, Volume 55, Issue 1, pp 95–110 | Cite as

Incremental Construction of Minimal Tree Automata

  • Rafael C. CarrascoEmail author
  • Jan Daciuk
  • Mikel L. Forcada


We describe an algorithm that allows the incremental addition or removal of unranked ordered trees to a minimal frontier-to-root deterministic finite-state tree automaton (DTA). The algorithm takes a tree t and a minimal DTA A as input; it outputs a minimal DTA A′ which accepts the language L(A) accepted by A incremented (or decremented) with the tree t. The algorithm can be used to efficiently maintain dictionaries which store large collections of trees or tree fragments.


Deterministic tree automata Incremental construction of minimal tree automata 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation and Compiling. Vol. I: Parsing. Prentice-Hall, London (1972) Google Scholar
  2. 2.
    Aoe, J., Morimoto, K., Hase, M.: An algorithm for compressing common suffixes used in tree structures. Syst. Comput. Jpn. 24(12), 31–42 (1993) (translated from Trans. IEICE J75-D-II(4), 770–779, 1992) Google Scholar
  3. 3.
    Bod, R.: A computational model of language performance: Data oriented parsing. In: Proceedings of the 14th Conference on Computational Linguistics, pp. 855–859. Association for Computational Linguistics, Morristown (1992) Google Scholar
  4. 4.
    Brainerd, W.S.: The minimalization of tree automata. Inf. Control 13(5), 484–491 (1968) zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Carrasco, R.C., Daciuk, J., Forcada, M.L.: An implementation of deterministic tree automata minimization. In: Holub., J., Zdárek, J. (eds.) CIAA2007, 12th International Conference on Implementation and Application of Automata Proceedings. Lecture Notes in Computer Science, vol. 4783, pp. 122–129. Springer, New York (2007) Google Scholar
  6. 6.
    Carrasco, R.C., Forcada, M.L.: Incremental construction and maintenance of minimal finite-state automata. Comput. Linguistics 28(2), 207–216 (2002) CrossRefMathSciNetGoogle Scholar
  7. 7.
    Ciura, M., Deorowicz, S.: How to squeeze a lexicon. Softw. Pract. Experience 31(11), 1077–1090 (2001) zbMATHCrossRefGoogle Scholar
  8. 8.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications. Available on: (1997), release 1 October 2002
  9. 9.
    Daciuk, J.: Comments on incremental construction and maintenance of minimal finite-state automata by R.C. Carrasco and M.L. Forcada. Comput. Linguistics 30(2), 227–235 (2004) CrossRefMathSciNetGoogle Scholar
  10. 10.
    Daciuk, J., Mihov, S., Watson, B.W., Watson, R.E.: Incremental construction of minimal acyclic finite-state automata. Comput. Linguistics 26(1), 3–16 (2000) CrossRefMathSciNetGoogle Scholar
  11. 11.
    Daciuk, J., van Noord, G.: Finite automata for compact representation of language models in NLP. In: Implementation and Application of Automata, 6th International Conference, CIAA 2001. Lecture Notes in Computer Science, vol. 2494, pp. 65–73. Springer, New York (2002) Google Scholar
  12. 12.
    de la Briandais, R.: File searching using variable length keys. In: Proceedings of the Western Joint Computer Conference, pp. 295–298 (1959) Google Scholar
  13. 13.
    Fredkin, E.: Tree memory. Commun. ACM 3(9), 490–499 (1960) CrossRefGoogle Scholar
  14. 14.
    Garrido-Alenda, A., Forcada, M.L., Carrasco, R.C.: Incremental construction and maintenance of morphological analysers based on augmented letter transducers. In: Proceedings of TMI 2002, Theoretical and Methodological Issues in Machine Translation, Keihanna/Kyoto, Japan, March 2002, pp. 53–62 (2002) Google Scholar
  15. 15.
    Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984) zbMATHGoogle Scholar
  16. 16.
    Hopcroft, J., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979) zbMATHGoogle Scholar
  17. 17.
    Lucchesi, C.L., Kowaltowski, T.: Applications of finite automata representing large vocabularies. Softw. Pract. Experience 23(1), 15–30 (1993) CrossRefGoogle Scholar
  18. 18.
    Revuz, D.: Dynamic acyclic minimal automaton. In: Yu, S., Paun, A. (eds.) CIAA 2000, Fifth International Conference on Implementation and Application of Automata. Lecture Notes in Computer Science, vol. 2088, pp. 226–232. Springer, New York (2000) Google Scholar
  19. 19.
    Sgarbas, K., Fakotakis, N., Kokkinakis, G.: Two algorithms for incremental construction of directed acyclic word graphs. Int. J. Artif. Intell. Tools 4(3), 369–381 (1995) CrossRefGoogle Scholar
  20. 20.
    Watson, B.W., Daciuk, J.: An efficient incremental DFA minimization algorithm. Nat. Lang. Eng. 9(1), 49–64 (2003) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Rafael C. Carrasco
    • 1
    Email author
  • Jan Daciuk
    • 2
  • Mikel L. Forcada
    • 3
  1. 1.Dep. de Lenguajes y Sistemas InformáticosUniversidad de AlicanteAlicanteSpain
  2. 2.Knowledge Engineering DepartmentGdańsk University of TechnologyGdańskPoland
  3. 3.Dep. de Llenguatges i Sistemes InformáticsUniversitat d’AlacantAlacantSpain

Personalised recommendations