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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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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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