Abstract
Recently Clark and Eyraud (2005, 2007) have shown that substitutable context-free languages are polynomial-time identifiable in the limit from positive data. Substitutability in context-free languages can be thought of as the analogue of reversibility in regular languages. While reversible languages admit a hierarchy, namely k-reversible regular languages for each nonnegative integer k, Clark and Eyraud targeted the subclass of context-free languages that corresponds to zero-reversible regular languages only. Following Clark and Eyraud’s proposal, this paper introduces a hierarchy of substitutable context-free languages as the analogue of that of k-reversible regular languages and shows that each class in the hierarchy is also polynomial-time identifiable in the limit from positive data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Angluin, D.: Inference of reversible languages. Journal of the Association for Computing Machinery 29(3), 741–765 (1982)
Angluin, D.: Negative results for equivalence queries. Machine Learning 5, 121–150 (1990)
Boasson, L., Sénizergues, G.: NTS languages are deterministic and congruential. Journal of Computer and System Sciences 31(3), 332–342 (1985)
Carme, J., Gilleron, R., Lemay, A., Niehren, J.: Interactive learning of node selecting tree transducer. Machine Learning 66(1), 33–67 (2007)
Clark, A.: PAC-learning unambiguous NTS languages. In: Sakakibara, Y., Kobayashi, S., Sato, K., Nishino, T., Tomita, E. (eds.) ICGI 2006. LNCS (LNAI), vol. 4201, pp. 59–71. Springer, Heidelberg (2006)
Clark, A., Eyraud, R.: Identification in the limit of substitutable context-free languages. In: Jain, S., Simon, H.U., Tomita, E. (eds.) ALT 2005. LNCS (LNAI), vol. 3734, pp. 283–296. Springer, Heidelberg (2005)
Clark, A., Eyraud, R.: Polynomial identification in the limit of context-free substitutable languages. Journal of Machine Learning Research 8, 1725–1745 (2007)
Engelfriet, J.: An elementary proof of double Greibach normal form. Information Processing Letters 44(6), 291–293 (1992)
Gold, E.M.: Language identification in the limit. Information and Control 10(5), 447–474 (1967)
Greibach, S.A.: A new normal-form theorem for context-free phrase structure grammars. Journal of the Association for Computing Machinery 12(1), 42–52 (1965)
de la Higuera, C.: Characteristic sets for polynomial grammatical inference. Machine Learning 27, 125–138 (1997)
de la Higuera, C.: A bibliographical study of grammatical inference. Pattern Recognition 38(9), 332–1348 (2005)
Kobayashi, S.: Iterated transductions and efficient learning from positive data: A unifying view. In: Oliveira, A.L. (ed.) ICGI 2000. LNCS (LNAI), vol. 1891, pp. 157–170. Springer, Heidelberg (2000)
Kobayashi, S., Yokomori, T.: On approximately identifying concept classes in the limit. In: Zeugmann, T., Shinohara, T., Jantke, K.P. (eds.) ALT 1995. LNCS, vol. 997, pp. 298–312. Springer, Heidelberg (1995)
Kobayashi, S., Yokomori, T.: Identifiability of subspaces and homomorphic images of zero-reversible languages. In: Li, M., Maruoka, A. (eds.) ALT 1997. LNCS, vol. 1316, pp. 48–61. Springer, Heidelberg (1997)
Kobayashi, S., Yokomori, T.: Learning approximately regular languages with reversible languages. Theoretical Computer Science 174(1-2), 251–257 (1997)
Lange, S., Zeugmann, T., Zilles, S.: Learning indexed families of recursive languages from positive data: A survey. Theoretical Computer Science 397(1-3), 194–232 (2008)
Lee, L.: Learning of context-free languages: A survey of the literature. Technical Report TR-12-96, Harvard University (1996), ftp://deas-ftp.harvard.edu/techreports/tr-12-96.ps.gz
Mäkinen, E.: On inferring zero-reversible languages. Acta Cybernetica 14(3), 479–484 (2000)
Rosenkrantz, D.J.: Matrix equations and normal forms for context-free grammars. Journal of ACM 14(3), 501–507 (1967)
Sempere, J.M.: Learning reversible languages with terminal distinguishability. In: Sakakibara, Y., Kobayashi, S., Sato, K., Nishino, T., Tomita, E. (eds.) ICGI 2006. LNCS (LNAI), vol. 4201, pp. 354–355. Springer, Heidelberg (2006)
Sénizergues, G.: The equivalence and inclusion problems for NTS languages. Journal of Computer and System Sciences 31(3), 303–331 (1985)
Tîrnauca, C., Knuutila, T.: Polynomial time algorithms for learning k-reversible languages and pattern languages with correction queries. In: Hutter, M., Servedio, R.A., Takimoto, E. (eds.) ALT 2007. LNCS (LNAI), vol. 4754, pp. 272–284. Springer, Heidelberg (2007)
Wakatsuki, M., Tomita, E.: A fast algorithm for checking the inclusion for very simple deterministic pushdown automata. IEICE transactions on information and systems E76-D(10), 1224–1233 (1993)
Yokomori, T.: Polynomial-time identification of very simple grammars from positive data. Theoretical Computer Science 298, 179–206 (2003)
Yokomori, T.: Erratum to Polynomial-time identification of very simple grammars from positive data. Theoret. Comput. Sci. 298, 179–206 (2003); Theoretical Computer Science 377(1-3), 282–283 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yoshinaka, R. (2008). Identification in the Limit of k,l-Substitutable Context-Free Languages. In: Clark, A., Coste, F., Miclet, L. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2008. Lecture Notes in Computer Science(), vol 5278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88009-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-88009-7_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88008-0
Online ISBN: 978-3-540-88009-7
eBook Packages: Computer ScienceComputer Science (R0)