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Deterministic Biautomata and Subclasses of Deterministic Linear Languages

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Book cover Language and Automata Theory and Applications (LATA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11417))

Abstract

We propose the notion of a deterministic biautomaton, a machine reading an input word from both ends. We focus on various subclasses of deterministic linear languages and give their characterizations by certain subclasses of deterministic biautomata. We use these characterizations to establish closure properties of the studied subclasses of languages and to get basic decidability results concerning them.

G. Jirásková—Research supported by VEGA grant 2/0132/19 and grant APVV-15-0091.

O. Klíma—Research supported by Institute for Theoretical Computer Science (ITI), project No. P202/12/G061 of the Grant Agency of the Czech Republic.

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References

  1. Autebert, J.-M., Berstel, J., Boasson, L.: Context-free languages and pushdown automata. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 111–174. Springer, Heidelberg (1997). https://doi.org/10.1007/978-3-642-59136-5_3

    Chapter  Google Scholar 

  2. Baker, B.S., Book, R.V.: Reversal-bounded multipushdown machines. J. Comput. Syst. Sci. 8(3), 315–332 (1974)

    Article  MathSciNet  Google Scholar 

  3. Bedregal, B.R.C.: Some subclasses of linear languages based on nondeterministic linear automata. Preprint (2016). http://arxiv.org/abs/1611.10276

  4. de la Higuera, C., Oncina, J.: Inferring deterministic linear languages. In: Kivinen, J., Sloan, R.H. (eds.) COLT 2002. LNCS (LNAI), vol. 2375, pp. 185–200. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45435-7_13

    Chapter  Google Scholar 

  5. Holzer, M., Jakobi, S.: Minimization and characterizations for biautomata. Fundam. Informaticae 136(1–2), 113–137 (2015)

    MathSciNet  MATH  Google Scholar 

  6. Holzer, M., Lange, K.-J.: On the complexities of linear LL(1) and LR(1) grammars. In: Ésik, Z. (ed.) FCT 1993. LNCS, vol. 710, pp. 299–308. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57163-9_25

    Chapter  MATH  Google Scholar 

  7. Hoogeboom, H.J.: Undecidable problems for context-free grammars. Unpublished (2015). https://liacs.leidenuniv.nl/~hoogeboomhj/second/codingcomputations.pdf

  8. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory. Languages and Computation. Addison-Wesley, Boston (1979)

    MATH  Google Scholar 

  9. Ibarra, O.H., Jiang, T., Ravikumar, B.: Some subclasses of context-free languages in NC1. Inf. Process. Lett. 29(3), 111–117 (1988)

    Article  Google Scholar 

  10. Jakobi, S.: Modern Aspects of Classical Automata Theory: Finite Automata, Biautomata, and Lossy Compression. Logos Verlag, Berlin (2015)

    Google Scholar 

  11. Jones, N.D.: Space-bounded reducibility among combinatorial problems. J. Comput. Syst. Sci. 11(1), 68–85 (1975)

    Article  MathSciNet  Google Scholar 

  12. Klíma, O., Polák, L.: On biautomata. RAIRO - Theor. Inf. Appl. 46(4), 573–592 (2012)

    Article  MathSciNet  Google Scholar 

  13. Kurki-Suonio, R.: On top-to-bottom recognition and left recursion. Commun. ACM 9(7), 527–528 (1966)

    Article  Google Scholar 

  14. Loukanova, R.: Linear context free languages. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) ICTAC 2007. LNCS, vol. 4711, pp. 351–365. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75292-9_24

    Chapter  Google Scholar 

  15. Nasu, M., Honda, N.: Mappings induced by pgsm-mappings and some recursively unsolvable problems of finite probabilistic automata. Inf. Control 15(3), 250–273 (1969)

    Article  MathSciNet  Google Scholar 

  16. Rosenberg, A.L.: A machine realization of the linear context-free languages. Inf. Control 10(2), 175–188 (1967)

    Article  Google Scholar 

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Acknowledgments

We would like to thank Professor Erkki Mäkkinen who proposed the topic of deterministic linear languages to us. We are also grateful to Libor Polák for useful discussions in the beginning of this research.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovak Republic

    Galina Jirásková

  2. Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Ondřej Klíma

Authors
  1. Galina Jirásková
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  2. Ondřej Klíma
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Correspondence to Ondřej Klíma .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. Saint Petersburg State University, St. Petersburg, Russia

    Alexander Okhotin

  3. Ariel University, Ariel, Israel

    Dana Shapira

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Jirásková, G., Klíma, O. (2019). Deterministic Biautomata and Subclasses of Deterministic Linear Languages. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham. https://doi.org/10.1007/978-3-030-13435-8_23

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  • DOI: https://doi.org/10.1007/978-3-030-13435-8_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-13434-1

  • Online ISBN: 978-3-030-13435-8

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