Abstract
In this paper, we will not focus on a learnability result of some specific language class, but on giving a set of language classes each of which is efficiently learnable in the limit from positive data. Furthermore, the set contains the class of k-reversible languages and the class of k-locally testable languages in the strict sense just as example language classes. This paper also proposes a framework for defining language classes based on iterated transductions. We believe that the framework is quite adequate for theoretically investigate the classes of languages which are efficiently learnable from positive data.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45, 117–135 (1980)
Angluin, D.: Inference of reversible languages. Journal of the ACM 29, 741–765 (1982)
Arikawa, S., Shinohara, T., Yamamoto, A.: Learning Elementary Formal Systems. Theoretical Computer Science 95, 97–113 (1992)
García, P., Vidal, E.: Inference of k-Testable Languages in the Strict Sense and Application to Syntactic Pattern Recognition. IEEE Trans. on Pattern Analysis and Machine Intelligence 12, 920–925 (1990)
Mark Gold, E.: Language identification in the limit. Information and Control 10, 447–474 (1967)
Head, T.: Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. Bulletin of Mathematical Biology 49, 737–759 (1987)
Head, T., Kobayashi, S., Yokomori, T.: Locality, Reversibility, and Beyond: Learning Languages from Positive Data. In: Richter, M.M., Smith, C.H., Wiehagen, R., Zeugmann, T. (eds.) ALT 1998. LNCS (LNAI), vol. 1501, pp. 191–204. Springer, Heidelberg (1998)
Kobayashi, S.: Approximate Identification, Finite Elasticity and Lattice Structure of Hypothesis Space, Technical Report, CSIM 96-04, Dept. of Compt. Sci. and Inform. Math., Univ. of Electro-Communications (1996)
Kobayashi, S., Mitrana, V., Păun, G., Rozenberg, G.: Formal Properties of PA-Matching. Theoretical Computer Science (accepted for publication)
Kobayashi, S., Yokomori, T.: Learning Approximately Regular Languages with Reversible Languages. Theoretical Computer Science 174, 251–257 (1997)
Koshiba, T., Mäkinen, E., Takada, Y.: Learning Strongly Deterministic Even Linear Languages from Positive Examples. In: Zeugmann, T., Shinohara, T., Jantke, K.P. (eds.) ALT 1995. LNCS (LNAI), vol. 997, pp. 41–54. Springer, Heidelberg (1995)
De Luca, A., Restivo, A.: A characterization of strictly locally testable languages and its application to subsemigroups of a free semigroup. Information and Control 44, 300–319 (1980)
Manca, V., Martín-Vide, C., Păn, G.: Iterated GSM Mappings: A Collapsing Hierarchy, Turku Centre for Computer Science, Technical Report No. 206 (October 1998)
McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press, Cambridge (1971)
Pitt, L.: Inductive Inference, DFAs, and Computational Complexity. In: Jantke, K.P. (ed.) AII 1989. LNCS (LNAI), vol. 397, pp. 18–44. Springer, Heidelberg (1989)
Pixton, D.: Regularity of splicing languages. Discrete Applied Mathematics 69, 101–124 (1996)
Schutzenberger, M.P.: Sur certaines operations de fermeture dans les languages rationnels. In: Symposium Mathematicum, vol. 15, pp. 245–253 (1975)
Shinohara, T.: Polynomial-time Inference of Extended Regular Pattern Languages. In: Goto, E., Nakajima, R., Yonezawa, A., Nakata, I., Furukawa, K. (eds.) RIMS 1982. LNCS, vol. 147, pp. 115–127. Springer, Heidelberg (1983)
Shinohara, T.: Rich Classes Inferable from Positive Data: Length Bounded Elementary Formal Systems. Information and Computation 108, 175–186 (1994)
Smullyan, R.M.: Theory of Formal Systems. Annals of Mathematics Studies, revised edn., vol. 47, Princeton University Press, Princeton (1961)
Wood, D.: Iterated a-NGSM Maps and Γ Systems. Information and Control 32, 1–26 (1976)
Yokomori, T., Ishida, N., Kobayashi, S.: Learning local languages and its application to protein alpha-chain identification. In: Proc. of 27th Hawaii Intern. Conf. on System Sciences, pp. 113–122. IEEE Press, Los Alamitos (1994)
Yokomori, T.: On polynomial-time learnability in the limit of strictly deterministic automata. Machine Learning 19, 153–179 (1995)
Yokomori, T., Kobayashi, S.: Learning local languages and its application to DNA sequence analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(10), 1067–1079 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kobayashi, S. (2000). Iterated Transductions and Efficient Learning from Positive Data: A Unifying View. In: Oliveira, A.L. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2000. Lecture Notes in Computer Science(), vol 1891. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45257-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-45257-7_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41011-9
Online ISBN: 978-3-540-45257-7
eBook Packages: Springer Book Archive