# Systems of Strings with High Mutual Complexity

Systems of Strings with High Mutual Complexity Consider a binary string x 0 of Kolmogorov complexity K(x 0) ≥ n. The question is whether there exist two strings x 1 and x 2 such that the approximate equalities K(x i ∣ x j ) ≈ n and K(x i ∣ x j , x k ) ≈ n hold for all 0 ≤ i, j, k ≤ 2, i ≠ j ≠ k, i ≠ k. We prove that the answer is positive if we require the equalities to hold up to an additive term O(log K(x 0)). It becomes negative in the case of better accuracy, namely, O(log n). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# Systems of Strings with High Mutual Complexity

, Volume 39 (4) – Oct 4, 2004
5 pages

/lp/springer_journal/systems-of-strings-with-high-mutual-complexity-QHhAo0hsoi
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.0000011277.12262.f0
Publisher site
See Article on Publisher Site

### Abstract

Consider a binary string x 0 of Kolmogorov complexity K(x 0) ≥ n. The question is whether there exist two strings x 1 and x 2 such that the approximate equalities K(x i ∣ x j ) ≈ n and K(x i ∣ x j , x k ) ≈ n hold for all 0 ≤ i, j, k ≤ 2, i ≠ j ≠ k, i ≠ k. We prove that the answer is positive if we require the equalities to hold up to an additive term O(log K(x 0)). It becomes negative in the case of better accuracy, namely, O(log n).

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 4, 2004

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