Shannon entropy vs. kolmogorov complexity

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Abstract

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. © Springer-Verlag Berlin Heidelberg 2006.

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Muchnik, A., & Vereshchagin, N. (2006). Shannon entropy vs. kolmogorov complexity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3967 LNCS, pp. 281–291). Springer Verlag. https://doi.org/10.1007/11753728_29

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