Skip to main content

A pumping lemma for output languages of macro tree transducers

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1059))

Abstract

The concept of macro tree transducer is a formal model for studying properties of syntax-directed translations. In this paper, for output languages of producing, nondeleting, and noncopying macro tree transducers, we introduce a pumping lemma. We apply the pumping lemma to gain the following result: there is no producing and nondeleting macro tree transducer which computes the set of all monadic trees with double exponential height as output.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.V. Aho and J.D. Ullman. Translations on a context free grammar. Inform. and Control, 19:439–475, 1971.

    Google Scholar 

  2. Y. Bar-Hillel, M. Perles, and E. Shamir. On formal properties of simple phrase structure grammars. Z. Phonetik. Sprach. Komm., 14:143–172, 1961.

    Google Scholar 

  3. B. Courcelle and P. Franchi-Zannettacci. Attribute grammars and recursive program schemes. Theoret. Comput. Sci., 17:163–191 and 235–257, 1982.

    Google Scholar 

  4. J. Engelfriet. Bottom-up and top-down tree transformations — a comparison. Math. Syst. Theory, 9:198–231, 1975.

    Google Scholar 

  5. J. Engelfriet. Some open questions and recent results on tree transducers and tree languages. In R.V. Book, editor, Formal language theory; perspectives and open problems. New York, Academic Press, 1980.

    Google Scholar 

  6. J. Engelfriet. Tree transducers and syntax directed semantics. Technical Report Memorandum 363, Technische Hogeschool Twente, 1981.

    Google Scholar 

  7. J. Engelfriet, G. Rozenberg, and G. Slutzki. Tree transducers, L systems, and two-way machines. J. Comput. Syst. Sci., 20:150–202, 1980.

    Google Scholar 

  8. J. Engelfriet and H. Vogler. Macro tree transducers. J. Comput. Syst. Sci., 31:71–145, 1985.

    Google Scholar 

  9. J. Engelfriet and H. Vogler. Modular tree transducers. Theoret. Comput. Sci., 78:267–304, 1991.

    Google Scholar 

  10. Z. ésik. Decidability results concerning tree transducers. Acta Cybernetica, 5:1–20, 1980.

    Google Scholar 

  11. Z. Fülöp. On attributed tree transducers. Acta Cybernetica, 5:261–279, 1981.

    Google Scholar 

  12. Z. Fülöp, F. Herrmann, S. Vagvölgyi, and H. Vogler. Tree transducers with external functions. Theoret. Comput. Sci., 108:185–236, 1993.

    Google Scholar 

  13. E.T. Irons. A syntax directed compiler for ALGOL 60. Comm. Assoc. Comput. Mach., 4:51–55, 1961.

    Google Scholar 

  14. A. Kühnemann. A pumping lemma for output languages of macro tree transducers. Technical Report TUD/FI95/08, Technical University of Dresden, 1995.

    Google Scholar 

  15. A. Kühnemann and H. Vogler. A pumping lemma for output languages of attributed tree transducers. Acta Cybernetica, 11:261–305, 1994.

    Google Scholar 

  16. A. Kühnemann and H. Vogler. Synthesized and inherited functions — a new computational model for syntax-directed semantics. Acta Informatica, 31:431–477, 1994.

    Google Scholar 

  17. C.R. Perrault. Intercalation lemmas for tree transducer languages. J. Comput. Syst. Sci., 13:246–277, 1976.

    Google Scholar 

  18. W.C. Rounds. Mappings and grammars on trees. Math. Syst. Theory, 4:257–287, 1970.

    Google Scholar 

  19. J.W. Thatcher. Generalized2 sequential machine maps. J. Comput. Syst. Sci., 4:339–367, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Hélène Kirchner

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kühnemann, A. (1996). A pumping lemma for output languages of macro tree transducers. In: Kirchner, H. (eds) Trees in Algebra and Programming — CAAP '96. CAAP 1996. Lecture Notes in Computer Science, vol 1059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61064-2_28

Download citation

  • DOI: https://doi.org/10.1007/3-540-61064-2_28

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61064-9

  • Online ISBN: 978-3-540-49944-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics