Abstract
Assume a tuple of words \(\bar x =\langle x_1,\ldots,x_n\rangle\) has negligible mutual information with another word y. Does this mean that properties of Kolmogorov complexity for \(\bar x\) do not change significantly if we relativize them conditional to y ? This question becomes very nontrivial when we try to formalize it. We investigate this question for a very particular kind of properties: we show that a random (conditional to \(\bar x\)) oracle y cannot help extract the mutual information from x i ’s.
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Muchnik, A., Romashchenko, A. (2008). A Random Oracle Does Not Help Extract the Mutual Information. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_43
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DOI: https://doi.org/10.1007/978-3-540-85238-4_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85237-7
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