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

Loading next page...
 
/lp/springer_journal/systems-of-strings-with-high-mutual-complexity-QHhAo0hsoi
Publisher
Springer Journals
Copyright
Copyright © 2003 by MAIK “Nauka/Interperiodica”
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

There are no references for this article.

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
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

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.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off