Advertisement

Unidirectional Derivation Semantics for Synchronous Tree-Adjoining Grammars

  • Matthias Büchse
  • Andreas Maletti
  • Heiko Vogler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)

Abstract

Synchronous tree-adjoining grammars have been given two types of semantics: one based on bimorphisms and one based on synchronous derivations, in both of which the input and output trees are constructed synchronously. We introduce a third type of semantics that is based on unidirectional derivations. It derives output trees based on a given input tree and thus marks a first step towards conditional probability distributions. We prove that the unidirectional semantics coincides with the bimorphism-based semantics with the help of a strong correspondence to linear and nondeleting extended top-down tree transducers with explicit substitution. In addition, we show that stateful synchronous tree-adjoining grammars admit a normal form in which only adjunction is used. This contrasts the situation encountered in the stateless case.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation, and Compiling. Prentice Hall (1972)Google Scholar
  2. 2.
    Büchse, M., Nederhof, M.J., Vogler, H.: Tree parsing with synchronous tree-adjoining grammars. In: Proc. Parsing Technologies, pp. 14–25. ACL (2011)Google Scholar
  3. 3.
    Büchse, M., Nederhof, M.J., Vogler, H.: Tree parsing for tree-adjoining machine translation (submitted, 2012), www.inf.tu-dresden.de/index.php?node_id=1571
  4. 4.
    Chiang, D.: Hierarchical phrase-based translation. Comput. Linguist. 33(2), 201–228 (2007)zbMATHCrossRefGoogle Scholar
  5. 5.
    Courcelle, B., Franchi-Zannettacci, P.: Attribute grammars and recursive program schemes I. Theoret. Comput. Sci. 17(2), 163–191 (1982)MathSciNetCrossRefGoogle Scholar
  6. 6.
    DeNeefe, S.: Tree-Adjoining Machine Translation. Ph.D. thesis, University of Southern California (2011)Google Scholar
  7. 7.
    DeNeefe, S., Knight, K., Vogler, H.: A decoder for probabilistic synchronous tree insertion grammars. In: Proc. Applications of Tree Automata in Natural Language Processing, pp. 10–18. ACL (2010)Google Scholar
  8. 8.
    Engelfriet, J.: Bottom-up and top-down tree transformations—a comparison. Math. Systems Theory 9(3), 198–231 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Engelfriet, J.: Some open questions and recent results on tree transducers and tree languages. In: Book, R.V. (ed.) Formal Language Theory—Perspectives and Open Problems, pp. 241–286. Academic Press (1980)Google Scholar
  10. 10.
    Engelfriet, J., Vogler, H.: Macro tree transducers. J. Comput. System Sci. 31(1), 71–146 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Fülöp, Z., Maletti, A., Vogler, H.: Preservation of recognizability for synchronous tree substitution grammars. In: Proc. Applications of Tree Automata in Natural Language Processing, pp. 1–9. ACL (2010)Google Scholar
  12. 12.
    Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984)Google Scholar
  13. 13.
    Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg and Salomaa [23], ch. 1, pp. 1–68Google Scholar
  14. 14.
    Graehl, J., Knight, K., May, J.: Training tree transducers. Comput. Linguist. 34(3), 391–427 (2008)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Joshi, A., Schabes, Y.: Tree-adjoining grammars. In: Rozenberg and Salomaa [23], ch. 2, pp. 69–123Google Scholar
  16. 16.
    Knight, K., Graehl, J.: An Overview of Probabilistic Tree Transducers for Natural Language Processing. In: Gelbukh, A. (ed.) CICLing 2005. LNCS, vol. 3406, pp. 1–24. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Koehn, P.: Statistical Machine Translation. Cambridge University Press (2010)Google Scholar
  18. 18.
    Maletti, A.: Compositions of extended top-down tree transducers. Inform. and Comput. 206(9-10), 1187–1196 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Maletti, A.: A tree transducer model for synchronous tree-adjoining grammars. In: Proc. Association for Computational Linguistics, pp. 1067–1076. ACL (2010)Google Scholar
  20. 20.
    Maletti, A., Engelfriet, J.: Strong lexicalization of tree adjoining grammars. In: Proc. Association for Computational Linguistics. ACL (to appear, 2012)Google Scholar
  21. 21.
    Nesson, R., Shieber, S.M., Rush, A.: Induction of probabilistic synchronous tree-insertion grammars for machine translation. In: Proc. Association for Machine Translation in the Americas (2006)Google Scholar
  22. 22.
    Rounds, W.C.: Mappings and grammars on trees. Math. Systems Theory 4(3), 257–287 (1970)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 3. Springer (1997)Google Scholar
  24. 24.
    Schabes, Y.: Mathematical and Computational Aspects of Lexicalized Grammars. Ph.D. thesis, University of Pennsylvania, Philadelphia (1990)Google Scholar
  25. 25.
    Shieber, S.M.: Synchronous grammars as tree transducers. In: Proc. Tree Adjoining Grammar and Related Formalisms, pp. 88–95 (2004)Google Scholar
  26. 26.
    Shieber, S.M.: Unifying synchronous tree adjoining grammars and tree transducers via bimorphisms. In: Proc. European Chapter of the Association for Computational Linguistics, pp. 377–384. ACL (2006)Google Scholar
  27. 27.
    Shieber, S.M.: Probabilistic synchronous tree-adjoining grammars for machine translation: The argument from bilingual dictionaries. In: Proc. Syntax and Structure in Statistical Translation, pp. 88–95. ACL (2007)Google Scholar
  28. 28.
    Shieber, S.M., Schabes, Y.: Synchronous tree-adjoining grammars. In: Proc. Computational Linguistics, pp. 253–258. University of Helsinki (1990)Google Scholar
  29. 29.
    Thatcher, J.W.: Generalized2 sequential machine maps. J. Comput. System Sci. 4(4), 339–367 (1970)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    The XTAG Project, www.cis.upenn.edu/~xtag/

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Matthias Büchse
    • 1
  • Andreas Maletti
    • 2
  • Heiko Vogler
    • 1
  1. 1.Department of Computer ScienceTechnische Universität DresdenDresdenGermany
  2. 2.Institute for Natural Language ProcessingUniversität StuttgartStuttgartGermany

Personalised recommendations