Abstract
Strings can be mapped into Hilbert spaces using feature maps such as the Parikh map. Languages can then be defined as the pre-image of hyperplanes in the feature space, rather than using grammars or automata. These are the planar languages. In this paper we show that using techniques from kernel-based learning, we can represent and efficiently learn, from positive data alone, various linguistically interesting context-sensitive languages. In particular we show that the cross-serial dependencies in Swiss German, that established the non-context-freeness of natural language, are learnable using a standard kernel. We demonstrate the polynomial-time identifiability in the limit of these classes, and discuss some language theoretic properties of these classes, and their relationship to the choice of kernel/feature map.
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
Aizerman, M.A., Braverman, E.M., Rozonoer, L.I.: Theoretical foundations of the potential function method in pattern recognition. Automation and Remote Control 25, 821–837 (1964)
Asveld, P.R.J.: Generating all permutations by context-free grammars in Chomsky normal form. Theoretical Computer Science (TCS) 354(1), 118–130 (2006)
Clark, A., Florêncio, C.C., Watkins, C.: Languages as hyperplanes: grammatical inference with string kernels. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) ECML 2006. LNCS (LNAI), vol. 4212, pp. 90–101. Springer, Heidelberg (2006)
de la Higuera, C.: Characteristic sets for polynomial grammatical inference. In: Miclet, L., de la Higuera, C. (eds.) ICGI 1996. LNCS, vol. 1147. Springer, Heidelberg (1996)
Mark Gold, E.: Language identification in the limit. Information and Control 10, 447–474 (1967)
Huybregts, R.: The weak inadequacy of context-free phrase structure grammars. In: de Haan, G.J., Trommelen, M., Zonneveld, W. (eds.) Van Periferie naar Kern, Foris, Dordrecht (1984)
Joshi, A.K., Schabes, Y.: Tree-adjoining grammars. In: Rosenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 69–123. Springer, New York (1996)
Kontorovich, L.: Learning linearly separable languages. Technical Report CMU-CALD-04-105, School of Computer Science, CMU (2004)
Motoki, T., Shinohara, T., Wright, K.: The correct definition of finite elasticity: Corrigendum to identification of unions. In: The Fourth Workshop on Computational Learning Theory. Morgan Kaufmann, San Mateo, Calif (1991)
Salomaa, A.: On languages defined by numerical parameters. Technical Report 663, Turku Centre for Computer Science (2005)
Shieber, S.M.: Evidence against the context-freeness of natural language. Linguistics and Philosophy 8, 333–343 (1985)
Shawe-Taylor, J., Christianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Watkins, C.: Dynamic alignment kernels. Technical Report CSD-TR-98-11, Department of Computer Science, Royal Holloway College, University of London (1999)
Wright, K.: Identification of unions of languages drawn from an identifiable class. In: The 1989 Workshop on Computational Learning Theory, pp. 328–333. Morgan Kaufmann, San Mateo (1989)
Yokomori, T., Kobayashi, S.: Learning local languages and their application to DNA sequence analysis. IEEE Trans. Pattern Anal. Mach. Intell. 20(10), 1067–1079 (1998)
Yokomori, T.: Polynomial-time learning of very simple grammars from positive data. In: Proceedings of the Fourth Annual Workshop on Computational Learning Theory, University of California, Santa Cruz, August 5–7, 1991, pp. 213–227. ACM Press, New York (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clark, A., Florêncio, C.C., Watkins, C., Serayet, M. (2006). Planar Languages and Learnability. In: Sakakibara, Y., Kobayashi, S., Sato, K., Nishino, T., Tomita, E. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2006. Lecture Notes in Computer Science(), vol 4201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11872436_13
Download citation
DOI: https://doi.org/10.1007/11872436_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45264-5
Online ISBN: 978-3-540-45265-2
eBook Packages: Computer ScienceComputer Science (R0)