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Learnable Algorithm on the Continuum

  • Zhimin Li
  • Xiang Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)

Abstract

Based on limiting recursive function proposed by Gold [2], learnable algorithm on the continuum are defined. We discuss the class of learnable real numbers and learnable real sequence in various ways. In this paper we summarize some attempts to classify the learnably approximable real numbers by the convergence rates of the corresponding computable(or learnable) sequences of rational numbers.

Keywords

Real Number Learnable Algorithm Rational Number Learnable Sequence Recursive Function 
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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References

  1. 1.
    Ambos-Spies, K., Weihrauch, K., Zheng, X.: Weakly computable real numbers. Journal of complexity 16, 676–690 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Gold, E.M.: Limiting recursive. Journal of symolic logic 30, 28–48 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Hayashi, S., Nakata, K.: Towards limit computable mathematics. In: Callaghan, P., et al. (eds.) TYPES 2000. LNCS, vol. 2277, pp. 125–144. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Pour-El, M.B., Richards, J.I.: Computability in Analysis and Physics. Springer, Heidelberg (1989)zbMATHGoogle Scholar
  5. 5.
    Yasugi, M., et al.: Computability aspects of some discontinuous functions. SCMJ 5 (2001)Google Scholar
  6. 6.
    Zheng, X.: Recursive approximability of real numbers. Math. Log. Quart., 473–485 (2002)Google Scholar
  7. 7.
    Li, Z., Yasugi, M.: Computability of continuous and discontinuous real recursive functions. Lecture Series on Computer and Computational Sciences (LECCS 2006) (To appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Zhimin Li
    • 1
    • 2
  • Xiang Li
    • 1
  1. 1.Institute of Computer Science, Guizhou University, Guiyang550025China
  2. 2.School of Mathematics and Computer Science, Guizhou University for Nationalities, Guiyang550025China

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