A Random Oracle Does Not Help Extract the Mutual Information

Authors:
Andrei Muchnik;Andrei Romashchenko
Affiliations:
Andrei Muchnik (24.02.1958 --- 18.03.2007) worked at the Institute of New Technologies in Education,;Laboratoire de l'Informatique du Parallélisme (Lyon) and Institute for Information Transmission Problems (Moscow),
Venue:
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Year:
2008

Citing 5
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An introduction to Kolmogorov complexity and its applications (2nd ed.)
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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 ycannot help extract the mutual information from xi's.