Residual Finite Tree Automata

  • Julien Carme
  • Rémi Gilleron
  • Aurélien Lemay
  • Alain Terlutte
  • Marc Tommasi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2710)


Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with the development of standards such as XML. In this paper, we define new classes of non deterministic tree automata, namely residual finite tree automata (RFTA). In the bottom-up case, we obtain a new characterization of regular tree languages. In the top-down case, we obtain a subclass of regular tree languages which contains the class of languages recognized by deterministic top-down tree automata. RFTA also come with the property of existence of canonical non deterministic tree automata.


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  1. [CDG+97]_H. Comon, M. Dauchet, R. Gilleron, F. Jacquemard, D. Lugiez, S. Tison, and M. Tommasi. Tree automata techniques and applications. Available on:, 1997.Google Scholar
  2. [CGL+03]_J. Carme, R. Gilleron, A. Lemay, A. Terlutte, and M. Tommasi. Residual finite tree automata. Technical report, GRAPPA, 2003.Google Scholar
  3. [DLT01]
    F. Denis, A. Lemay, and A. Terlutte. Learning regular languages using rfsa. In ALT 2001, number 2225 in Lecture Notes in Artificial Intelligence. Springer Verlag, 2001.Google Scholar
  4. [DLT02a]
    F. Denis, A. Lemay, and A. Terlutte. Residual finite state automata. Fundamenta Informaticae, 51(4):339–368, 2002.zbMATHMathSciNetGoogle Scholar
  5. [DLT02b]
    F. Denis, A. Lemay, and A. Terlutte. some language classes identifiable in the limit from positive data. In ICGI 2002, number 2484 in Lecture Notes in Artificial Intelligence, pages 63–76. Springer Verlag, 2002.MathSciNetGoogle Scholar
  6. [Fer02]
    Henning Fernau. Learning tree languages from text. In Proc. 15th Annual Conference on Computational Learning Theory, COLT 2002, pages 153–168, 2002.Google Scholar
  7. [GK02]
    Sally A. Goldman and Stephen S. Kwek. On learning unions of pattern languages and tree patterns in the mistake bound model. Theorical Computer Science, 288(2):237–254, 2002.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [Gol67]
    E.M. Gold. Language identification in the limit. Inform. Control, 10:447–474, 1967.CrossRefzbMATHGoogle Scholar
  9. [GS84]
    F. Gécseg and M. Steinby. Tree Automata. Akademiai Kiado, 1984.Google Scholar
  10. [GS96]
    F. Gécseg and M. Steinby. Tree languages. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume 3, pages 1–68. Springer Verlag, 1996.Google Scholar
  11. [LPH00]
    Ling Liu, Calton Pu, and Wei Han. XWRAP: An XML-enabled wrapper construction system for web information sources. In ICDE, pages 611–621, 2000.Google Scholar
  12. [MLM01]
    M. Murata, D. Lee, and M. Mani. “Taxonomy of XML Schema Languages using Formal Language Theory”. In Extreme Markup Languages, Montreal, Canada, 2001.Google Scholar
  13. [Nev02]
    F. Neven. Automata, xml and logic. In Proceedings of CSL, pages 2–26, 2002.Google Scholar
  14. [NP97]
    M. Nivat and A. Podelski. Minimal ascending and descending tree automata. SIAM Journal on Computing, 26(1):39–58, February 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [Sak90]
    Yasubumi Sakakibara. learning context-free grammars from structural data in polynomial time. Theorical Computer Science, 76:223–242, 1990.CrossRefzbMATHMathSciNetGoogle Scholar
  16. [Tha73]
    J.W. Thatcher. Tree automata: an informal survey. In A.V. Aho, editor, Currents in the theory of computing, pages 143–178. Prentice Hall, 1973.Google Scholar
  17. [Tho84]
    Wolfgang Thomas. Logical aspects in the study of tree languages. In Proceedings of the 9th International Colloquium on Trees in Algebra and Programming, CAAP’ 84, pages 31–50, 1984.Google Scholar
  18. [Vir81]
    J. Viragh. Deterministic ascending tree automata. Acta Cybernetica, 5:33–42, 1981.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Julien Carme
    • 1
  • Rémi Gilleron
    • 1
  • Aurélien Lemay
    • 1
  • Alain Terlutte
    • 1
  • Marc Tommasi
    • 1
  1. 1.Grappa — EA 3588 — Lille 3 UniversityLille

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