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Probl. Peredachi Inf., 2000, Volume 36, Issue 1, Pages 3–20 (Mi ppi466)  

This article is cited in 4 scientific papers (total in 4 papers)

Information Theory

Pairs of Words with Nonmaterializable Mutual Information

A. E. Romashchenko


Abstract: Let there be a pair of words $\langle a,b\rangle$ with sufficiently large mutual information. Can we always “materialize” this information, i.e., point out a word $c$ that can be computed from $a$ and $b$ simply and whose Kolmogorov complexity equals the mutual information between $a$ and $b$? In this paper, we propose a better estimate for the amount of mutual information which may be materialized for words from the construction of Gács and Körner, and also give a new method for constructing pairs of words with nonmaterializable mutual information.

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English version:
Problems of Information Transmission, 2000, 36:1, 1–18

Bibliographic databases:
UDC: 621.391.1:519.722:510.5
Received: 29.03.1999
Revised: 30.11.1999

Citation: A. E. Romashchenko, “Pairs of Words with Nonmaterializable Mutual Information”, Probl. Peredachi Inf., 36:1 (2000), 3–20; Problems Inform. Transmission, 36:1 (2000), 1–18

Citation in format AMSBIB
\Bibitem{Rom00}
\by A.~E.~Romashchenko
\paper Pairs of Words with Nonmaterializable Mutual Information
\jour Probl. Peredachi Inf.
\yr 2000
\vol 36
\issue 1
\pages 3--20
\mathnet{http://mi.mathnet.ru/ppi466}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1746005}
\zmath{https://zbmath.org/?q=an:1025.94007}
\transl
\jour Problems Inform. Transmission
\yr 2000
\vol 36
\issue 1
\pages 1--18


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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. Chernov, A, “Upper semi-lattice of binary strings with the relation “x is simple conditional to y””, Theoretical Computer Science, 271:1–2 (2002), 69  crossref  mathscinet  zmath  isi
    2. A. E. Romashchenko, “A Criterion of Extractability of the Mutual Information for a Triple of Strings”, Problems Inform. Transmission, 39:1 (2003), 148–157  mathnet  crossref  mathscinet  zmath
    3. An. A. Muchnik, A. E. Romashchenko, “Stability of properties of Kolmogorov complexity under relativization”, Problems Inform. Transmission, 46:1 (2010), 38–61  mathnet  crossref  mathscinet  isi  elib
    4. Makarychev K., Makarychev Yu., “Chain Independence and Common Information”, IEEE Trans. Inf. Theory, 58:8 (2012), 5279–5286  crossref  mathscinet  isi
  • Проблемы передачи информации Problems of Information Transmission
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