Skip to main content
SpringerLink
Log in

Pushdown tree automata

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

We define topdown pushdown tree automata (PDTA's) which extend the usual string pushdown automata by allowing trees instead of strings in both the input and the stack. We prove that PDTA's recognize the class of context-free tree languages. (Quasi)realtime and deterministic PDTA's accept the classes of Greibach and deterministic tree languages, respectively. Finally, PDTA's are shown to be equivalent to restricted PDTA's, whose stack is linear: this both yields a more operational way of recognizing context-free tree languages and connects them with the class of indexed languages.

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. A. V. Aho, Indexed grammars: An extension of the context-free case,JACM 15, 647–671 (1968).

    Google Scholar 

  2. A. V. Aho, Nested stack automata,JACM 16, 383–406 (1969).

    Google Scholar 

  3. A. Arnold, M. Dauchet, Transductions de forêts reconnaissables monadiques. Forêts corégulières, RAIRO Inf. Théor. 10, 5–28 (1976).

    Google Scholar 

  4. A. Arnold, B. Leguy, Une propriété des forêts algébriques de Greibach, Information & Control, Vol. 46, 108–134 (1980).

    Google Scholar 

  5. A. Arnold, M. Nivat, Formal computations of nondeterministic program schemes,MST 13, 219–236 (1980).

    Google Scholar 

  6. J. Berstel,Transductions and Context-Free Languages, Teubner, Stuttgart (1979).

    Google Scholar 

  7. G. Boudol, Langages algébriques d'arbres, LITP report n° 81–2.

  8. B. Courcelle, On jump deterministic pushdown automata,MST 11, 87–109 (1977).

    Google Scholar 

  9. W. Damm, Personal communication.

  10. P. Downey, Formal languages and recursion schemes, Ph.D. Harvard (1974).

  11. J. Engelfriet, Bottom-up and top-down tree transformations. A comparison,MST 9, 198–231 (1975).

    Google Scholar 

  12. J. Engelfriet, Some open questions and recent results on tree transducers and tree languages, inFormal Languages: Perspectives and Open Problems, Academic Press, London (1980), 241–286.

    Google Scholar 

  13. J. Engelfriet, E. M. Schmidt, IO and OI,JCSS 15, 328–353, (1977) andJCSS 16, 67–99 (1978).

    Google Scholar 

  14. J. Engelfriet, G. Slutzki, Extended macrogrammars and stack controlled machines, Memo n° 379, T. H. Twente, (1982).

  15. M. J. Fischer, Grammars with macro-like productions, 9thSWAT, 131–142 (1968).

  16. J. H. Gallier, DPDA's in “Atomic normal form” and applications to equivalence problems,TCS 14, 155–186 (1981).

    Google Scholar 

  17. S. Gorn, Explicit definitions and linguistic dominoes, in J. Hart, S. Takasu, Eds,Systems and Computer Science (1965).

  18. I. Guessarian,Algebraic semantics, Lect. Notes in Comp. Sc. n° 99, Springer-Verlag, Berlin (1981).

    Google Scholar 

  19. M. Harrison,Introduction to Formal Languages Theory, Addison-Wesley, London, (1978).

    Google Scholar 

  20. J. E. Hopcroft, A. J. Korenjak, Simple deterministic languages, 7th Symp. Switching and Automata Theory, Berkeley, 36–46 (1966).

    Google Scholar 

  21. B. Leguy, Réductions, transformations et classification des grammaires algébriques d'arbres, Thèse 3ème Cycle, Univ. Lille 1 (1980).

  22. M. Nivat, On the interpretation of recursive polyadic program schemes, Symp. Mat. 15, Rome, 255–281 (1975).

  23. N. Polian, Adhérences et centres de langages d'arbres, Thèse de 3ème cycle, Poitiers (1981).

  24. M. Rabin, Automata on infinite objects and Church's problem, CBSM regional Conf. series in Math. n° 13, AMS (1969).

  25. W. C. Rounds, Mappings and grammars on trees,MST 4, 257–287 (1970).

    Google Scholar 

  26. W. C. Rounds, Tree oriented proofs of some theorems on context-free and indexed languages, 2nd Symposium on Theory of Computing, 109–116 (1970).

  27. A. Saoudi, Forêts infinitaires reconnaissables, Thèse de 3ème cycle, Université Paris 7 (1982).

  28. K. Schimpf, A parsing method for context-free tree languages, Ph.D. University of Pennsylvania (1982).

  29. K. Schimpf, J. Gallier, Parsing tree languages using bottom-up tree automata with tree pushdown stores, Extended abstract, University of Pennsylvania (1981), to appear.

  30. J. M. Steyaert, Lemmes d'itération pour les familles d'arbres, Actes du Séminaire d'Inf. Théor. 1977–1978, LITP Report, Paris (1979).

  31. J. W. Thatcher, Tree automata: An informal survey, inCurrents in Theory of Comp., Aho (ed.), Prentice-Hall, London (1973).

    Google Scholar 

  32. J. W. Thatcher, J. B. Wright, Generalized finite automata theory with an application to a decision problem of second order logic,MST 2, 57–81 (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LITP-CNRS-UER de Mathématiques, Université Paris 7-T. 55/56, 2, Pl. Jussieu, 75251, Paris Cedex 05, France

    Inène Guessarian

Authors
  1. Inène Guessarian
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guessarian, I. Pushdown tree automata. Math. Systems Theory 16, 237–263 (1983). https://doi.org/10.1007/BF01744582

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01744582

Keywords

Search

Navigation