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.
This work was partially supported by MIUR under the project PRIN “Automi e Linguaggi Formali: aspetti matematici e applicativi”.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Ginsburg, S., Spanier, E.H.: Finite-turn pushdown automata. SIAM Journal on Control 4(3), 429–453 (1966)
Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading MA (1978)
Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. International Journal of Foundations of Computer Science 14(6), 1087–1102 (2003)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading MA (1979)
Kelemenova, A.: Complexity of Normal Form Grammars. Theoretical Computer Science 28, 299–314 (1984)
Kutrib, M.: The phenomenon of non-recursive trade-offs. International Journal of Foundations of Computer Science 16(5), 957–973 (2005)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Malcher, A., Pighizzini, G. (2007). Descriptional Complexity of Bounded Context-Free Languages. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-73208-2_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73207-5
Online ISBN: 978-3-540-73208-2
eBook Packages: Computer ScienceComputer Science (R0)