We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: rand...
Hartmanis used Kolmogorov complexity to provide an alternate proof of the classical result of Baker, Gill, and Solovay that there is an oracle relative to which P is not NP. We re...
We show the existence of various versions of expander graphs using Kolmogorov complexity. This method seems superior to the usual “probabilistic construction”. Also, the best k...
Abstract-- Biological sequences from different species are called orthologs if they evolved from a sequence of a common ancestor species and they have the same biological function....
We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypothesis testing in a framework of classical mathe...
Epilepsy is the most common neurological disorder in the world, second only to stroke. There are nearly 15 million patients suffer from refractory epilepsy, with no available ther...
In 1928, George D. Birkhoff introduced the Aesthetic Measure, defined as the ratio between order and complexity, and, in 1965, Max Bense analyzed Birkhoff's measure from an i...
Abstract. In this paper, we survey a few recent applications of Kolmogorov complexity to lower bounds in several models of computation. We consider KI complexity of Boolean functio...
Abstract. Beth and Dai studied in their Eurocrypt paper [1] the relationship between linear complexity (that is, the length of the shortest Linear Feedback Shift Register that gene...