Shannon Entropy vs. Kolmogorov Complexity

  • An. Muchnik
  • N. Vereshchagin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3967)


Most assertions involving Shannon entropy have their Kolmogorov complexity counterparts. A general theorem of Romashchenko [4] states that every information inequality that is valid in Shannon’s theory is also valid in Kolmogorov’s theory, and vice verse. In this paper we prove that this is no longer true for ∀ ∃-assertions, exhibiting the first example where the formal analogy between Shannon entropy and Kolmogorov complexity fails.


Shannon Entropy Binary String Kolmogorov Complexity Vice Verse Kolmogorov Theory 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • An. Muchnik
    • 1
  • N. Vereshchagin
    • 2
  1. 1.Institute of New TechnologiesMoscowRussia
  2. 2.Department of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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