Kolmogorov complexity conditional to large integers

  • Authors:
  • Nikolai K. Vereshchagin

  • Affiliations:
  • Moscow State Univ., Moscow, Russia

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2002

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Abstract

The main result of the paper states that the following two values coincide for any string x: limsupnK(x|n) and the minimum length of a program that producesx given all sufficiently large integers. Previously it was known that the latter value is equal to the Kolmogorov complexity of x relativized by 0. (All equalities hold up to a constant additive term.)