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MiS Preprint

Effective complexity of stationary process realizations

Nihat Ay, Markus Mueller and Arleta Szkola


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, that is 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 uses less parameters in its definition. A similar modification of the related concept of sophistication has been suggested by Antunes and Fortnow.

MSC Codes:
60, 94
Effective complexity, Kolmogorov complexity, stochastic processes

Related publications

2011 Journal Open Access
Nihat Ay, Markus Müller and Arleta Szkoła

Effective complexity of stationary process realizations

In: Entropy, 13 (2011) 6, pp. 1200-1211