Hostname: page-component-77c78cf97d-hf2s2 Total loading time: 0 Render date: 2026-04-25T03:49:04.000Z Has data issue: false hasContentIssue false
  • English
  • Français

Learning tree languages from text

Published online by Cambridge University Press:  25 September 2007

Henning Fernau
Henning Fernau*
Affiliation:
Fachbereich IV, Abteilung Informatik, Universität Trier, 54286 Trier, Germany; fernau@uni-trier.de
Get access

Abstract

We study the problem of learning regular tree languages from text. We show that the framework of function distinguishability, as introduced by the author in [Theoret. Comput. Sci.290 (2003) 1679–1711], can be generalized from the case of string languages towards tree languages. This provides a large source of identifiable classes of regular tree languages. Each of these classes can be characterized in various ways. Moreover, we present a generic inference algorithm with polynomial update time and prove its correctness. In this way, we generalize previous works of Angluin, Sakakibara and ourselves. Moreover, we show that this way all regular tree languages can be approximately identified.

Keywords

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 4 , October 2007 , pp. 351 - 374
Copyright
© EDP Sciences, 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Ahonen, H., Mannila, H. and Nikunen, E., Forming grammars for structured documents: an application of grammatical inference, in Proceedings of the Second International Colloquium on Grammatical Inference (ICGI-94): Grammatical Inference and Applications, edited by R.C. Carrasco and J. Oncina. Lect. Notes Artif. Int. 862 (1994) 153–167.
Angluin, D., Inductive inference of formal languages from positive data. Inform. Comput. 45 (1980) 117–135.
Angluin, D., Inference of reversible languages. J. ACM 29 (1982) 741–765. CrossRef
Angluin, D., Learning regular sets from queries and counterexamples. Inform. Comput. 75 (1987) 87–106. CrossRef
M. Bernard and C. de la Higuera, GIFT: grammatical inference for terms, in Conférence d'Apprentissage, Palaiseau, May 1999. English version: Late breaking paper of International Conference on Inductive Logic Programming; French journal version: Apprentissage de programmes logiques par inférence grammaticale. Revue d'Intelligence Artificielle 14 (2001) 375–396.
J. Besombes and J.-Y. Marion, Identification of reversible dependency tree languages, in Proc. 3rd Workshop on Learning Languages in Logic LLL'01, edited by L. Popelínský and M. Nepil, 11–22. Technical report FIMU-RS-2001-08, FI MU Brno, Czech Republic, see http://www.fi.muni.cz/ilpnet2/LLL2001/#proceedings, September 2001.
Besombes, J. and Marion, J.-Y., Learning tree languages from positive examples and membership queries, in Algorithmic Learning Theory, 15th International Conference, ALT, edited by S. Ben-David, J. Case and A. Maruoka. Lect. Notes Comput. Sci. 3244 (2004) 440–453. CrossRef
H. Boström, Theory-guided induction of logic programs by inference of regular languages. in Proc. of the 13th International Conference on Machine Learning, Morgan Kaufmann, (1996) 46–53.
Carrasco, R.C., Oncina, J. and Calera-Rubio, J., Stochastic inference of regular tree languages. Mach. Learn. 44 (2001) 185–197. CrossRef
Carrasco, R. C. and Rico-Juan, J. R., A similarity between probabilistic tree languages: Application to XML document families. Pattern Recogn. 36 (2003) 2197–2199. CrossRef
M. Ceresna and G. Gottlob, Query based learning of XPath fragments, in Proceedings of Dagstuhl Seminar on Machine Learning for the Semantic Web (05071), Dagstuhl, Germany, (2005).
Crespi-Reghizzi, S., Melkanoff, M.A. and Lichten, L., The use of grammatical inference for designing programming languages. Comm. ACM 16 (1972) 83–90. CrossRef
E. Cypher, D.C. Halbert, D. Kurlander, H. Liebermanand D. Maulsby, B.A. Myers and A. Turransky, Eds. Watch What I Do: Programming by Demonstration. MIT Press, 1993. Available online at http://www.acypher.com/wwid/WWIDToC.html
A. Dix and A. Patrick, Query by browsing. in Proceedings of IDS'94: The 2nd International Workshop on User Interfaces to Databases, edited by P. Sawyer, Springer (1994) 236–248. HTML version: http://www.comp.lancs.ac.uk/computing/users/dixa/papers/QbB-IDS94/
F. Drewes, Grammatical Picture Generation – A Tree-Based Approach. Texts in Theoretical Computer Science. An EATCS Series. Springer, (2006). More information can be found on the web page http://www.cs.umu.se/~drewes/picgen/index.html
Drewes, F. and Högberg, J., Learning a regular tree language from a teacher. In Proc. Developments in Language Theory DLT 2003, edited by Z. Ésik and Z. Fülöp. Lect. Notes Comput. Sci. 2710 (2003) 279–291. CrossRef
F. Drewes and J. Högberg, Query learning of regular tree languages: How to avoid dead states. Theor. Comput. Syst. (2006). To appear.
L.F. Fass, Learning context-free languages from their structured sentences. SIGACT News, 15 (1983) 24–35.
Fernau, H., k-gram extensions of terminal distinguishable languages. In International Conference on Pattern Recognition (ICPR 2000). IEEE/IAPR 2 (2000) 125–128.
Fernau, H., Learning XML grammars. in Machine Learning and Data Mining in Pattern Recognition MLDM'01, edited by P. Perner. Lect. Notes Artif. Int. 2123 (2001) 73–87.
Fernau, H., Learning tree languages from text. in Computational Learning Theory COLT 2002, edited by J. Kivinen and R.H. Sloan. Lect. Notes Artif. Int. 2375 (2002) 153–168.
Fernau, H., Identification of function distinguishable languages. Theoret. Comput. Sci. 290 (2003) 1679–1711. CrossRef
Fernau, H., Identifying terminal distinguishable languages. Ann. Math. Artif. Intell. 40 (2004) 263–281. CrossRef
Fernau, H. and de la Higuera, C., Grammar induction: An invitation to formal language theorists. GRAMMARS 7 (2004) 45–55.
Fernau, H. and Radl, A., Algorithms for learning function distinguishable regular languages. in Structural, Syntactic, and Statistical Pattern Recognition SSPR and SPR 2002, edited by T. Caelli, A. Amin, R.P.W. Duin, M. Kamel and D. de Ridder. Lect. Notes Comput. Sci. 2396 (2002) 64–72. CrossRef
H. Fernau and J.M. Sempere, Permutations and control sets for learning non-regular language families. in Grammatical Inference: Algorithms and Applications, 5th International Colloquium (ICGI 2000), edited by A.L. Oliveira. Lect. Notes Artif. Int., 1891 (2000) 75–88.
Florêncio, C.C., Consistent identification in the limit of any of the classes of k-valued is NP-hard. in Logical Aspects of Computational Linguistics LACL'01, edited by P. de Groote, G. Morrill and C. Retoré. Lect. Notes Artif. Int. 2099 (2001) 125–138.
Fukuda, H. and Kamata, K., Inference of tree automata from sample set of trees. Int. J. Comput. Inform. Sci. 13 (1984) 177–196. CrossRef
P. García, Learning k-testable tree sets from positive data. Technical Report DSIC/II/46/1993, Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, http://www.dsic.upv.es/users/tlcc/tlcc.html (1993).
P. García and J. Oncina, Inference of recognizable tree sets. Technical Report DSIC-II/47/93, Departamento de Sistemas Informáticos y Computación (1993).
Garofalakis, M., Gionis, A., Rastogi, R., Seshadri, S. and Shim, K., XTRACT: learning document type descriptors from XML document collections. Data Min. Knowl. Discov. 7 (2003) 23–56. CrossRef
Gold, E.M., Language identification in the limit. Inform. Comput. 10 (1967) 447–474.
R.C. Gonzalez and M.G. Thomason, Syntactic Pattern Recognition; An Introduction. Addison-Wesley (1978).
Gregor, J., Data-driven inductive inference of finite-state automata. Int. J. Pattern Recogn. 8 (1994) 305–322. CrossRef
de la Higuera, C., A bibliographical study of grammatical inference. Pattern Recogn. 38 (2005) 1332–1348. CrossRef
C. de la Higuera, Current trends in grammatical inference. in Advances in Pattern Recognition, Joint IAPR International Workshops SSPR+SPR'2000, edited by F.J. Ferri et al. Lect. Notes Comput. Sci. 1876 (2000) 28–31.
E. Jeong and C.-H. Hsu, Induction of integrated view for XML data with heterogenous DTDs. In Proceedings of the 10th International Conference on Information and Knowledge Management CIKM, ACM, (2001) 151–158.
M. Kanazawa, Learnable Classes of Categorial Grammars. Ph.D., CSLI (1998).
Kimia, B.B., Tannenbaum, A.R. and Zucker, S.W., Shapes, shocks, and deformations, I. Int. J. Comput. Vision 15 (1995) 189–224. CrossRef
Knobe, B. and Knobe, K., A method for inferring context-free grammars. Inform. Comput. 31 (1976) 129–146.
T. Knuutila, Inference of k-testable tree languages, in Proc. IAPR Workshop on Structural and Syntactical Pattern Recognition. World Scientific (1992) 109–120.
T. Knuutila, How to invent characterizable methods for regular languages. in 4th Workshop on Algorithmic Learning Theory ALT'93, edited by K.P. Jantke et al. Lect. Notes Artif. Int. 744 (1993) 209–222.
Knuutila, T. and Steinby, M., The inference of tree languages from finite samples: an algebraic approach. Theoret. Comput. Sci. 129 (1994) 337–367. CrossRef
Kobayashi, S. and Yokomori, T., Learning approximately regular languages with reversible languages. Theoret. Comput. Sci. 174 (1997) 251–257. CrossRef
Kozen, D., On the Myhill-Nerode theorem for trees. EATCS Bull. 47 (1992) 170–173.
H. Lieberman, editor. Your Wish is My Command: Programming by Example. Morgan Kaufmann (2001).
López, D. and España, S., Error correcting tree language inference. Pattern Recogn. Lett. 23 (2002) 1–12. CrossRef
D. López and I. Piñaga, Syntactic pattern recognition by error correcting analysis on tree automata, in Advances in Pattern Recognition, Joint IAPR International Workshops SSPR+SPR'2000, edited by F.J. Ferri et al. Lect. Notes Comput. Sci. 1876 (2000) 133–142.
López, D., Sempere, J.M. and García, P., Error correcting analysis for tree languages. Int. J. Pattern Recogn. 14 (2000) 357–368.
López, D., Sempere, J.M. and García, P., Inference of reversible tree languages. IEEE T. Syst. Man Cy. 34 (2004) 1658–1665. CrossRef
Lu, H.R. and Error-correcting, K.S. Fu tree automata for syntactic pattern recognition. IEEE T. Comput. 27 (1978) 1040–1053.
Matsumoto, S. and Shoudai, T., Learning of ordered tree languages with height-bounded variables using queries. in Algorithmic Learning Theory, 15th International Conference, ALT, edited by S. Ben-David, J. Case and A. Maruoka. Lect. Notes Comput. Sci. 3244 (2004) 425–439. CrossRef
Neven, F., Automata, logic, and XML. In Computer Science Logic; 16th International Workshop, CSL 2002, edited by J. Bradfield. Lect. Notes Comput. Sci. 2471 (2002) 2–26. CrossRef
Radhakrishnan, V. and Nagaraja, G., Inference of regular grammars via skeletons. IEEE T. Syst. Man Cy. 17 (1987) 982–992. CrossRef
Radhakrishnan, V. and Nagaraja, G., Inference of even linear grammars and its application to picture description languages. Pattern Recogn. 21 (1988) 55–62. CrossRef
Rico-Juan, J.R., Calera-Rubio, J. and Carrasco, R.C., Probabilistic k-testable tree languages. in Grammatical Inference: Algorithms and Applications, 5th International Colloquium (ICGI 2000), edited by A.L. Oliveira. Lect. Notes Artif. Int. 1891 (2000) 221–228.
Rico-Juan, J.R., Calera-Rubio, J. and Carrasco, R.C., Stochastic k-testable tree languages and applications, in Grammatical Inference: Algorithms and Applications, 6th International Colloquium, ICGI 2002, edited by P. Adriaans, H. Fernau and M. van Zaanen. Lect. Notes Artif. Int. 2484 (2002) 199–212.
G. Rozenberg and A. Salomaa, eds. Handbook of Formal Languages, Volume III. Springer, Berlin (1997).
Sakakibara, Y., Learning context-free grammars from structural data in polynomial time. Theoret. Comput. Sci. 76 (1990) 223–242. CrossRef
Sakakibara, Y., Efficient learning of context-free grammars from positive structural examples. Inform. Comput. 97 (1992) 23–60. CrossRef
Sakakibara, Y. and Muramatsu, H., Learning context-free grammars from partially structured examples, in Grammatical Inference: Algorithms and Applications, 5th International Colloquium (ICGI 2000), edited by A.L. Oliveira. Lect. Notes Artif. Int. 1891 (2000) 229–240.
Sempere, J.M. and Nagaraja, G., Learning a subclass of linear languages from positive structural information. in Proceedings of the Fourth International Colloquium on Grammatical Inference (ICGI-98), edited by V. Honavar and G. Slutski. Lect. Notes Artif. Int. 1433 (1998) 162–174.
Siddiqi, K., Shakoufandeh, A., Dickinson, S. and Zucker, S., Shock graphs and shape matching. Int. J. Comput. Vision 30 (1999) 1–24.
B. Starkie, Developing Spoken Dialog Systems using Grammatical Inference. Ph.D. Thesis, The University of Newcastle (AUS) (2005).
Starkie, B. and Fernau, H., The Boisdale algorithm — an induction method for a subclass of unification grammar from positive data, in Grammatical Inference: Algorithms and Applications; 7th International Colloquium ICGI, edited by G. Paliouras and Y. Sakakibara. Lect. Notes Artif. Int. 3264 (2004) 235–247.
Takada, Y. and Nishida, T.Y., A note on grammatical inference of slender context-free languages, in Proceedings of the Third International Colloquium on Grammatical Inference (ICGI-96): Learning Syntax from Sentences, edited by L. Miclet and C. de la Higuera. Lect. Notes Artif. Int. 1147 (1996) 117–125.
Tanaka, E. and Error-correcting, K.S. Fu parsers for formal languages. IEEE T. Comput. 27 (1978) 605–616. CrossRef
Verdú-Mas, J.L., Forcada, M.L., Carrasco, R.C. and Calera-Rubio, J., Tree k-grammar models for natural language modelling and parsing, in Structural, Syntactic, and Statistical Pattern Recognition SSPR and SPR 2002, edited by T. Caelli, A. Amin, R.P.W. Duin, M. Kamel and D. de Ridder. Lect. Notes Comput. Sci. 2396 (2002) 56–63. CrossRef
J.L. Verdú-Mas, R.C. Carrasco and J. Calera-Rubio, Parsing with probabilistic strictly locally testable tree languages. IEEE T. Pattern Anal., 27 (2005) 1040–1050.
H. Volger, Grammars with generalized contextfree rules and their tree automata. in Proceedings of CLIN '99; Selected Papers (1999) 223–233, see http://www-uilots.let.uu.nl/publications/clin1999/papers.html
Yokomori, T., Inductive inference of context-free languages based on context-free expressions. Int. J. Comput. Math. 24 (1988) 115–140. CrossRef
Yokomori, T., On learning systolic languages. in Proceedings of the 3rd Workshop on Algorithmic Learning Theory (ALT '92), edited by K.P. Jantke, S. Doshita, K. Furukawa and T. Nishida. Lect. Notes Artif. Int. 743 (1992) 41–52.
Yokomori, T., Polynomial-time identification of very simple grammars from positive data. Theoret. Comput. Sci. 298 (2003) 179–206. CrossRef