Deterministic Biautomata and Subclasses of Deterministic Linear Languages

  • Galina Jirásková
  • Ondřej KlímaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11417)


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.



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.


  1. 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). Scholar
  2. 2.
    Baker, B.S., Book, R.V.: Reversal-bounded multipushdown machines. J. Comput. Syst. Sci. 8(3), 315–332 (1974)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bedregal, B.R.C.: Some subclasses of linear languages based on nondeterministic linear automata. Preprint (2016).
  4. 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). Scholar
  5. 5.
    Holzer, M., Jakobi, S.: Minimization and characterizations for biautomata. Fundam. Informaticae 136(1–2), 113–137 (2015)MathSciNetzbMATHGoogle Scholar
  6. 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). Scholar
  7. 7.
    Hoogeboom, H.J.: Undecidable problems for context-free grammars. Unpublished (2015).
  8. 8.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory. Languages and Computation. Addison-Wesley, Boston (1979)zbMATHGoogle Scholar
  9. 9.
    Ibarra, O.H., Jiang, T., Ravikumar, B.: Some subclasses of context-free languages in NC1. Inf. Process. Lett. 29(3), 111–117 (1988)CrossRefGoogle Scholar
  10. 10.
    Jakobi, S.: Modern Aspects of Classical Automata Theory: Finite Automata, Biautomata, and Lossy Compression. Logos Verlag, Berlin (2015)Google Scholar
  11. 11.
    Jones, N.D.: Space-bounded reducibility among combinatorial problems. J. Comput. Syst. Sci. 11(1), 68–85 (1975)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Klíma, O., Polák, L.: On biautomata. RAIRO - Theor. Inf. Appl. 46(4), 573–592 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kurki-Suonio, R.: On top-to-bottom recognition and left recursion. Commun. ACM 9(7), 527–528 (1966)CrossRefGoogle Scholar
  14. 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). Scholar
  15. 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)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Rosenberg, A.L.: A machine realization of the linear context-free languages. Inf. Control 10(2), 175–188 (1967)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceSlovak Republic
  2. 2.Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic

Personalised recommendations