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An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
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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.