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chytil, M.P., Platek, M., Vogel, J.: A note on the Chomsky hierarchy. Bull. EATCS 27, 23–30 (1985)

    Google Scholar 

  8. Jancar, P., Mráz, F., Plátek, M.: A taxonomy of forgetting automata. In: Borzyszkowski, A.M., Sokołowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 527–536. Springer, Heidelberg (1993). doi:10.1007/3-540-57182-5_44

    Chapter  Google Scholar 

  9. Marcus, S.: Contextual Grammars. Revue Roumane de Mathematiques Pures et Appliques 14(10), 1525–1534 (1969)

    Google Scholar 

  10. Paun, G., Nguyen, X.M.: On the inner contextual grammars. Rev. Roum. Pures. Appl. 25, 641–651 (1980)

    MATH  MathSciNet  Google Scholar 

  11. Paun, G.: Marcus Contextual Grammars. Kluwer Academic Publishers, Dordrecht (1997)

    Book  MATH  Google Scholar 

  12. Cerno, P., Mráz, F.: Clearing restarting automata. Fundam. Inform. 104, 17–54 (2010)

    MATH  MathSciNet  Google Scholar 

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Acknowledgments

Tool Development - Poorna Chandra Tejasvi, Btech third year student of Computer Science and Engineering, Christ University Faculty of Engineering, Bangalore.

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Authors and Affiliations

  1. Computer Science & Engineering, ICFAI Tech School, Hyderabad, 501203, India

    Abhisek Midya

  2. Theoretical Computer Science Lab, School of Computer Science and Engineering, VIT University, Vellore, 632014, India

    Lakshmanan Kuppusamy

  3. Computer Science and Engineering, Christ University Faculty of Engineering, Bangalore, 560074, India

    V. S. Sumitha & Alok Kumar Pani

Authors
  1. Abhisek Midya
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  2. Lakshmanan Kuppusamy
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  3. V. S. Sumitha
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  4. Alok Kumar Pani
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Correspondence to Abhisek Midya .

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Editors and Affiliations

  1. Kalasalingam University, Krishnankoil, India

    S. Arumugam

  2. Ball State University, Muncie, Indiana, USA

    Jay Bagga

  3. Indiana University – Purdue University, Fort Wayne, Indiana, USA

    Lowell W. Beineke

  4. Indian Institute of Technology, New Delhi, India

    B.S. Panda

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Midya, A., Kuppusamy, L., Sumitha, V.S., Pani, A.K. (2017). 1-Normal DRA for Insertion Languages. In: Arumugam, S., Bagga, J., Beineke, L., Panda, B. (eds) Theoretical Computer Science and Discrete Mathematics. ICTCSDM 2016. Lecture Notes in Computer Science(), vol 10398. Springer, Cham. https://doi.org/10.1007/978-3-319-64419-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-64419-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64418-9

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