Learning strongly deterministic even linear languages from positive examples
We consider the problem of learning deterministic even linear languages from positive examples. By a “deterministic” even linear language we mean a language generated by an LR(k) even linear grammar. We introduce a natural subclass of LR(k) even linear languages, called LR(k) in the strong sense, and show that this subclass is learnable in the limit from positive examples. Furthermore, we propose a learning algorithm that identifies this subclass in the limit with almost linear time in updating conjectures. As a corollary, in terms of even linear grammars, we have a learning algorithm for k-reversible languages that is more efficient than the one proposed by Angluin[Ang82].
KeywordsLearning Algorithm Nonnegative Integer Regular Language Finite Automaton Input String
Unable to display preview. Download preview PDF.
- [Ang82]D. Angluin. Inference of reversible languages. Journal of the Association for Computing Machinery, Vol. 29, No. 3, pp. 741–765, 1982.Google Scholar
- [GI91]Z. Galil and G. F. Italiano. Data structures and algorithms for disjoint set union problems. ACM Computing Surveys, Vol. 23, No. 3, pp. 319–344, 1991.Google Scholar
- [Har78]M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesley 1978.Google Scholar
- [Lew94]B. Lewin. Genes V. Oxford University Press, 1994.Google Scholar
- [Mäk94]E. Mäkinen. A note on the grammatical inference problem for even linear languages. Report A-1994-9, University of Tampere, 1994. To appear in Fundamenta Informaticae.Google Scholar
- [Tak94]Y. Takada. A hierarchy of languages families learnable by regular language learning. Research Report ISIS-RR-94-15E, ISIS, Fujitsu Laboratories Ltd., 1994. To appear in Information and Computation.Google Scholar
- [Tar75]R. E. Tarjan. Efficiency of a good but not linear set union algorithm. Journal of the Association for Computing Machinery, Vol. 22, No. 2, pp. 215–225, 1975.Google Scholar