Descriptional Complexity of Bounded Context-Free Languages

  • Andreas Malcher
  • Giovanni Pighizzini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4588)

Abstract

Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear context-free languages. Furthermore, the increase in size when converting arbitrary PDAs accepting ultralinear languages to finite-turn PDAs cannot be bounded by any recursive function. The latter phenomenon is known as non-recursive trade-off. In this paper, finite-turn PDAs accepting letter-bounded languages are considered. It turns out that in this case the non-recursive trade-off is reduced to a recursive trade-off, more precisely, to an exponential trade-off. A conversion algorithm is presented and the optimality of the construction is shown by proving tight lower bounds. Furthermore, the question of reducing the number of turns of a given finite-turn PDA is studied. Again, a conversion algorithm is provided which shows that in this case the trade-off is at most polynomial.

Keywords

automata and formal languages descriptional complexity finite-turn pushdown automata recursive trade-offs bounded languages 

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References

  1. 1.
    Goldstine, J., Kappes, M., Kintala, C.M.R., Leung, H., Malcher, A., Wotschke, D.: Descriptional complexity of machines with limited resources. Journal of Universal Computer Science 8(2), 193–234 (2002)MathSciNetGoogle Scholar
  2. 2.
    Ginsburg, S., Spanier, E.H.: Finite-turn pushdown automata. SIAM Journal on Control 4(3), 429–453 (1966)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading MA (1978)MATHGoogle Scholar
  4. 4.
    Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. International Journal of Foundations of Computer Science 14(6), 1087–1102 (2003)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading MA (1979)MATHGoogle Scholar
  6. 6.
    Kelemenova, A.: Complexity of Normal Form Grammars. Theoretical Computer Science 28, 299–314 (1984)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kutrib, M.: The phenomenon of non-recursive trade-offs. International Journal of Foundations of Computer Science 16(5), 957–973 (2005)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Malcher, A.: On recursive and non-recursive trade-offs between finite-turn pushdown automata. In: Descriptional Complexity of Formal Systems (DCFS 2005), Università degli Studi di Milano, Rapporto Tecnico 06-05, pp. 215–226 (2005)Google Scholar
  9. 9.
    Meyer, A.R., Fischer, M.J.: Economy of descriptions by automata, grammars, and formal systems. IEEE Symp. on Foundations of Computer Science, pp. 188–191 (1971)Google Scholar
  10. 10.
    Pighizzini, G., Shallit, J., Wang, M.-W.: Unary context-free grammars and pushdown automata, descriptional complexity and auxiliary space lower bounds. Journal of Computer and System Sciences 65, 393–414 (2002)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Andreas Malcher
    • 1
  • Giovanni Pighizzini
    • 2
  1. 1.Institut für Informatik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am MainGermany
  2. 2.Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, via Comelico 39, I-20135 MilanoItaly

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