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The Online Algorithmic Complexity Calculator


The Online Algorithmic Complexity Calculator (OACC) is an online tool developed by the Algorithmic Nature Group to provide reliable estimations to functions of complexity that are ultimately semi-computable but represent true and universal measures of randomness (unlike statistical or entropic approaches). This is done through various numerical methods based upon the mathematical theory of algorithmic probability and algorithmic randomness. The estimations have a wide range of applications in a very wide range of disciplines, they have been used in molecular biology and bioinformatics, psychometrics, economics and graph theory (see Publications).

The OACC retrieves numerical approximations (upper bounds) of Algorithmic (Kolmogorov) Complexity (AC) for short strings (CTM), any length (BDM 1D), and binary matrices (BDM 2D). The techniques are not only an alternative to the widespread use of lossless compression algorithms to approximate AC, but true approaches to AC unlike lossless compression algorithms (e.g. BZIP2, LZ) that are based upon Entropy rate and are thus not more related to AC than Shannon Entropy itself (which is unable to compress anything but statistical regularities).


The following is an example for block size = 6 and block overlap = 1 :

Optimal parameters are usually largest possible block size (= 12) and no overlaping (= 0).

In the BDM formula, $|block|$ denotes the number of occurrences (multiplicity) of the block.



This video provides a short non-expert overview of how CTM and BDM work:


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