Effective Complexity of Stationary Process Realizations

Entropy

Nihat Ay¹  Markus Müller¹ 

[1] Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, Leipzig 04103, Germany; E-Mail:

关键词: effective complexity;    Kolmogorov complexity;    Shannon entropy;    computable stationary processes;    coarse effective complexity;   

DOI  :  10.3390/e13061200

来源: mdpi

【 摘 要 】

The concept of effective complexity of an object as the minimal description length of its regularities has been initiated by Gell-Mann and Lloyd. The regularities are modeled by means of ensembles, which is the probability distributions on finite binary strings. In our previous paper [1] we propose a definition of effective complexity in precise terms of algorithmic information theory. Here we investigate the effective complexity of binary strings generated by stationary, in general not computable, processes. We show that under not too strong conditions long typical process realizations are effectively simple. Our results become most transparent in the context of coarse effective complexity which is a modification of the original notion of effective complexity that needs less parameters in its definition. A similar modification of the related concept of sophistication has been suggested by Antunes and Fortnow.

【 授权许可】

CC BY   
© 2011 by the authors; licensee MDPI, Basel, Switzerland.