Abstract
Conditions are presented under which the maximum of the Kolmogorov complexity (algorithmic entropy) K(ω1...ω N ) is attained, given the cost \(\sum\limits_{i = 1}^N {} \) f(ω i ) of a message ω1...ω N . Various extremal relations between the message cost and the Kolmogorov complexity are also considered; in particular, the minimization problem for the function \(\sum\limits_{i = 1}^N {} \) f(ω i ) − θK(ω1...ω N ) is studied. Here, θ is a parameter, called the temperature by analogy with thermodynamics. We also study domains of small variation of this function.
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V'yugin, V.V., Maslov, V.P. Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity. Problems of Information Transmission 39, 380–394 (2003). https://doi.org/10.1023/B:PRIT.0000011276.88154.91
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DOI: https://doi.org/10.1023/B:PRIT.0000011276.88154.91