Compositions of Top-Down Tree Transducers with ε-Rules

  • Andreas Maletti
  • Heiko Vogler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6062)

Abstract

Top-down tree transducers with ε-rules (εtdtts) are a restricted version of extended top-down tree transducers. They are implemented in the framework Tiburon and fulfill some criteria desirable in a machine translation model. However, they compute a class of transformations that is not closed under composition (not even for linear and nondeleting εtdtts). A composition construction that composes two εtdtts M and N is presented, and it is shown that the construction is correct, whenever (i) N is linear, (ii) M is total or N is nondeleting, and (iii) M has at most one output symbol in each rule.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hopcroft, J.E., Ullman, J.D.: Introduction to automata theory, languages, and computation. Addison-Wesley, Reading (1979)MATHGoogle Scholar
  2. 2.
    Mohri, M.: Weighted Automata Algorithms. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, pp. 209–252. Springer, Heidelberg (2009)Google Scholar
  3. 3.
    Mohri, M., Pereira, F.C.N., Riley, M.: The design principles of a weighted finite-state transducer library. Theoret. Comput. Sci. 231(1), 17–32 (2000)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kaplan, R.M., May, M.: Regular models of phonological rule systems. Computational Linguistics 20(3), 331–378 (1994)Google Scholar
  5. 5.
    Kanthak, S., Ney, H.: Fsa: an efficient and flexible C + +  toolkit for finite state automata using on-demand computation. In: Proc. ACL, pp. 510–517 (2004)Google Scholar
  6. 6.
    Graehl, J.: Carmel: finite-state toolkit. ISI/USC (1997), http://www.isi.edu/licensed-sw/carmel/
  7. 7.
    Allauzen, C., Riley, M., Schalkwyk, J., Skut, W., Mohri, M.: OpenFst — a general and efficient weighted finite-state transducer library. In: Holub, J., Žďárek, J. (eds.) CIAA 2007. LNCS, vol. 4783, pp. 11–23. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Rounds, W.C.: Mappings and grammars on trees. Math. Syst. Theory 4(3), 257–287 (1970)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Thatcher, J.W.: Generalized2 sequential machine maps. J. Comput. Syst. Sci. 4(4), 339–367 (1970)MATHMathSciNetGoogle Scholar
  10. 10.
    Arnold, A., Dauchet, M.: Transductions inversibles de forêts. Thèse 3ème cycle M. Dauchet, Université de Lille (1975)Google Scholar
  11. 11.
    Arnold, A., Dauchet, M.: Bi-transductions de forêts. In: Proc. ICALP, pp. 74–86. Cambridge University Press, Cambridge (1976)Google Scholar
  12. 12.
    Graehl, J., Knight, K., May, J.: Training tree transducers. Computational Linguistics 34(3), 391–427 (2008)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Shabes, Y.: Mathematical and computational aspects of lexicalized grammars. PhD thesis, University of Pennsylvania (1990)Google Scholar
  14. 14.
    Shieber, S.M., Schabes, Y.: Synchronous tree-adjoining grammars. In: Proc. ACL, pp. 253–258 (1990)Google Scholar
  15. 15.
    Lilin, E.: Une généralisation des transducteurs d’états finis d’arbres: les S-transducteurs. Thèse 3ème cycle, Université de Lille (1978)Google Scholar
  16. 16.
    Lilin, E.: Propriétés de clôture d’une extension de transducteurs d’arbres déterministes. In: Astesiano, E., Böhm, C. (eds.) CAAP 1981. LNCS, vol. 112, pp. 280–289. Springer, Heidelberg (1981)Google Scholar
  17. 17.
    Fülöp, Z., Kühnemann, A., Vogler, H.: A bottom-up characterization of deterministic top-down tree transducers with regular look-ahead. Inf. Process. Lett. 91(2), 57–67 (2004)MATHCrossRefGoogle Scholar
  18. 18.
    Fülöp, Z., Kühnemann, A., Vogler, H.: Linear deterministic multi bottom-up tree transducers. Theoret. Comput. Sci. 347(1-2), 276–287 (2005)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Engelfriet, J., Lilin, E., Maletti, A.: Extended multi bottom-up tree transducers. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 289–300. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Shieber, S.M.: Synchronous grammars as tree transducers. In: Proc. TAG+7, pp. 88–95 (2004)Google Scholar
  21. 21.
    Maletti, A.: Compositions of extended top-down tree transducers. Inf. Comput. 206(9-10), 1187–1196 (2008)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    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
  23. 23.
    Knight, K., May, J.: Applications of Weighted Automata in Natural Language Processing. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, pp. 555–580. Springer, Heidelberg (2009)Google Scholar
  24. 24.
    May, J., Knight, K.: Tiburon: A weighted tree automata toolkit. In: Ibarra, O.H., Yen, H.-C. (eds.) CIAA 2006. LNCS, vol. 4094, pp. 102–113. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  25. 25.
    Maletti, A., Graehl, J., Hopkins, M., Knight, K.: The power of extended top-down tree transducers. SIAM J. Comput. 39(2), 410–430 (2009)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Yamada, K., Knight, K.: A decoder for syntax-based statistical MT. In: ACL, pp. 303–310 (2002)Google Scholar
  27. 27.
    Baker, B.S.: Composition of top-down and bottom-up tree transformations. Inform. Control 41(2), 186–213 (1979)MATHCrossRefGoogle Scholar
  28. 28.
    Engelfriet, J.: Bottom-up and top-down tree transformations—a comparison. Math. Systems Theory 9(3), 198–231 (1975)MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Berstel, J.: Transductions and context-free languages. Teubner, Stuttgart (1979)MATHGoogle Scholar
  30. 30.
    Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984)MATHGoogle Scholar
  31. 31.
    Gécseg, F., Steinby, M.: Tree languages. In: Handbook of Formal Languages, vol. 3, pp. 1–68. Springer, Heidelberg (1997)Google Scholar
  32. 32.
    Kuich, W.: Full abstract families of tree series I. In: Jewels Are Forever, pp. 145–156. Springer, Heidelberg (1999)Google Scholar
  33. 33.
    Heger, C.: Composition of linear and nondeleting top-down tree transducers with ε-rules. Master’s thesis, TU Dresden (2008)Google Scholar
  34. 34.
    Knight, K.: Capturing practical natural language transformations. Machine Translation 21(2), 121–133 (2007)CrossRefGoogle Scholar
  35. 35.
    Knight, K.: Requirements on an MT system. Personal communication (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andreas Maletti
    • 1
  • Heiko Vogler
    • 2
  1. 1.Departament de Filologies RomàniquesUniversitat Rovira i VirgiliTarragonaSpain
  2. 2.Faculty of Computer ScienceTechnische Universität DresdenDresdenGermany

Personalised recommendations