Skip to main content

Survey: Weighted Extended Top-Down Tree Transducers Part III — Composition

  • Chapter

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7020))

Abstract

In this survey (functional) compositions of weighted tree transformations computable by weighted extended top-down tree transducers are investigated. The existing results in the literature are explained and illustrated. It is argued, why certain compositions are not possible in the general case, and 3 informed conjectures provide an insight into potentially 3 new composition results that extend and complement the existing results. In particular, if all were true, then the beautiful symmetry in the composition results for weighted top-down and bottom-up tree transducers would be recovered.

The work was carried out while the first author was an intern at Universität Stuttgart.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alexandrakis, A., Bozapalidis, S.: Weighted grammars and Kleene’s theorem. Inf. Process. Lett. 24(1), 1–4 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  2. Arnold, A., Dauchet, M.: Bi-transductions de forêts. In: Michaelson, S., Milner, R. (eds.) ICALP 1976, pp. 74–86. Edinburgh University Press, Edinburgh (1976)

    Google Scholar 

  3. Arnold, A., Dauchet, M.: Morphismes et bimorphismes d’arbres. Theoret. Comput. Sci. 20(4), 33–93 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  5. Baker, B.S.: Composition of top-down and bottom-up tree transductions. Inform. and Control 41(2), 186–213 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  6. Berstel, J., Reutenauer, C.: Recognizable formal power series on trees. Theoret. Comput. Sci. 18(2), 115–148 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  7. Borchardt, B.: The Theory of Recognizable Tree Series. Ph.D. thesis, Technische Universität Dresden (2005)

    Google Scholar 

  8. Borchardt, B., Vogler, H.: Determinization of finite state weighted tree automata. J. Autom. Lang. Combin. 8(3), 417–463 (2003)

    MathSciNet  MATH  Google Scholar 

  9. Bozapalidis, S., Louscou-Bozapalidou, O.: The rank of a formal tree power series. Theoret. Comput. Sci. 27(1-2), 211–215 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  10. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Löding, C., Tison, S., Tommasi, M.: Tree automata techniques and applications (2007), http://tata.gforge.inria.fr

  11. Dauchet, M.: Transductions inversibles de forêts. Thèse 3ème cycle, Université de Lille (1975)

    Google Scholar 

  12. Engelfriet, J.: Bottom-up and top-down tree transformations: A comparison. Math. Systems Theory 9(3), 198–231 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  13. Engelfriet, J.: Top-down tree transducers with regular look-ahead. Math. Systems Theory 10(1), 289–303 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  14. Engelfriet, J., Fülöp, Z., Vogler, H.: Bottom-up and top-down tree series transformations. J. Autom. Lang. Combin. 7(1), 11–70 (2002)

    MathSciNet  MATH  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. Engelfriet, J., Lilin, E., Maletti, A.: Composition and decomposition of extended multi bottom-up tree transducers. Acta Inform. 46(8), 561–590 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Ésik, Z., Kuich, W.: Formal tree series. J. Autom. Lang. Combin. 8(2), 219–285 (2003)

    MathSciNet  MATH  Google Scholar 

  18. Fülöp, Z., Gazdag, Z., Vogler, H.: Hierarchies of tree series transformations. Theoret. Comput. Sci. 314(3), 387–429 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Fülöp, Z., Vogler, H.: Tree series transformations that respect copying. Theory Comput. Systems 36(3), 247–293 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Fülöp, Z., Vogler, H.: Weighted tree automata and tree transducers. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata, ch. 9, pp. 313–403. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984)

    MATH  Google Scholar 

  22. Gécseg, F., Steinby, M.: Tree languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, ch. 1, pp. 1–68. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  23. Golan, J.S.: Semirings and their Applications. Kluwer Academic, Dordrecht (1999)

    Book  MATH  Google Scholar 

  24. Graehl, J., Knight, K., May, J.: Training tree transducers. Comput. Linguist. 34(3), 391–427 (2008)

    Article  MathSciNet  Google Scholar 

  25. Hebisch, U., Weinert, H.J.: Semirings — Algebraic Theory and Applications in Computer Science. Algebra, vol. 5. World Scientific, Singapore (1998)

    Book  MATH  Google Scholar 

  26. Knight, K., Graehl, J.: An overview of probabilistic tree transducers for natural language processing. In: Gelbukh, A.F. (ed.) CICLing 2005. LNCS, vol. 3406, pp. 1–24. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  27. Koehn, P.: Statistical Machine Translation. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  28. Koehn, P., Och, F.J., Marcu, D.: Statistical phrase-based translation. In: NAACL 2003, pp. 48–54. Association for Computational Linguistics (2003)

    Google Scholar 

  29. Kühnemann, A.: Benefits of tree transducers for optimizing functional programs. In: Arvind, V., Sarukkai, S. (eds.) FST TCS 1998. LNCS, vol. 1530, pp. 146–158. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  30. Kuich, W.: Formal power series over trees. In: Bozapalidis, S. (ed.) DLT 1997, pp. 61–101. Aristotle University of Thessaloniki (1998)

    Google Scholar 

  31. Kuich, W.: Full abstract families of tree series I. In: Karhumäki, J., Maurer, H.A., Paun, G., Rozenberg, G. (eds.) Jewels are Forever, pp. 145–156. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  32. Kuich, W.: Tree transducers and formal tree series. Acta Cybernet. 14(1), 135–149 (1999)

    MathSciNet  MATH  Google Scholar 

  33. Maletti, A.: Compositions of tree series transformations. Theoret. Comput. Sci. 366(3), 248–271 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  34. Maletti, A.: The Power of Tree Series Transducers. Ph.D. thesis, Technische Universität Dresden (2006)

    Google Scholar 

  35. Maletti, A.: Compositions of extended top-down tree transducers. Inform. and Comput. 206(9-10), 1187–1196 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. Maletti, A.: Survey: Weighted extended top-down tree transducers — Part I: Basics and expressive power. Acta Cybernet (2011), preprint available at: http://www.ims.uni-stuttgart.de/~maletti/pub/mal11.pdf

  37. Maletti, A.: Survey: Weighted extended top-down tree transducers — Part II: Application in machine translation. Fund. Inform (2011)

    Google Scholar 

  38. Maletti, A., Graehl, J., Hopkins, M., Knight, K.: The power of extended top-down tree transducers. SIAM J. Comput. 39(2), 410–430 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. Maletti, A., Vogler, H.: Compositions of top-down tree transducers with ε-rules. In: Yli-Jyrä, A., Kornai, A., Sakarovitch, J., Watson, B. (eds.) FSMNLP 2009. LNCS (LNAI), vol. 6062, pp. 69–80. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  40. May, J., Knight, K., Vogler, H.: Efficient inference through cascades of weighted tree transducers. In: ACL 2010, pp. 1058–1066. Association for Computational Linguistics (2010)

    Google Scholar 

  41. Rounds, W.C.: Mappings and grammars on trees. Math. Systems Theory 4(3), 257–287 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  42. Thatcher, J.W.: Generalized2 sequential machine maps. J. Comput. System Sci. 4(4), 339–367 (1970)

    Article  MATH  Google Scholar 

  43. Thatcher, J.W.: Tree automata: An informal survey. In: Aho, A.V. (ed.) Currents in the Theory of Computing, ch. 4, pp. 143–172. Prentice Hall, Englewood Cliffs (1973)

    Google Scholar 

  44. Wang, H.: On characters of semirings. Houston J. Math. 23(3), 391–405 (1997)

    MathSciNet  MATH  Google Scholar 

  45. Wang, H.: On rational series and rational languages. Theoret. Comput. Sci. 205(1-2), 329–336 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  46. Yamada, K., Knight, K.: A decoder for syntax-based statistical MT. In: ACL 2002, pp. 303–310. Association for Computational Linguistics (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lagoutte, A., Maletti, A. (2011). Survey: Weighted Extended Top-Down Tree Transducers Part III — Composition. In: Kuich, W., Rahonis, G. (eds) Algebraic Foundations in Computer Science. Lecture Notes in Computer Science, vol 7020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24897-9_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24897-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24896-2

  • Online ISBN: 978-3-642-24897-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics