Statistic Complexity: Combining Kolmogorov Complexity with an Ensemble Approach

Statistic Complexity: Combining Kolmogorov Complexity with an Ensemble Approach

BACKGROUND The evaluation of the complexity of an observed object is an old but outstanding problem. In this paper we are tying on this problem introducing a measure called statistic complexity. METHODOLOGY/PRINCIPAL FINDINGS This complexity measure is different to all other measures in the following senses. First, it is a bivariate measure that compares two objects, corresponding to pattern ...

Kolmogorov Complexity with Error

We introduce the study of Kolmogorov complexity with error. For a metric d, we define Ca(x) to be the length of a shortest program p which prints a string y such that d(x, y) ≤ a. We also study a conditional version of this measure Ca,b(x|y) where the task is, given a string y′ such that d(y, y′) ≤ b, print a string x′ such that d(x, x′) ≤ a. This definition admits both a uniform measure, where...

A Kolmogorov Complexity Approach for Measuring Attack Path Complexity

The difficulty associated with breaching an enterprise network is commensurate with the security of that network. A security breach, or a security policy violation, occurs as a result of an attacker successfully executing some attack path. The difficulty associated with this attack path, then, is critical to understanding how secure a given network is. Currently, however, there are no consisten...

Kolmogorov Complexity Computational Complexity Course Report

Randomized Communication Complexity of Approximating Kolmogorov Complexity

The paper [Harry Buhrman, Michal Koucký, Nikolay Vereshchagin. Randomized Individual Communication Complexity. IEEE Conference on Computational Complexity 2008: 321-331] considered communication complexity of the following problem. Alice has a binary string x and Bob a binary string y, both of length n, and they want to compute or approximate Kolmogorov complexity C(x|y) of x conditional to y. ...