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

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
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
Related articles on Google Scholar: Russian articles, English articles

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
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
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
4. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122
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
6. Maslov V.P., Maslova T.V., “Synergetics and architecture”, Russ. J. Math. Phys., 15:1 (2008), 102–121
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