# 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

### 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.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 4, 2004

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### DeepDyve Freelancer ### DeepDyve Pro Price FREE$49/month

\$360/year
Save searches from