# Nonreducible Descriptions for the Conditional Kolmogorov Complexity

Nonreducible Descriptions for the Conditional Kolmogorov Complexity Assume that a program p produces an output string b for an input string a: p(a) = b. We look for a “reduction” (simplification) of p, i.e., a program q such that q(a) = b but q has Kolmogorov complexity smaller than p and contains no additional information as compared to p (this means that the conditional complexity K(q|p) is negligible). We show that, for any two strings a and b (except for some degenerate cases), one can find a nonreducible program p of any arbitrarily large complexity (any value larger than K(a) + K(b|a) is possible). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# Nonreducible Descriptions for the Conditional Kolmogorov Complexity

, Volume 41 (3) – Oct 17, 2005
6 pages

/lp/springer_journal/nonreducible-descriptions-for-the-conditional-kolmogorov-complexity-4jHNUFt97y
Publisher
Springer Journals
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1007/s11122-005-0028-0
Publisher site
See Article on Publisher Site

### Abstract

Assume that a program p produces an output string b for an input string a: p(a) = b. We look for a “reduction” (simplification) of p, i.e., a program q such that q(a) = b but q has Kolmogorov complexity smaller than p and contains no additional information as compared to p (this means that the conditional complexity K(q|p) is negligible). We show that, for any two strings a and b (except for some degenerate cases), one can find a nonreducible program p of any arbitrarily large complexity (any value larger than K(a) + K(b|a) is possible).

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 17, 2005

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