Skip to main content
SpringerLink
Log in

Deep pushdown automata

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

This paper introduces and discusses deep pushdown automata as a generalization of the classical pushdown automata. This generalization consists in allowing them to make expansions deeper in the pushdown. Based on the expansion depth, the present paper establishes an infinite hierarchy of language families that coincides with the hierarchy resulting from the n-limited state grammars, so the deep pushdown automata actually represent the automaton counterpart to these grammars. In its conclusion, this paper suggests some open problem areas.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation and Compiling, vol. 1. Parsing, Prentice Hall, Englewood Cliffs, New Jersey (1972)

  2. Autebert, J., Berstel, J., Boasson, L.: Context-free languages and pushdown automata. In: Rozenberg, G., Salomaa, A., (eds.) Handbook of Formal Languages, vol. 1. Springer (1997)

  3. Courcelle, B.: On jump deterministic pushdown automata. Math. Systems Theory 11, 87–109 (1977)

    Article  Google Scholar 

  4. Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Akademie Verlag, Berlin (1989)

    Google Scholar 

  5. Greibach, S.A.: Checking automata and one-way stack languages. JCSS 3, 196–217

  6. Ginsburg, S., Greibach, S.A., Harrison, M.A.: One-way stack automata. JACM 14, 389–418 (1967)

    Article  Google Scholar 

  7. Ginsburg, S., Spanier, E.: Finite-turn pushdown automata. SIAM J. Control 4, 429–453 (1968)

    Article  Google Scholar 

  8. Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley, Reading, Massachusetts (1978)

    Google Scholar 

  9. Kasai, T.: An hierarchy between context-free and context-sensitive languages. Journal of Computer and System Sciences 4, 492–508 (1970)

    Google Scholar 

  10. Lewis, H.R., Papadimitriou, C.H.: Elements of the Theory of Computation. Prentice-Hall, Englewood Cliffs (1981)

  11. Martin, J.C.: Introduction to Languages and the Theory of Computation, McGraw-Hill, New York (1991)

    Google Scholar 

  12. Meduna, A.: Automata and Languages: Theory and Applications. Springer, London (2000)

    Google Scholar 

  13. Meduna, A., Horwath, G.: On state grammars. Acta Cybernetica 8, 237–245 (1988)

    Google Scholar 

  14. Meduna, A.: Simultaneously one-turn two-pushdown automata. Inter. Computer Math. 679–687 (2003)

  15. Meduna, A., Kolář, D.: Regulated pushdown automata. Acta Cybernetica 653–664 (2000)

  16. Moriya, E.: Some remarks on state grammars and matrix grammars. Information and Control 23, 48–57 (1973)

    Article  Google Scholar 

  17. Moriya, E., Hofbauer, D., Huber, M., Otto, F.: On state-alternating context-free grammars. Theoretical Computer Science 337, 183–216 (2005)

    Article  Google Scholar 

  18. Sakarovitch, J.: Pushdown automata with terminating languages. Languages and Automata Symposium, RIMS 421, pp. 15–29, Kyoto University (1981)

    Google Scholar 

  19. Sudkamp, T.A.: Languages and Machines. Addison Wesley, Reading, Massachusetts (1988)

    Google Scholar 

  20. Valiant, L.: The equivalence problem for deterministic finite turn pushdown automata. Information and Control 81, 265–279 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Systems, Faculty of Information Technology, Brno University of Technology, Božetěchova 2, Brno, 61266, Czech Republic

    Alexander Meduna

Authors
  1. Alexander Meduna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Meduna.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meduna, A. Deep pushdown automata. Acta Informatica 42, 541–552 (2006). https://doi.org/10.1007/s00236-006-0005-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-006-0005-0

Keywords

Search

Navigation