Darboux’s lemma once more

Once more unto the breach, dear friends, once more.

The first issue of the World Journal of Critical Care Medicine (WJCCM), whose preparatory work was initiated on December 16, 2010, will be published on February 4, 2012. The WJCCM Editorial Board has now been established and consists of 105 distinguished experts from 27 countries. Our purpose of launching the WJCCM is to publish peer-reviewed, high-quality articles via an open-access online pub...

Divided Once More

Once More With Feeling

Limit complexities revisited [once more]

The main goal of this article is to put some known results in a common perspective and to simplify their proofs. We start with a simple proof of a result of Vereshchagin [13] saying that limsupnC(x|n) (here C(x|n) is conditional (plain) Kolmogorov complexity of x when n is known) equals C0 ′ (x), the plain Kolmogorov complexity with 0′-oracle. Then we use the same argument to prove similar resu...

Derandomizing the Lovasz Local Lemma more effectively

The famous Lovasz Local Lemma [EL75] is a powerful tool to non-constructively prove the existence of combinatorial objects meeting a prescribed collection of criteria. Kratochvil et al. applied this technique to prove that a k-CNF in which each variable appears at most 2^k/(ek) times is always satisfiable [KST93]. In a breakthrough paper, Beck found that if we lower the occurrences to O(2^(k/48...