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The query complexity of learning DFA

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Abstract

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.

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References

  1. Angluin, D., “Learning Regular Sets from Queries and Counterexamples,”Information and Computation, 75, pp. 87–106, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  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.

  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.

  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.

  7. Gold, E. M., “Identification in the Limit,”Information and Control, 10, pp. 447–474, 1967.

    Article  MATH  Google Scholar 

  8. Hopcroft, J. and Ullman, J.,Introduction to 'Automata Theory, Languages, and Computation, Addison-Wesley, Reading, 1979.

    MATH  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.

  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.

  11. Pitt, L. and Warmuth, M., “Prediction Preserving Reducibility”,Journal Comput. Syst. Sci., 41, pp. 430–467, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  12. Valiant, L., “A Theory of the Learnable,”Communications of the ACM, 27, pp. 1134–1142, 1984.

    Article  MATH  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.

  14. Watanabe, O., “A Framework for Polynomial Time Query Learnability,”Mathematical Computation Theory, 27, pp. 211–230, 1994.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Llenguatges i Sistemes Informàtics, Universitat Politècnica Catalunya, Pau Gargallo 5, 08028, Barcelona, Spain

    José L. Balcázar, Josep Díaz & Ricard Gavaldà

  2. Department of Computer Science, Tokyo Institute of Technology, Meguro-ku, 152, Tokyo, Japan

    Osamu Watanabe

Authors
  1. José L. Balcázar
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  2. Josep Díaz
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  3. Ricard Gavaldà
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  4. Osamu Watanabe
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Additional information

This research was partially supported by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM). While this research was done, the third author was visiting the University of California at Santa Barbara, supported in part by the National. Science Foundation under grant CCR89-13584. The fourth author was supported in part by Takayanagi Foundation of Electronics and Science Technology. E-mail addresses: balqui@lsi. upc.es, diaz@siva.upc.es, gavalda@lsi.upc.es, watanabe@cs.titech.ac.jp

José L. Balcázar, Dr. Became “Licenciado” in Mathematics, 1981, and passed the Essay Degree (“tesina”) in Mathematics, 1982, both at Universidad Complutense de Madrid. He joined in 1981 the Universitat Politècnica de Catalunya, where he obtained the title of “Doctor en Informática” in 1984. Presently Catedrático (Full Professor) in the same University. His main research interest is computational complexity and its applications, but has also worked, for short periods, in other mathematically oriented areas of Computer Science such as Interconnection Networks or Programming Methodology.

Josep Díaz, Dr.: He received Dr. of Sciences in 1981 from Universidad Valencia. He has been Catedrático (Full Professor) on Theoretical Computer Science in the Universitat Politècnica de Catalunya since 1983. His main research interests are design and analysis of algorithms and computational complexity.

Ricard Gavaldà, Dr.: Received his “Licenciado” (M. Sc.) degree in Computer Science in 1987, and his doctorate in 1992, both from Universitat Politècnica de Catalunya. He is currently an associate professor at the same university. His main research interests are complexity theory and computational learning.

Osamu Watanabe, Dr. Eng: He received the B. Sc. in 1980, M. Sc. degrees in 1982, and Dr. Eng. degree in 1987 from Tokyo Institute of Technology. Presently, he is an associate professor of Tokyo Institute of Technology. He has been working on computational complexity and its applications.

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Balcázar, J.L., Díaz, J., Gavaldà, R. et al. The query complexity of learning DFA. New Gener Comput 12, 337–358 (1994). https://doi.org/10.1007/BF03037351

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  • DOI: https://doi.org/10.1007/BF03037351

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