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Transformations that preserve malignness of universal distributions

  • Kojiro Kobayashi
Session 7B: Complexity Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)

Abstract

A function μ(x) that assigns a nonnegative real number μ(x) to each bit string x is said to be malign if, for any algorithm, the worst-case computation time and the average computation time of the algorithm are functions, of the same order when each bit string x is given to the algorithm as an input with the probability that is proportional to the value μ(x). M. Li and P. M. B. Vitányi found that functions that are known as “universal distributions” are malign. We show that if μ(x) is a universal distribution and t is a positive real number, then the function μ(x)t is malign or not according as t≥1 or t<1. For t>1, μ(x)t is an example of malign functions that are not universal distributions.

Keywords

Computation Time Positive Real Number Partial Function Nonnegative Real Number 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.
    Kobayashi, K.: On malign input distributions for algorithms. IEICE Trans. on Information and Systems E76-D (1993) 634–640Google Scholar
  2. 2.
    Li, M., Vitányi, P. M. B.: Worst case complexity is equal to average case complexity under the universal distribution. Inform. Process. Lett. 42 (1992) 145–149CrossRefMathSciNetGoogle Scholar
  3. 3.
    Li, M., Vitányi, P. M. B.: An Introduction to Kolmogorov Complexity and Its Applications. Springer-Verlag (1993)Google Scholar
  4. 4.
    Miltersen, P. B.: The complexity of malign ensembles. SIAM J. Computing 22 (1993) 147–156CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Kojiro Kobayashi
    • 1
  1. 1.Tokyo Institute of TechnologyTokyoJapan

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