Advertisement

Inductive Inference of Languages from Samplings

  • Sanjay Jain
  • Efim Kinber
Conference paper
  • 775 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6331)

Abstract

We introduce, discuss, and study a model for inductive inference from samplings, formalizing an idea of learning different “projections” of languages. One set of our results addresses the problem of finding a uniform learner for all samplings of a language from a certain set when learners for particular samplings are available. Another set of results deals with extending learnability from a large natural set of samplings to larger sets. A number of open problems is formulated.

Keywords

Inductive inference samplings sublanguages 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BB75]
    Blum, L., Blum, M.: Toward a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [Blu67]
    Blum, M.: A machine-independent theory of the complexity of recursive functions. Journal of the ACM 14, 322–336 (1967)zbMATHCrossRefGoogle Scholar
  3. [CL82]
    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
  4. [CS83]
    Case, J., Smith, C.: Comparison of identification criteria for machine inductive inference. Theoretical Computer Science 25, 193–220 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  5. [Fre74]
    Freivalds, R.: Uniform and non-uniform predictability. In: Theory of Algorithms and Programs, vol. 1, pp. 89–100. Latvian State University, Riga (1974)Google Scholar
  6. [Ful90]
    Fulk, M.: Prudence and other conditions on formal language learning. Information and Computation 85, 1–11 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  7. [Gol67]
    Gold, E.M.: Language identification in the limit. Information and Control 10, 447–474 (1967)zbMATHCrossRefGoogle Scholar
  8. [HU79]
    Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)zbMATHGoogle Scholar
  9. [JK08]
    Jain, S., Kinber, E.: Learning and extending sublanguages. Theoretical Computer Science A 397(1-3), 233–246 (2008); Special Issue on Forty Years of Inductive Inference. Dedicated to the 60th Birthday of Rolf WiehagenzbMATHCrossRefMathSciNetGoogle Scholar
  10. [OSW86]
    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
  11. [OW82]
    Osherson, D., Weinstein, S.: Criteria of language learning. Information and Control 52, 123–138 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  12. [Rog67]
    Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967); Reprinted by MIT Press in 1987zbMATHGoogle Scholar
  13. [Tra73]
    Trakhtenbrot, B.A.: Frequency computations. In: Proceedings of Steklov Mathematical Institute, vol. 133, pp. 221–232. Academy of Sciences of USSR (1973) (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sanjay Jain
    • 1
  • Efim Kinber
    • 2
  1. 1.School of ComputingNational University of SingaporeSingaporeRepublic of Singapore
  2. 2.Department of Computer ScienceSacred Heart UniversityFairfieldU.S.A.

Personalised recommendations