On malign input distributions for algorithms

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


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.


Rational Number Unit Interval Binary Sequence Computable Function Kolmogorov Complexity 
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  1. 1.
    M. Blum: A machine-independent theory of the complexity of recursive functions. J. ACM 14, 322–336 (1967)CrossRefGoogle Scholar
  2. 2.
    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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