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On malign input distributions for algorithms

  • Kojiro Kobayashi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)

Abstract

By a measure we mean a function Μ from {0,1}* (the set of all binary sequences) to real numbers such that Μ(x)≥0 and Μ({0,1}*)<∞. A malign measure is a measure such that if an input x in {0,1}n (the set of all binary sequences of length n) is selected with the probability Μ(i)/Μ({0,1}n) then the worst-case computation time t A wo (n) and the average-case computation time t A av, μ (n) of an algorithm A for inputs of length n are functions of n of the same order for any algorithm A. Li and Vitányi found that a priori measures are malign. We show that “a priori”-ness and malignness are different in one strong sense.

Keywords

Rational Number Unit Interval Binary Sequence Computable Function Kolmogorov Complexity 
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.
    M. Blum: A machine-independent theory of the complexity of recursive functions. J. ACM 14, 322–336 (1967)CrossRefGoogle Scholar
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    M. Li, P.M.B. Vitányi: A theory of learning simple concepts under simple distributions and average case complexity for the universal distribution. In: Proc. of the 30th FOCS, 1989, pp.34–39Google Scholar
  3. 3.
    M. Li, P.M.B. Vitányi: Kolmogorov complexity and its applications. In: J. van Leeuwen (ed.): Handbook of Theoretical Computer Science, Vol. A, Chap. IV. Elsevier and MIT Press 1990, pp.187–254Google Scholar
  4. 4.
    P.B. Miltersen: The complexity of malign ensembles. In: Proc. of the 6th SICT, 1991, pp.164–171Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Kojiro Kobayashi
    • 1
  1. 1.Department of Information SciencesTokyo Institute of TechnologyTokyoJapan

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