Noisy inference and oracles

  • Frank Stephan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 997)


A learner noisily infers a function or set, if every correct item is presented infinitely often while in addition some incorrect data (”noise”) is presented a finite number of times. It is shown that learning from a noisy informant is equal to finite learning with K-oracle from a usual informant. This result has several variants for learning from text and using different oracles. Furthermore, partial identification of all r.e. sets can cope also with noisy input.


Recursive Function Infinite Sequence Inductive Inference Correct Item Faulty Data 
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. 1.
    Angluin, D. (1980), Inductive inference of formal languages from positive data, Information and Control45, pp. 117–135.CrossRefGoogle Scholar
  2. 2.
    Baliga, G., Jain, S., and Sharma, A. (1992), Learning from Multiple Sources of Inaccurate Data, in “Proceedings of the International Workshop on Analogical and Inductive Inference in Dagstuhl Castle, Germany”, October 1992, pp. 108–128.Google Scholar
  3. 3.
    Blum, M., and Blum, L. (1975), Towards a mathematical theory of inductive inference, Information and Control, 28, pp. 125–155.CrossRefGoogle Scholar
  4. 4.
    Fortnow, L., Gasarch, W. I., Jain, S., Kinber, E., Kummer, M., Kurtz, S., Pleszkoch, M., Slaman, T., Solovay, R., Stephan, F. C. (1994), Extremes in the degrees of inferability. Annals of Pure and Applied Logic, 66, pp. 231–276.Google Scholar
  5. 5.
    Fulk, M., and Jain, S. (1989), Learning in the presence of inaccurate information, in “Proceedings of the 2nd Annual ACM Conference on Computational Learning Theory,” Santa Cruz, July 1989, pp. 175–188, Morgan Kauffmann Publishers.Google Scholar
  6. 6.
    Gold, E.M. (1967), Language identification in the limit, Information and Control 10, pp. 447–474.CrossRefGoogle Scholar
  7. 7.
    Jain, S. (1994), Program Synthesis in the Presence of Infinite Number of Inaccuracies, in “Proceedings of the 5th Workshop on Algorithmic Learning Theory”, October 1994.Google Scholar
  8. 8.
    Jain, S., and Sharma, A. (1994), On monotonic strategies for learning r.e. languages, in “Proceedings of the 5th Workshop on Algorithmic Learning Theory”, October 1994, pp. 349–364.Google Scholar
  9. 9.
    Jantke, K.P. (1991) Monotonic and non-monotonic inductive inference, New Generation Computing 8, pp. 349–360.Google Scholar
  10. 10.
    Jockusch, C. (1981) Degrees of generic sets. London Mathematical Society Lecture Notes 45, pp. 110–139.Google Scholar
  11. 11.
    Kapur, S. (1992), Monotonic language learning, in “Proceedings of the 3rd Workshop on Algorithmic Learning Theory”, October 1992, Tokyo, JSAI, pp. 147–158.Google Scholar
  12. 12.
    Kinber, E., and Stephan, F. (1995), Language Learning from Texts: Mind Changes, Limited Memory and Monotonicity, Information and Computation, to appear. An extended extract appears in “Proceedings of the 8th Annual ACM Conference on Computational Learning Theory,” Santa Cruz, July 1995.Google Scholar
  13. 13.
    Kummer, M., and Stephan, F. (1993) On the structure of degrees of inferability, in “Proceedings of the 6th Annual ACM Conference on Computational Learning Theory,” Santa Cruz, July 1993, pp. 117–126, ACM Press, New York.Google Scholar
  14. 14.
    Lange, S., Zeugmann, T., and Kapur, S. (1992), Monotonic and dual monotonic language learning, GOSLER-Report 14/94, TH Leipzig, FB Mathematik und Informatik, August 1992.Google Scholar
  15. 15.
    Schäfer, G. (1995), Some results in the theory of effective program synthesis — learning by defective information. Lecture Notes in Computer Science 225, pp. 219–225.Google Scholar
  16. 16.
    Odifreddi, P. (1989), “Classical Recursion Theory”, North-Holland, Amsterdam.Google Scholar
  17. 17.
    Osherson, D., Stob, M., and Weinstein, S. (1986), “Systems that Learn, An Introduction to Learning Theory for Cognitive and Computer Scientists,” MIT-Press, Cambridge, Massachusetts.Google Scholar
  18. 18.
    Soare, R. (1987), “Recursively Enumerable Sets and Degrees”, Springer-Verlag, Heidelberg.Google Scholar
  19. 19.
    Zeugmann, T. (1993), Algorithmisches Lernen von Funktionen und Sprachen. Habitilationsschrift, Technische Hochschule Darmstadt, Fachbereich Informatik.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Frank Stephan
    • 1
  1. 1.Institut für Logik, Komplexität und DeduktionssystemeUniversität KarlsruheKarlsruheGermany

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