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Probl. Peredachi Inf., 2010, Volume 46, Issue 1, Pages 42–67 (Mi ppi2009)  

This article is cited in 2 scientific papers (total in 2 papers)

Large Systems

Stability of properties of Kolmogorov complexity under relativization

An. A. Muchnik, A. E. Romashchenkoa

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: Assume that a tuple of binary strings $\bar a=\langle a_1,…,a_n\rangle$ has negligible mutual information with another string $b$. Does this mean that properties of the Kolmogorov complexity of $\bar a$ do not change significantly if we relativize them to $b$? This question becomes very nontrivial when we try to formalize it. In this paper we investigate this problem for a special class of properties (for properties that can be expressed by an $\exists$-formula). In particular, we show that a random (conditional on $\bar a$) oracle b does not help to extract common information from the strings $a_i$.

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English version:
Problems of Information Transmission, 2010, 46:1, 38–61

Bibliographic databases:

UDC: 621.391.1+519.2
Received: 08.06.2009
Revised: 15.01.2010

Citation: An. A. Muchnik, A. E. Romashchenko, “Stability of properties of Kolmogorov complexity under relativization”, Probl. Peredachi Inf., 46:1 (2010), 42–67; Problems Inform. Transmission, 46:1 (2010), 38–61

Citation in format AMSBIB
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\by An.~A.~Muchnik, A.~E.~Romashchenko
\paper Stability of properties of Kolmogorov complexity under relativization
\jour Probl. Peredachi Inf.
\yr 2010
\vol 46
\issue 1
\pages 42--67
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2675298}
\elib{http://elibrary.ru/item.asp?id=15332059}
\transl
\jour Problems Inform. Transmission
\yr 2010
\vol 46
\issue 1
\pages 38--61
\crossref{https://doi.org/10.1134/S0032946010010059}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77951617221}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kaced T., Romashchenko A., “On essentially conditional information inequalities”, 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), 2011  isi
    2. Vereshchagin N., Shen A., “Algorithmic Statistics: Forty Years Later”, Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60Th Birthday, Lecture Notes in Computer Science, 10010, eds. Day A., Fellows M., Greenberg N., Khoussainov B., Melnikov A., Rosamond F., Springer International Publishing Ag, 2017, 669–737  crossref  mathscinet  zmath  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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