# Learning tree languages from text

RAIRO - Theoretical Informatics and Applications (2007)

- Volume: 41, Issue: 4, page 351-374
- ISSN: 0988-3754

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topFernau, Henning. "Learning tree languages from text." RAIRO - Theoretical Informatics and Applications 41.4 (2007): 351-374. <http://eudml.org/doc/250053>.

@article{Fernau2007,

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.
},

author = {Fernau, Henning},

journal = {RAIRO - Theoretical Informatics and Applications},

language = {eng},

month = {9},

number = {4},

pages = {351-374},

publisher = {EDP Sciences},

title = {Learning tree languages from text},

url = {http://eudml.org/doc/250053},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Fernau, Henning

TI - Learning tree languages from text

JO - RAIRO - Theoretical Informatics and Applications

DA - 2007/9//

PB - EDP Sciences

VL - 41

IS - 4

SP - 351

EP - 374

AB -
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.

LA - eng

UR - http://eudml.org/doc/250053

ER -

## References

top- H. Ahonen, H. Mannila and E. Nikunen, 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.
- D. Angluin, Inductive inference of formal languages from positive data. Inform. Comput.45 (1980) 117–135. Zbl0459.68051
- D. Angluin, Inference of reversible languages. J. ACM29 (1982) 741–765. Zbl0485.68066
- D. Angluin, Learning regular sets from queries and counterexamples. Inform. Comput.75 (1987) 87–106. Zbl0636.68112
- 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 Artificielle14 (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 , September 2001. URIhttp://www.fi.muni.cz/ilpnet2/LLL2001/#proceedings
- J. Besombes and J.-Y. Marion, 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. Zbl1110.68390
- 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.
- R.C. Carrasco, J. Oncina and J. Calera-Rubio, Stochastic inference of regular tree languages. Mach. Learn.44 (2001) 185–197. Zbl0983.68106
- R. C. Carrasco and J. R. Rico-Juan, A similarity between probabilistic tree languages: Application to XML document families. Pattern Recogn.36 (2003) 2197–2199. Zbl1047.68550
- 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).
- S. Crespi-Reghizzi, M.A. Melkanoff and L. Lichten, The use of grammatical inference for designing programming languages. Comm. ACM16 (1972) 83–90. Zbl0248.68037
- 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 URIhttp://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: URIhttp://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 URIhttp://www.cs.umu.se/~drewes/picgen/index.html
- F. Drewes and J. Högberg, 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. Zbl1037.68082
- F. Drewes and J. Högberg, Query learning of regular tree languages: How to avoid dead states. Theor. Comput. Syst. (2006). To appear. Zbl1107.68049
- L.F. Fass, Learning context-free languages from their structured sentences. SIGACT News, 15 (1983) 24–35. Zbl0528.68051
- H. Fernau, k-gram extensions of terminal distinguishable languages. In International Conference on Pattern Recognition (ICPR 2000). IEEE/IAPR2 (2000) 125–128.
- H. Fernau, 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. Zbl0997.68607
- H. Fernau, 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. Zbl1050.68060
- H. Fernau, Identification of function distinguishable languages. Theoret. Comput. Sci.290 (2003) 1679–1711. Zbl1051.68092
- H. Fernau, Identifying terminal distinguishable languages. Ann. Math. Artif. Intell.40 (2004) 263–281. Zbl1081.68035
- H. Fernau and C. de la Higuera, Grammar induction: An invitation to formal language theorists. GRAMMARS7 (2004) 45–55.
- H. Fernau and A. Radl, 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.
- 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. Zbl0974.68089
- C.C. Florêncio, 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.
- H. Fukuda and K. Kamata, Inference of tree automata from sample set of trees. Int. J. Comput. Inform. Sci.13 (1984) 177–196. Zbl0566.68064
- 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, (1993). URIhttp://www.dsic.upv.es/users/tlcc/tlcc.html
- P. García and J. Oncina, Inference of recognizable tree sets. Technical Report DSIC-II/47/93, Departamento de Sistemas Informáticos y Computación (1993).
- M. Garofalakis, A. Gionis, R. Rastogi, S. Seshadri and K. Shim, XTRACT: learning document type descriptors from XML document collections. Data Min. Knowl. Discov.7 (2003) 23–56.
- E.M. Gold, Language identification in the limit. Inform. Comput.10 (1967) 447–474. Zbl0259.68032
- R.C. Gonzalez and M.G. Thomason, Syntactic Pattern Recognition; An Introduction. Addison-Wesley (1978). Zbl0383.68065
- J. Gregor, Data-driven inductive inference of finite-state automata. Int. J. Pattern Recogn.8 (1994) 305–322.
- C. de la Higuera, A bibliographical study of grammatical inference. Pattern Recogn.38 (2005) 1332–1348.
- 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). Zbl0937.68130
- B.B. Kimia, A.R. Tannenbaum and S.W. Zucker, Shapes, shocks, and deformations, I. Int. J. Comput. Vision15 (1995) 189–224.
- B. Knobe and K. Knobe, A method for inferring context-free grammars. Inform. Comput.31 (1976) 129–146. Zbl0333.68065
- 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. Zbl0925.68365
- T. Knuutila and M. Steinby, The inference of tree languages from finite samples: an algebraic approach. Theoret. Comput. Sci.129 (1994) 337–367. Zbl0822.68055
- S. Kobayashi and T. Yokomori, Learning approximately regular languages with reversible languages. Theoret. Comput. Sci.174 (1997) 251–257. Zbl0908.68146
- D. Kozen, On the Myhill-Nerode theorem for trees. EATCS Bull.47 (1992) 170–173. Zbl0757.68083
- H. Lieberman, editor. Your Wish is My Command: Programming by Example. Morgan Kaufmann (2001).
- D. López and S. España, Error correcting tree language inference. Pattern Recogn. Lett.23 (2002) 1–12. Zbl0993.68057
- 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. Zbl0996.68532
- D. López, J.M. Sempere and P. García, Error correcting analysis for tree languages. Int. J. Pattern Recogn.14 (2000) 357–368.
- D. López, J.M. Sempere and P. García, Inference of reversible tree languages. IEEE T. Syst. Man Cy.34 (2004) 1658–1665.
- H.R. Lu and K.S. Fu, Error-correcting tree automata for syntactic pattern recognition. IEEE T. Comput.27 (1978) 1040–1053. Zbl0392.68076
- S. Matsumoto and T. Shoudai, 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. Zbl1110.68402
- F. Neven, 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.
- V. Radhakrishnan and G. Nagaraja, Inference of regular grammars via skeletons. IEEE T. Syst. Man Cy.17 (1987) 982–992.
- V. Radhakrishnan and G. Nagaraja, Inference of even linear grammars and its application to picture description languages. Pattern Recogn.21 (1988) 55–62. Zbl0653.68077
- J.R. Rico-Juan, J. Calera-Rubio and R.C. Carrasco, 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. Zbl0974.68514
- J.R. Rico-Juan, J. Calera-Rubio and R.C. Carrasco, 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. Zbl1028.68608
- G. Rozenberg and A. Salomaa, eds. Handbook of Formal Languages, Volume III. Springer, Berlin (1997).
- Y. Sakakibara, Learning context-free grammars from structural data in polynomial time. Theoret. Comput. Sci.76 (1990) 223–242. Zbl0704.68067
- Y. Sakakibara, Efficient learning of context-free grammars from positive structural examples. Inform. Comput.97 (1992) 23–60. Zbl0764.68146
- Y. Sakakibara and H. Muramatsu, 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. Zbl0974.68530
- J.M. Sempere and G. Nagaraja, 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.
- K. Siddiqi, A. Shakoufandeh, S. Dickinson and S. Zucker, Shock graphs and shape matching. Int. J. Comput. Vision30 (1999) 1–24.
- B. Starkie, Developing Spoken Dialog Systems using Grammatical Inference. Ph.D. Thesis, The University of Newcastle (AUS) (2005).
- B. Starkie and H. Fernau, 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. Zbl1111.68481
- Y. Takada and T.Y. Nishida, 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.
- E. Tanaka and K.S. Fu, Error-correcting parsers for formal languages. IEEE T. Comput.27 (1978) 605–616. Zbl0379.68050
- J.L. Verdú-Mas, M.L. Forcada, R.C. Carrasco and J. Calera-Rubio, 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. Zbl1073.68842
- 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 URIhttp://www-uilots.let.uu.nl/publications/clin1999/papers.html
- T. Yokomori, Inductive inference of context-free languages based on context-free expressions. Int. J. Comput. Math.24 (1988) 115–140. Zbl0658.68095
- T. Yokomori, 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. Zbl0925.68368
- T. Yokomori, Polynomial-time identification of very simple grammars from positive data. Theoret. Comput. Sci.298 (2003) 179–206. Zbl1038.68074

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