Resource Bounded Kolmogorov Complexity and Statistical Tests

  • Luc Longpré
Part of the EATCS Monographs on Theoretical Computer Science book series (EATCS)


This paper investigates the statistical properties of resource bounded Kolmogorov-random strings. In an attempt to define random sequences, Martin-Löf has shown that the Kolmogorov-random strings (strings with no short description) possess all the statistical properties of random strings. We look at the statistical properties of resource bounded Kolmogorov-random strings. For space bounds, we show that there is a direct relation between the space bound on the Kolmogorov randomness classes and the space required to check a statistical property. The problem is still open for time bounds. We then relate this notion of random sequences to Yao’s definition of secure pseudo random number generators.


Number Generator Random Sequence Universal Test Random Number Generator Turing Machine 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Luc Longpré
    • 1
  1. 1.College of Computer ScienceNortheastern UniversityBostonUSA

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