# Effective Complexity of Stationary Process Realizations

@article{Ay2010EffectiveCO, title={Effective Complexity of Stationary Process Realizations}, author={Nihat Ay and Markus M{\"u}ller and Arleta Szkola}, journal={Entropy}, year={2010}, volume={13}, pages={1200-1211} }

Abstract: The concept of effective complexity of an object as the minimal descriptionlength of its regularities has been initiated by Gell-Mann and Lloyd. The regularities aremodeled by means of ensembles, which is the probability distributions on ﬁnite binarystrings. In our previous paper [1] we propose a deﬁnition of effective complexity in preciseterms of algorithmic information theory. Here we investigate the effective complexity ofbinary strings generated by stationary, in general not…

## 5 Citations

### Effective Complexity and Its Relation to Logical Depth

- Computer ScienceIEEE Transactions on Information Theory
- 2010

A remarkable relation between effective complexity and Bennett's logical depth is shown: If the effective complexity of a string x exceeds a certain explicit threshold then that string must have astronomically large depth; otherwise, the depth can be arbitrarily small.

### Fields of Application of Information Geometry

- Computer Science
- 2017

1.
Complexity measures can be geometrically built by using the information distance (Kullback–Leibler divergence) from families with restricted statistical dependencies. The Pythagorean geometry…

### A geometric approach to complexity.

- Computer ScienceChaos
- 2011

A geometric approach to complexity based on the principle that complexity requires interactions at different scales of description is developed, which presents a theory of complexity measures for finite random fields using the geometric framework of hierarchies of exponential families.

### Abstraction in Artificial Intelligence and Complex Systems

- Computer ScienceSpringer New York
- 2013

A formal model, the KRAmodel, is presented to capture the characterizing properties of abstraction, and its pragmatic power is illustrated with three case studies: Model-based diagnosis, Cartographic Generalization, and learning Hierarchical Hidden Markov Models.

### Some comments on computational mechanics, complexity measures, and all that

- Computer Science
- 2017

It is shown that there exist simple models where none of the nodes of the "$\epsilon$-machine" (the "causal states") corresponds to an element of a state (or history) space partition, and a simple and precise way of estimating excess entropy is presented.

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