It is known that the class of deterministic finite automata is polynomial time learnable by using membership and equivalence queries. We investigate the query complexity of learning deterministic finite automata, i.e., the number of membership and equivalence queries made during the process of learning. We extend a known lower bound on membership queries to the case of randomized learning algorithms, and prove lower bounds on the number of alternations between membership and equivalence queries. We also show that a trade-off exists, allowing us to reduce the number of equivalence queries at the price of increasing the number of membership queries.
KeywordsQuery Learning Deterministic Finite Automata Membership Query Equivalence Query Trade-off
Unable to display preview. Download preview PDF.
- 2).Angluin, D., “Queries and Concept Learning,”Machine Learning, 2, pp. 319–342, 1988.Google Scholar
- 3).Angluin, D., “Negative Results for Equivalence Queries,”Machine Learning, 5, pp. 121–150, 1990.Google Scholar
- 4).Angluin, D. and Kharitonov, M., “When Won't Membership Queries Help?” inProc. 23rd ACM Symposium. on Theory of Computing, ACM, pp. 444–454, 1991.Google Scholar
- 5).Balcázar, J., Díaz, J., Gavaldà, R., and Watanabe, O., “An Optimal Parallel Algorithm for Learning DFA,”Technical Report, 93TR-0031, Department of Computer Science, Tokyo Institute of Technology, 1993. To appear inProc. 7th Annual ACM Conference on Computational Learning Theory, 1994.Google Scholar
- 6).Bshouty, N. H., Goldman, S. A., Hancock, T. R., and Matar, S., “Asking Queries to Minimize Errors,” inProc. 6th Annual ACM Conference on Computational Learning Theory, ACM Press, pp. 41–50, 1993.Google Scholar
- 9).Kearns, M. and Valiant, L., “Cryptographic Limitations on Learning Boolean Formulae and Finite Automata,” inProc. 21st ACM Symposium on Theory of Computing, ACM, pp. 433–444, 1989.Google Scholar
- 10).Pitt, L., “Inductive Inference, DFAs, and Computational Complexity,” inProc. International Workshop on Analogical and Inductive Inference AII'89, Lecture Notes in Artificial Intelligence 397, Springer-Verlag., pp. 18–42, 1989.Google Scholar
- 13).Watanabe O., “A Formal Study of Learning via Queries,” inProc. 17th International Colloquium on Automata, Languages and Programming, Lecture Notes in Computer Science 443, Springer-Verlag, pp. 137–152, 1990.Google Scholar