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Application of kolmogorov complexity to inductive inference with limited memory

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

Abstract

We consider inductive inference with limited memory[1].

We show that there exists a set U of total recursive functions such that
  • U can be learned with linear long-term memory (and no short-term memory);

  • U can be learned with logarithmic long-term memory (and some amount of short-term memory);

  • if U is learned with sublinear long-term memory, then the short-term memory exceeds arbitrary recursive function.

Thus an open problem posed by Freivalds, Kinber and Smith[1] is solved. To prove our result, we use Kolmogorov complexity.

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References

  1. 1. [FKS93]
    R. Freivalds, E. Kinber and C. Smith, On the impact of forgetting on learning machines, Proceedings of the 6-th ACM COLT, 1993, pp. 165–174. To appear in Information and Computation.Google Scholar
  2. 2. [Gol67]
    E. M. Gold, Language identification in the limit, Information and Control, vol. 10(1967), pp. 447–474CrossRefGoogle Scholar
  3. 3. [Kol65]
    A. N. Kolmogorov, Three approaches to the quantitative definition of’ information', Problems of Information Transmission, vol. 1 (1965), pp. 1–7Google Scholar
  4. 4. [LV93]
    M. Li, P.Vitanyi, Introduction to Kolmogorov complexity and its applications, Springer, 1993Google Scholar
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    M. Machtey and P. Young, An Introduction to the General Theory of Algorithms, North-Holland, New York, 1978Google Scholar
  6. 6. [Rog67]
    H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, 1967. Reprinted by MIT Press, Cambridge, MA, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  1. 1.University of LatviaLatvia
  2. 2.Riga Institute of Information TechnologyUSSR

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