Effective Complexity and Its Relation to Logical Depth

@article{Ay2010EffectiveCA,
  title={Effective Complexity and Its Relation to Logical Depth},
  author={Nihat Ay and Markus M{\"u}ller and Arleta Szkola},
  journal={IEEE Transactions on Information Theory},
  year={2010},
  volume={56},
  pages={4593-4607}
}
Effective complexity measures the information content of the regularities of an object. It has been introduced by Gell-Mann and Lloyd to avoid some of the disadvantages of Kolmogorov complexity. In this paper, we derive a precise definition of effective complexity in terms of algorithmic information theory. We analyze rigorously its basic properties such as effective simplicity of incompressible binary strings and existence of strings that have effective complexity close to their lengths. Since… 
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This work investigates the effective complexity of binary strings generated by stationary, in general not computable, processes and shows that under not too strong conditions long typical process realizations are effectively simple.
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