Skip to main content
SpringerLink
Log in

Minimizing Weighted Tree Grammars Using Simulation

  • Conference paper
Finite-State Methods and Natural Language Processing (FSMNLP 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6062))

Abstract

Weighted tree grammars (for short: WTG) are an extension of weighted context-free grammars that generate trees instead of strings. They can be used in natural language parsing to directly generate the parse tree of a sentence or to encode the set of all parse trees of a sentence. Two types of simulations for WTG over idempotent, commutative semirings are introduced. They generalize the existing notions of simulation and bisimulation for WTG. Both simulations can be used to reduce the size of WTG while preserving the semantics, and are thus an important tool in toolkits. Since the new notions are more general than the existing ones, they yield the best reduction rates achievable by all minimization procedures that rely on simulation or bisimulation. However, the existing notions might allow faster minimization.

This work was financially supported by the Ministerio de EducaciĂłn y Ciencia (MEC) grants JDCI-2007-760 and MTM-2007-63422.

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dale, R., Moisl, H., Somers, H.L. (eds.): Handbook of Natural Language Processing. CRC Press, Boca Raton (2000)

    Google Scholar 

  2. Abdulla, P.A., Jonsson, B., Mahata, P., d’Orso, J.: Regular tree model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 555–568. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  3. 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)

    Chapter  Google Scholar 

  4. Klarlund, N., Møller, A.: MONA Version 1.4 User Manual. BRICS, Department of Computer Science, University of Aarhus (2001)

    Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. Cleophas, L.: Forest FIRE and FIRE wood: Tools for tree automata and tree algorithms. In: Proc. FSMNLP, pp. 191–198 (2008)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  9. Borchardt, B.: The Theory of Recognizable Tree Series. PhD thesis, Technische Universität Dresden (2005)

    Google Scholar 

  10. Hopcroft, J.E.: An n logn algorithm for minimizing states in a finite automaton. Theory of Machines and Computations, pp. 189–196. Academic Press, London (1971)

    Google Scholar 

  11. Högberg, J., Maletti, A., May, J.: Backward and forward bisimulation minimisation of tree automata. In: Holub, J., Žďárek, J. (eds.) CIAA 2007. LNCS, vol. 4783, pp. 109–121. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Maletti, A.: Minimizing deterministic weighted tree automata. Inform. and Comput. 207(11), 1284–1299 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Meyer, A.R., Stockmeyer, L.J.: The equivalence problem for regular expressions with squaring requires exponential space. In: Proc. FOCS, pp. 125–129. IEEE Computer Society, Los Alamitos (1972)

    Google Scholar 

  14. Gramlich, G., Schnitger, G.: Minimizing nfa’s and regular expressions. J. Comput. System Sci. 73(6), 908–923 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gruber, H., Holzer, M.: Inapproximability of nondeterministic state and transition complexity assuming P ≠ NP. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 205–216. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Abdulla, P.A., Högberg, J., Kaati, L.: Bisimulation minimization of tree automata. Int. J. Found. Comput. Sci. 18(4), 699–713 (2007)

    Article  MATH  Google Scholar 

  17. Abdulla, P.A., Bouajjani, A., Holík, L., Kaati, L., Vojnar, T.: Computing simulations over tree automata. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 93–108. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Maletti, A.: A backward and a forward simulation for weighted tree automata. In: Bozapalidis, S., Rahonis, G. (eds.) CAI 2009. LNCS, vol. 5725, pp. 288–304. Springer, Heidelberg (2009)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  20. Bozapalidis, S.: Effective construction of the syntactic algebra of a recognizable series on trees. Acta Inform. 28(4), 351–363 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  21. Högberg, J., Maletti, A., May, J.: Bisimulation minimisation for weighted tree automata. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 229–241. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. Huang, L., Chiang, D.: Better k-best parsing. In: Proc. IWPT, pp. 53–64 (2005)

    Google Scholar 

  23. Alexandrakis, A., Bozapalidis, S.: Weighted grammars and Kleene’s theorem. Information Processing Letters 24(1), 1–4 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  24. Bozapalidis, S.: Equational elements in additive algebras. Theory Comput. Systems 32(1), 1–33 (1999)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  26. Abdulla, P.A., Holík, L., Kaati, L., Vojnar, T.: A uniform (bi-)simulation-based framework for reducing tree automata. In: Proc. MEMICS, pp. 3–11 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departament de Filologies Romàniques, Universitat Rovira i Virgili, Avinguda de Catalunya 35, 43002, Tarragona, Spain

    Andreas Maletti

Authors
  1. Andreas Maletti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Modern Languages, University of Helsinki, 00014, Finland

    Anssi Yli-Jyrä

  2. Institute for Quantitative Social Science, Harvard University, 1737, 02138, Cambridge, MA, USA

    András Kornai

  3. Laboratoire Traitement et Communication de L’Informations, Département Infoamtique et Réseaux, CNRS, 75634, Paris Cedex 13, France

    Jacques Sakarovitch

  4. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, 5600, Eindhoven, MB, The Netherlands

    Bruce Watson

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Maletti, A. (2010). Minimizing Weighted Tree Grammars Using Simulation. In: Yli-Jyrä, A., Kornai, A., Sakarovitch, J., Watson, B. (eds) Finite-State Methods and Natural Language Processing. FSMNLP 2009. Lecture Notes in Computer Science(), vol 6062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14684-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14684-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14683-1

  • Online ISBN: 978-3-642-14684-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation