# Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity

Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity

, Volume 39 (4) – Oct 4, 2004
15 pages

Publisher
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/B:PRIT.0000011276.88154.91
Publisher site
See Article on Publisher Site

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