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Probl. Peredachi Inf., 2003, Volume 39, Issue 4, Pages 71–87 (Mi ppi317)  

This article is cited in 6 scientific papers (total in 6 papers)

Large Systems

On Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity

V. V. V'yugina, V. P. Maslovb

a Institute for Information Transmission Problems, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University

Abstract: Conditions are presented under which the maximum of the Kolmogorov complexity (algorithmic entropy) $K(\omega_1…\omega_N)$ is attained, given the cost $\sum_{i=1}^Nf(\omega_i)$ of a message $\omega_1…\omega_N$. Various extremal relations between the message cost and the Kolmogorov complexity are also considered; in particular, the minimization problem for the function $\sum_{i=1}^Nf(\omega_i)-\theta K(\omega_1…\omega_N)$ is studied. Here, $\theta$ is a parameter, called the temperature by analogy with thermodynamics. We also study domains of small variation of this function.

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English version:
Problems of Information Transmission, 2003, 39:4, 380–394

Bibliographic databases:

UDC: 621.391.1:519.2
Received: 09.01.2003
Revised: 11.06.2003

Citation: V. V. V'yugin, V. P. Maslov, “On Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity”, Probl. Peredachi Inf., 39:4 (2003), 71–87; Problems Inform. Transmission, 39:4 (2003), 380–394

Citation in format AMSBIB
\Bibitem{VyuMas03}
\by V.~V.~V'yugin, V.~P.~Maslov
\paper On Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity
\jour Probl. Peredachi Inf.
\yr 2003
\vol 39
\issue 4
\pages 71--87
\mathnet{http://mi.mathnet.ru/ppi317}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2102721}
\zmath{https://zbmath.org/?q=an:1091.94015}
\transl
\jour Problems Inform. Transmission
\yr 2003
\vol 39
\issue 4
\pages 380--394
\crossref{https://doi.org/10.1023/B:PRIT.0000011276.88154.91}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Maslov, “Nonlinear financial averaging, the evolution process, and laws of econophysics”, Theory Probab. Appl., 49:2 (2005), 221–244  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Maslov V.P., “Quasistable economics and its relationship to the thermodynamics of superfluids. Default as a zero order phase transition”, Russ. J. Math. Phys., 11:4 (2004), 429–455  mathscinet  zmath  isi
    3. V. V. V'yugin, V. P. Maslov, “Theorems on Concentration for the Entropy of Free Energy”, Problems Inform. Transmission, 41:2 (2005), 134–149  mathnet  crossref  mathscinet  zmath  elib  elib
    4. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Maslov V.P., “Revision of probability theory from the point of view of quantum statistics”, Russ. J. Math. Phys., 14:1 (2007), 66–95  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Maslov V.P., Maslova T.V., “Synergetics and architecture”, Russ. J. Math. Phys., 15:1 (2008), 102–121  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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