International Conference on Machines, Computations, and Universality

MCU 2015: Machines, Computations, and Universality pp 94-112 | Cite as

Tinput-Driven Pushdown Automata

  • Martin Kutrib
  • Andreas Malcher
  • Matthias Wendlandt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9288)

Abstract

In input-driven pushdown automata (\(\text {IDPDA}\)) the input alphabet is divided into three distinct classes and the actions on the pushdown store (push, pop, nothing) are solely governed by the input symbols. Here, this model is extended in such a way that the input of an \(\text {IDPDA}\) is preprocessed by a deterministic sequential transducer. These automata are called tinput-driven pushdown automata (\(\text {TDPDA}\)) and it turns out that \(\text {TDPDA}\)s are more powerful than \(\text {IDPDA}\)s but still not as powerful as real-time deterministic pushdown automata. Nevertheless, even this stronger model has still good closure and decidability properties. In detail, it is shown that \(\text {TDPDA}\)s are closed under the Boolean operations union, intersection, and complementation. Furthermore, decidability procedures for the inclusion problem as well as for the questions of whether a given automaton is a \(\text {TDPDA}\) or an \(\text {IDPDA}\) are developed. Finally, representation theorems for the context-free languages using \(\text {IDPDA}\)s and \(\text {TDPDA}\)s are established.

Keywords

Input driven pushdown automata Sequential transducers Real-time deterministic context-free languages Closure properties Decidability questions 

References

  1. 1.
    Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Babai, L. (ed.) Symposium on Theory of Computing (STOC 2004), pp. 202–211. ACM (2004)Google Scholar
  2. 2.
    Alur, R., Madhusudan, P.: Adding nesting structure to words. J. ACM 56, 16 (2009)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bensch, S., Holzer, M., Kutrib, M., Malcher, A.: Input-driven stack automata. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds.) TCS 2012. LNCS, vol. 7604, pp. 28–42. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  4. 4.
    Bordihn, H., Holzer, M., Kutrib, M.: Economy of description for basic constructions on rational transductions. J. Autom. Lang. Comb. 9, 175–188 (2004)MathSciNetGoogle Scholar
  5. 5.
    von Braunmühl, B., Verbeek, R.: Input-driven languages are recognized in \(\log n\) space. In: Karpinski, M., van Leeuwen, J. (eds.) Topics in the Theory of Computation, Mathematics Studies, vol. 102, pp. 1–19. North-Holland (1985)Google Scholar
  6. 6.
    Chervet, P., Walukiewicz, I.: Minimizing variants of visibly pushdown automata. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 135–146. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  7. 7.
    Crespi-Reghizzi, S., Mandrioli, D.: Operator precedence and the visibly pushdown property. J. Comput. Syst. Sci. 78, 1837–1867 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dymond, P.W.: Input-driven languages are in \(\log n\) depth. Inform. Process. Lett. 26, 247–250 (1988)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hartmanis, J.: Context-free languages and turing machine computations. Proc. Symposia in Applied Mathematics 19, 42–51 (1967)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979) MATHGoogle Scholar
  11. 11.
    Kutrib, M., Malcher, A., Mereghetti, C., Palano, B., Wendlandt, M.: Deterministic input-driven queue automata: finite turns, decidability, and closure properties. Theor. Comput. Sci. 578, 58–71 (2015)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    La Torre, S., Madhusudan, P., Parlato, G.: A robust class of context-sensitive languages. In: Logic in Computer Science (LICS 2007), pp. 161–170. IEEE Computer Society (2007)Google Scholar
  13. 13.
    Madhusudan, P., Parlato, G.: The tree width of auxiliary storage. In: Ball, T., Sagiv, M. (eds.) Principles of Programming Languages (POPL 2011), pp. 283–294. ACM (2011)Google Scholar
  14. 14.
    Mehlhorn, K.: Pebbling mountain ranges and its application to DCFL-recognition. In: de Bakker, J.W., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 422–435. Springer, Heidelberg (1980) CrossRefGoogle Scholar
  15. 15.
    Myhill, J.: Finite automata and the representation of events. Technical Report TR 57–624, WADC (1957)Google Scholar
  16. 16.
    Okhotin, A., Salomaa, K.: Complexity of input-driven pushdown automata. SIGACT News 45, 47–67 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Schützenberger, M.P.: Sur les relations rationnelles. In: Brakhage, H. (ed.) Automata Theory and Formal Languages. LNCS, vol. 33, pp. 209–213. Springer, Heidelberg (1975)Google Scholar
  18. 18.
    Sheng, Y.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 41–110. Springer, Heidelberg (1997) Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Martin Kutrib
    • 1
  • Andreas Malcher
    • 1
  • Matthias Wendlandt
    • 1
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany

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