Backward and Forward Bisimulation Minimisation of Tree Automata

  • Johanna Högberg
  • Andreas Maletti
  • Jonathan May
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4783)

Abstract

We improve an existing bisimulation minimisation algorithm for tree automata by introducing backward and forward bisimulations and developing minimisation algorithms for them. Minimisation via forward bisimulation is also effective for deterministic automata and faster than the previous algorithm. Minimisation via backward bisimulation generalises the previous algorithm and is thus more effective but just as fast. We demonstrate implementations of these algorithms on a typical task in natural language processing.

Keywords

bisimulation tree automata minimisation natural language processing 

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References

  1. 1.
    Hopcroft, J.E.: An \(n\,\textrm{log}\, n\) algorithm for minimizing states in a finite automation. In: Kohavi, Z. (ed.) Theory of Machines and Computations, Academic Press, London (1971)Google Scholar
  2. 2.
    Meyer, A.R., Stockmeyer, L.J.: The equivalence problem for regular expressions with squaring requires exponential space. In: Proc. 13th Annual Symp. Foundations of Computer Science, pp. 125–129. IEEE Computer Society Press, Los Alamitos (1972)Google Scholar
  3. 3.
    Gramlich, G., Schnitger, G.: Minimizing NFAs and regular expressions. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 399–411. Springer, Heidelberg (2005)Google Scholar
  4. 4.
    Abdulla, P.A., Högberg, J., Kaati, L.: Bisimulation minimization of tree automata. In: IJFCS (2007)Google Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    Paige, R., Tarjan, R.: Three partition refinement algorithms. SIAM Journal on Computing 16, 973–989 (1987)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata: Techniques and applications (1997), available on http://www.grappa.univ-lille3.fr/tata
  9. 9.
    Buchholz, P.: Bisimulation relations for weighted automata (unpublished, 2007)Google Scholar
  10. 10.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)MATHGoogle Scholar
  11. 11.
    Jelinek, F.: Continuous speech recognition by statistical methods. Proc. IEEE 64, 532–557 (1976)CrossRefGoogle Scholar
  12. 12.
    Galley, M., Hopkins, M., Knight, K., Marcu, D.: What’s in a translation rule? In: Proc. 2004 Human Language Technology Conf. of the North American Chapter of the Association for Computational Linguistics, pp. 273–280 (2004)Google Scholar
  13. 13.
    Yamada, K., Knight, K.: A syntax-based statistical translation model. In: Proc. 39th Meeting of the Association for Computational Linguistics, pp. 523–530. Morgan Kaufmann, San Francisco (2001)Google Scholar
  14. 14.
    Marcus, M.P., Marcinkiewicz, M.A., Santorini, B.: Building a large annotated corpus of english: The Penn treebank. Computational Linguistics 19, 313–330 (1993)Google Scholar
  15. 15.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Johanna Högberg
    • 1
  • Andreas Maletti
    • 2
  • Jonathan May
    • 3
  1. 1.Dept. of Computing Science, Umeå University, S–90187 UmeåSweden
  2. 2.Faculty of Computer Science, Technische Universität Dresden, D–01062 DresdenGermany
  3. 3.Information Sciences Institute, University of Southern California, Marina Del Rey, CA 90292 

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