Abstract
In the last COLT Conference A.Burago showed that the class of structurally reversible grammars is learnable in polynomial time using membership and equivalence queries. The paper shows that this class of grammars is not learnable using either membership alone or equivalence alone. However, it turns out that structurally reversible grammars are a superclass of very simple grammars which are learnable using only equivalence queries. Furthermore, we prove that the number of alternations between equivalence and membership queries cannot be constant. We also prove a lower bound in the number of alternations between membership and equivalence queries which is an improvement with respect to the same lower bound for deterministic finite automata. Finally, we disccus a possible trade-off between membership and equivalence queries in Burago's algorithm that might allow us to reduce the number of equivalence queries.
Research supported by the Esprit EC program under project 7141 (ALCOM-II) and Working Group 8556 (NeuroColt), and by the Spanish DGICYT (project PB92-0709).
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References
D. Angluin. Learning regular sets from queries and counterexamples. Information and Control, 75, 87–106, 1987.
D. Angluin. Queries and concept learning. Machine Learning, 2, 319–342, 1988.
D. Angluin. Negative results for equivalence queries. Machine Learning, 5, 121–150, 1990.
J.L. Balcázar, J. Díaz, R. Gavaldà. O. Watanabe The Query Complexity of Learning DFA To appear in Journal of New Generation Computing. Preliminary version (with weaker results) in Proceedings of the Third Workshop on Algorithmic Learning Theory, pp. 53–62, 1992.
A. Burago. Learning structurally reversible context-free grammars from queries and counterexamples in polynomial time Proceedings of the Seventh Workshop on Computational Learning Theory, New Brunswick, USA, pp. 140–146, 1994.
R. Gavaldà. On the power of equivalence queries Proceedings of the First European Conferenc on Computational Learning Theory, Royal Holloway University, London, 1993.
J. Hopcroft, J. Ullman. Introduction to Automata, Languages and Computation. Addison-Wesley, Reading, Mass., 1979.
H. Ishizaka. Learning Simple Deterministic Languages. Proceedings of the Second Workshop on Computational Learning Theory, Morgan Kaufmann Publishers, Inc., San Mateo, CA, pp. 162–174, 1989.
Y. Sakakibara. Learning context-free grammars from structural data in polynomial time. Theoretical Computer Science, pp. 223–242, 1990.
O. Watanabe. A formal study of learning via queries. Lecture Notes in Computer Science 443: Proceedings of the 17th International Colloquium on Automata, Languages and Programming, M.S.Paterson, ed., Springer-Verlag, pp. 139–152, 1990.
O. Watanabe. A framework for polynomial time query learnability Mathematical Systems Theory, 27, 211–229, 1994.
O. Watanabe, R. Gavaldà. Structural analysis of polynomial time query learnability. Mathematics Systems Theory, 27, 231–256, 1994.
T. Yokomori. Polynomial-Time Identification of Very Simple Grammars from Positive Data Proceedings of the Fourth Workshop on Computational Learning Theory, Santa Cruz, CA, pp. 213–227, 1991.
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© 1995 Springer-Verlag Berlin Heidelberg
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Domingo, C., Lavín, V. (1995). The query complexity of learning some subclasses of context-free grammars. In: Vitányi, P. (eds) Computational Learning Theory. EuroCOLT 1995. Lecture Notes in Computer Science, vol 904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59119-2_195
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DOI: https://doi.org/10.1007/3-540-59119-2_195
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