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).
Problems of Information Transmission – Springer Journals
Published: Oct 4, 2004
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
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
All the latest content is available, no embargo periods.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud