In this paper we survey some results in inductive inference showing how learnability of a class of languages may depend on hypothesis space chosen. We also discuss results which consider how learnability is effected if one requires learning with respect to every suitable hypothesis space. Additionally, optimal hypothesis spaces, using which every learnable class is learnable, is considered.


Target Language Inductive Inference Iterative Learning Learning Criterion Learnable Class 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Angluin, D.: Finding patterns common to a set of strings. Journal of Computer and System Sciences 21, 46–62 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45, 117–135 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Angluin, D., Smith, C.: Inductive inference: Theory and methods. Computing Surveys 15, 237–289 (1983)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bārzdiņš, J.: Inductive inference of automata, functions and programs. In: Proceedings of the 20th International Congress of Mathematicians, Vancouver, pp. 455–560 (1974); (in Russian) English translation in American Mathematical Society Translations. Series 2 109, 107–112 (1977) Google Scholar
  5. 5.
    Bārzdiņš, J.: Two theorems on the limiting synthesis of functions. Theory of Algorithms and Programs 1, 82–88 (1974) (in Russian)Google Scholar
  6. 6.
    Blum, L., Blum, M.: Toward a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Baliga, G., Case, J., Merkle, W., Stephan, F., Wiehagen, R.: When unlearning helps. Information and Computation 206(5), 694–709 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Case, J.: The power of vacillation in language learning. SIAM Journal on Computing 28(6), 1941–1969 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Case, J., Jain, S., Suraj, M.: Control structures in hypothesis spaces: The influence on learning. Theoretical Computer Science 270(1–2), 287–308 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Case, J., Lynes, C.: Machine inductive inference and language identification. In: Nielsen, M., Schmidt, E.M. (eds.) ICALP 1982. LNCS, vol. 140, pp. 107–115. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  11. 11.
    Case, V., Smith, C.: Comparison of identification criteria for machine inductive inference. Theoretical Computer Science 25, 193–220 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Freivalds, R., Kinber, E., Wiehagen, R.: Inductive inference and computable one-one numberings. Zeitschr. f. math. Logik und Grundlagen d. Math. Bd. 28, 463–479 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Friedberg, R.: Three theorems on recursive enumeration. Journal of Symbolic Logic 23(3), 309–316 (1958)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Fulk, M.: Prudence and other conditions on formal language learning. Information and Computation 85, 1–11 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Freivalds, R., Wiehagen, R.: Inductive inference with additional information. Journal of Information Processing and Cybernetics (EIK) 15, 179–195 (1979)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Gold, E.M.: Language identification in the limit. Information and Control 10, 447–474 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Jantke, K.: Monotonic and non-monotonic inductive inference. New Generation Computing 8, 349–360 (1991)CrossRefzbMATHGoogle Scholar
  18. 18.
    Jain, S., Lange, S., Zilles, S.: A general comparision of language learning from examples and from queries. Theoretical Computer Science A 387(1), 51–66 (2007); Special Issue on Algorithmic Learning Theory (2005)CrossRefzbMATHGoogle Scholar
  19. 19.
    Jain, S., Osherson, D., Royer, J., Sharma, A.: Systems that Learn: An Introduction to Learning Theory, 2nd edn. MIT Press, Cambridge (1999)Google Scholar
  20. 20.
    Jain, S., Sharma, A.: Learning with the knowledge of an upper bound on program size. Information and Computation 102, 118–166 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Jain, S., Stephan, F.: Learning in Friedberg numberings. Information and Computation 206(6), 776–790 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Jain, S., Stephan, F.: Numberings optimal for learning. In: Györfi, L., Freund, Y., Turán, G., Zeugmann, T. (eds.) ALT 2008. LNCS (LNAI), vol. 5254, pp. 434–448. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Jain, S., Stephan, F., Ye, N.: Prescribed learning of R.E. classes. In: Hutter, M., Servedio, R., Takimoto, E. (eds.) ALT 2007. LNCS (LNAI), vol. 4754, pp. 64–78. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  24. 24.
    Jain, S., Stephan, F., Ye, N.: Prescribed learning of indexed families. Fundamenta Informaticae 83(1–2), 159–175 (2008)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Lange, S., Zeugmann, T.: Language learning in dependence on the space of hypotheses. In: Proceedings of the Sixth Annual Conference on Computational Learning Theory, pp. 127–136. ACM Press, New York (1993)CrossRefGoogle Scholar
  26. 26.
    Lange, S., Zeugmann, T.: The learnability of recursive languages in dependence on the space of hypotheses. Technical Report 20/93, GOSLER-Report, FB Mathematik und Informatik, TH Lepzig (1993)Google Scholar
  27. 27.
    Lange, S., Zeugmann, T.: Learning recursive languages with bounded mind changes. International Journal of Foundations of Computer Science 4, 157–178 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Lange, S., Zeugmann, T.: Incremental learning from positive data. Journal of Computer and System Sciences 53, 88–103 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Lange, S., Zeugmann, T.: Set-driven and rearrangement-independent learning of recursive languages. Mathematical Systems Theory 29, 599–634 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Lange, S., Zilles, S.: Comparison of query learning and gold-style learning in dependence of the hypothesis space. In: Ben-David, S., Case, J., Maruoka, A. (eds.) ALT 2004. LNCS (LNAI), vol. 3244, pp. 99–113. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  31. 31.
    Lange, S., Zeugmann, T., Kapur, S.: Monotonic and dual monotonic language learning. Theoretical Computer Science A 155, 365–410 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Osherson, D., Stob, M., Weinstein, S.: Learning strategies. Information and Control 53, 32–51 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Osherson, D., Stob, M., Weinstein, S.: Systems that Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge (1986)Google Scholar
  34. 34.
    Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967); reprinted by MIT Press (1987)zbMATHGoogle Scholar
  35. 35.
    Schäfer-Richter, G.: Über Eingabeabhängigkeit und Komplexität von Inferenzstrategien. PhD thesis, RWTH Aachen (1984)Google Scholar
  36. 36.
    Wexler, K., Culicover, P.: Formal Principles of Language Acquisition. MIT Press, Cambridge (1980)Google Scholar
  37. 37.
    Wiehagen, R.: Limes-Erkennung rekursiver Funktionen durch spezielle Strategien. Journal of Information Processing and Cybernetics (EIK) 12, 93–99 (1976)MathSciNetzbMATHGoogle Scholar
  38. 38.
    Wiehagen, R.: Zur Theorie der Algorithmischen Erkennung. Dissertation B, Humboldt University of Berlin (1978)Google Scholar
  39. 39.
    Wiehagen, R.: A thesis in inductive inference. In: Dix, J., Jantke, K., Schmitt, P. (eds.) NIL 1990. LNCS (LNAI), vol. 543, pp. 184–207. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  40. 40.
    Wiehagen, R., Zeugmann, T.: Learning and consistency. In: Jantke, K.P., Lange, S. (eds.) GOSLER 1994. LNCS (LNAI), vol. 961, pp. 1–24. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  41. 41.
    Zeugmann, T., Lange, S.: A guided tour across the boundaries of learning recursive languages. In: Jantke, K., Lange, S. (eds.) GOSLER 1994. LNCS (LNAI), vol. 961, pp. 190–258. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  42. 42.
    Zeugmann, T., Lange, S., Kapur, S.: Characterizations of monotonic and dual monotonic language learning. Information and Computation 120, 155–173 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Zeugmann, T., Zilles, S.: Learning recursive functions: A survey. Theoretical Computer Science A 397(1–3), 4–56 (2008); Special Issue on Forty Years of Inductive Inference. Dedicated to the 60th Birthday of Rolf WiehagenMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sanjay Jain
    • 1
  1. 1.Department of Computer ScienceNational University of SingaporeSingaporeRepublic of Singapore

Personalised recommendations