Descriptional Complexity of Bounded Context-Free Languages

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


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.


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


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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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