Abstract
This paper introduces the class of concatenations of locally testable languages and its subclasses, and presents some results on the learnability of the classes from positive data. We first establish several relationships among the language classes introduced, and give a sufficient condition for a concatenation operation to preserve finite elasticity of a language class C. Then we show that, for each k, the class CLT ≤ k, a subclass of concatenations of locally testable languages, is identifiable in the limit from positive data. Further, we introduce a notion of local parsability, and define a class (k, l)-CLTS, which is a subclass of the class of concatenations of strictly locally testable languages. Then, for each k, l ≥ 1, (k, l)-CLTS is proved to be identifiable in the limit from positive data using reversible automata with the conjectures updated in polynomial time. Some possible applications of this result are also briefly discussed.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
D. Angluin. Inductive inference of formal languages from positive data. Information and Control, vol. 45, pp. 117–135, 1980
D. Angluin. Inference of reversible languages. Journal of the ACM, vol. 29, pp. 741–765, 1982
L. Blum and M. Blum. Toward a Mathematical Theory of Inductive Inference. Information and Control, vol. 28, pp. 125–155, 1975
E. Mark Gold. Language identification in the limit. Information and Control, vol. 10, pp. 447–474, 1967
T. Head. Formal language theory and DNA: An analysis of the generative capacity of specific recombinant behaviors. Bulletin of Mathematical Biology, vol. 49, pp. 737–759, 1987
S. Lange and T. Zeugmann. Language Learning in Dependence on the Space of Hypotheses. Proc. of 6th Annual ACM Workshop on Computational Learning Theory, pp. 127–136, 1993
T. Moriyama and M. Sato. Properties of Language Classes with Finite Elasticity. Proc. 4th Workshop on Algorithmic Learning Theory, Lecture Notes in Artificial Intelligence 744, pp. 187–196, 1993
T. Motoki, T. Shinohara and K. Wright. The correct definition of finite elasticity: corrigendum to identification of unions. Proc. of 4th Workshop on Computational Learning Theory, pp. 375–375, 1991
R. McNaughton and S. Papert. Counter-Free Automata. MIT Press, Cambridge, MA, 1971
T. Yokomori. A note on the polynomial-time identification of strictly local languages in the limit. Report CSIM90-03, Dept. of Comput. Sci. and Inf. Math., Univ. of Elect.-Communi., 1990
T. Yokomori, N. Ishida and S. Kobayashi. Learning Local Languages and Its Application to Protein α-chain Identification. Proc. of 27th Hawaii International Conference on System Sciences, Hawaii, pp. 113–122, 1994, Janualy
K. Wright. Identification of unions of languages drawn from an identifiable class. Proc. of 2nd Workshop on Computational Learning Theory, pp. 328–333, 1989
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kobayashi, S., Yokomori, T. (1994). Learning concatenations of locally testable languages from positive data. In: Arikawa, S., Jantke, K.P. (eds) Algorithmic Learning Theory. AII ALT 1994 1994. Lecture Notes in Computer Science, vol 872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58520-6_80
Download citation
DOI: https://doi.org/10.1007/3-540-58520-6_80
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58520-6
Online ISBN: 978-3-540-49030-2
eBook Packages: Springer Book Archive