Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity

  • Authors:
  • V. V. V'Yugin;V. P. Maslov

  • Affiliations:
  • Institute for Information Transmission Problems, RAS, Moscow vld@vyugin.mccme.ru;M.V. Lomonosov Moscow State University viktor_maslov@hotmail.com

  • Venue:
  • Problems of Information Transmission
  • Year:
  • 2003

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Abstract

Conditions are presented under which the maximum of the Kolmogorov complexity (algorithmic entropy) K(ω1…ωN) is attained, given the cost \sum_{i=1}^{N} f(ωi) of a message ω1…ωN. 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}^{N} f(ωi) − &thetas;K(ω1…ωN) is studied. Here, &thetas; is a parameter, called the temperature by analogy with thermodynamics. We also study domains of small variation of this function.