A polynomial time incremental algorithm for learning DFA

  • Rajesh Parekh
  • Codrin Nichitiu
  • Vasant Honavar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1433)


We present an efficient incremental algorithm for learning deterministic unite state automata (DFA) from labeled examples and membership queries. This algorithm is an extension of Angluin's ID procedure to an incremental framework. The learning algorithm is intermittently provided with labeled examples and has access to a knowledgeable teacher capable of answering membership queries. The learner constructs an initial hypothesis from the given set of labeled examples and the teacher's responses to membership queries. If an additional example observed by the learner is inconsistent with the current hypothesis then the hypothesis is modified minimally to make it consistent with the new example. The update procedure ensures that the modified hypothesis is consistent with all examples observed thus far. The algorithm is guaranteed to converge to a minimum state DFA corresponding to the target when the set of examples observed by the learner includes a live complete set. We prove the convergence of this algorithm and analyze its time and space complexities.


Regular Language Learner Construct Incremental Algorithm State Transition Diagram Membership Query 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [Ang81]
    D. Angluin. A note on the number of queries needed to identify regular languages. Information and Control, 51:76–87, 1981.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [Ang87]
    D. Angluin. Learning regular sets from queries and counterexamples. Information and Computation, 75:87–106, 1987.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [BF72]
    A. Biermann and J. Feldman. A survey of results in grammatical inference. In S. Watanabe, editor, Frontiers of Pattern Recognition, Academic Press, pages 31–54, 1972.Google Scholar
  4. [CM96]
    D. Carmel and S. Markovitch. Learning models of intelligent agents. In Proceedings of the AAAI-96 (vol. 1), AAAI Press/MIT Press, pages 62–67, 1996.Google Scholar
  5. [Dup96]
    P. Dupont. Incremental regular inference. In L. Miclet and C. Higuera, editors, Proceedings of the Third ICGI-96, Montpellier, France, Lecture Notes in Artificial Intelligence 1147, Springer-Verlag, pages 222–237, 1996.Google Scholar
  6. [FB75]
    K. S. Fu and T. L. Booth. Grammatical inference: Introduction and survey (part 1). IEEE Transactions on Systems, Man and Cybernetics, 5:85–111, 1975.Google Scholar
  7. [Gol78]
    E. M. Gold. Complexity of automaton identification from given data. Information and Control, 37(3):302–320, 1978.zbMATHMathSciNetCrossRefGoogle Scholar
  8. [Lan95]
    P. Langley. Elements of Machine Learning. Morgan Kauffman, Palo Alto, CA, 1995.Google Scholar
  9. [MQ86]
    L. Miclet and J. Quinqueton. Learning from examples in sequences and grammatical inference. In G. Ferrate et al, editors, Syntactic and Structural Pattern Recognition, NATO ASI Series Vol. F45, pages 153–171, 1986.Google Scholar
  10. [OG92]
    J. Oncina and P. García. Inferring regular languages in polynomial update time. In N. Pérez et al, editors, Pattern Recognition and Image Analysis, World Scientific, pages 49–61, 1992.Google Scholar
  11. [PC78]
    T. Pao and J. Carr. A solution of the syntactic induction-inference problem for regular languages. Computer Languages, 3:53–64, 1978.zbMATHCrossRefGoogle Scholar
  12. [PF91]
    S. Porat and J. Feldman. Learning automata from ordered examples. Machine Learning, 7:109–138, 1991.zbMATHGoogle Scholar
  13. [PH96]
    R. G. Parekh and V. G. Honavar. An incremental interactive algorithm for regular grammar inference. In L. Miclet and C. Higuera, editors, Proceedings of the Third ICGI-96, Montpellier, France, Lecture Notes in Artificial Intelligence 1147, Springer-Verlag, pages 238–250, 1996.Google Scholar
  14. [PH97]
    R. G. Parekh and V. G. Honavar. Learning dfa from simple examples. In Proceedings of the Eighth International Workshop on Algorithmic Learning Theory (ALT'97), Sendai, Japan, Lecture Notes in Artificial Intelligence 1316, Springer-Verlag, pages 116–131, 1997. Also presented at the Workshop on Grammar Inference, Automata Induction, and Language Acquisition (ICML'97), Nashville, TN. July 12, 1997.Google Scholar
  15. [PH98]
    R. G. Parekh and V. G. Honavar. Grammar inference, automata induction, and language acquisition. In R. Dale, H. Moisl, and H. Somers, editors, Handbook of Natural Language Processing. Marcel Dekker, 1998. (To appear).Google Scholar
  16. [Pit89]
    L. Pitt. Inductive inference, dfas and computational complexity. In Analogical and Inductive Inference, Lecture Notes in Artificial Intelligence 397, Springer-Verlag, pages 18–44, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Rajesh Parekh
    • 1
  • Codrin Nichitiu
    • 2
  • Vasant Honavar
    • 3
  1. 1.Allstate Research and Planning CenterMenlo ParkUSA
  2. 2.Ecole Normale Superieure de LyonLyon Cedex 07France
  3. 3.Department of Computer ScienceIowa State UniversityAmesUSA

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