Abstract
Results are presented relating to the Probably Approximately Correct learning of a class of regular languages called Terminal Distinguishable Regular Languages and a class of linear languages called Terminal Distinguishable Even Linear Languages. The VC-dimension of these concept classes are infinite. However, when further restriction is imposed on the length and the structure of strings the classes are shown to have finite VC-dimension that grows linearly with l. This motivates the design and analysis of learning algorithms for these concept classes, which are then presented.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Amar V., Putzolu G., On a family of linear grammars, Information and Control, 7, 283–291, 1964.
Angluin D., Smith C.H., Inductive Inference: Theory and Methods, ACM Computing Surveys, vol. 15 (3), 236–269, 1983.
Blumer A., Ehrenfeucht A., Haussler D., Warmuth M.K., Learnability and Vapnik-Chervonenkis Dimension, JACM, 36(4), 929–965, 1989.
Bhattacharyya P., Nagaraja G., Learning Classes of Even Linear Languages in PAC Setting, TR No. 118-93, Dept of Comp. Sc. and Engg., Indian Institute of Technology, Bombay, 1993.
Crespi-Reghizzi S., Mandrioli D., Inferring Grammars by means of Profiles: An Unifying View, TR no. 80-3, First di Electrotechica ed Electronical del Politechnico di, Milan, Italy, 1980.
Crespi-Reghizzi S., Mandrioli D., Abstract Profiles for Context-free Languages, TR no. 80-6, First di Electrotechica ed Electronical del Politechnico di, Milan, Italy, 1980.
Gold E.M., Language identification in the limit, Information and Control, 10, 447–474, 1967.
Harrison, M.A., Introduction to Formal Language Theory, Addison Wesley Pub., Readings, Mass, 1978.
Radhakrishnan V., Nagaraja G., Inference of Regular Grammars via Skeletons, IEEE Transactions on Systems, Man and Cybernetics, smc-17(6), 982–992, 1987.
Radhakrishnan V., Nagaraja G., Inference of even linear grammars and its application to picture description languages, Pattern Recognition, 21 (1), 55–62, 1988.
Sakakibara Y., Learnability in the Presence of Classification Noise, in Fujitsu IIAS-SIS workshop on Computational Learning Theory, Japan, 1989.
Valiant L.G., A Theory of the Learnable, CACM, 27(11), 1134–1142, 1984.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bhattacharyya, P., Nagaraja, G. (1993). Learning classes of Regular and Linear Languages in Valiant's learnability framework. In: Shyamasundar, R.K. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1993. Lecture Notes in Computer Science, vol 761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57529-4_76
Download citation
DOI: https://doi.org/10.1007/3-540-57529-4_76
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57529-0
Online ISBN: 978-3-540-48211-6
eBook Packages: Springer Book Archive