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The Online Algorithmic Complexity Calculator

version 0.3 (Beta)

New version coming soon (2016)

covering non-binary strings and multidimensional arrays

Enter a (short) binary string:

If you make use of results from this calculator make sure to properly cite our papers (see bottom of this page),

the URL and the version you used (which will always be compatible with newer versions)

You have introduced the string 1111.
\[m(1111) = 3533212367/862157986084 \simeq 0.00409810315978\]\[K_m(1111) = -\log_2(3533212367/862157986084) \simeq 7.93082798352\]


The Online Algorithmic Complexity Calculator (OACC) is an on-going long-term project of the Algorithmic Nature Group to develop an online tool implementing semi-computable measures of complexity through various numerical methods and algorithms for potential applications in a very wide range of disciplines, from bioinformatics to psychometrics, from linguistics to economics.

It currently retrieves numerical approximations (upper bounds) of Kolmogorov Complexity for binary strings of short length by means of algorithmic probability (notably by using the Algorithmic Coding Theorem relating frequency and complexity), for string length which lossless compression algorithms fail to deal with, hence providing an alternative/complementary method to compression algorithms (in the future the calculator will smoothly make the transition between the algorithmic probability and the lossless compression methods using a technique that the group has developed called the Block Decomposition Method.

More algorithmic information measures, more data and more techniques will be incorporated gradually in the future, covering a wider range of objects such as longer binary strings, non-binary strings and n-dimensional objects (such as images). Data and tools such as an R package and a Mathematica notebook are also available.



Click here to access another tool: the Short String Complexity Explorer.
(it requires the free plug-in Wolfram CDF Player)

The Short String Complexity Explorer tool provides a comparison of the estimated Kolmogorov complexity (K), the Algorithmic Probability (m), Shannon's Entropy (E) and Compressibility (using Deflate) of a string. It also provides an indication of the relative complexity among all other strings for which K has been approximated and its distribution rank.


The OACC is brought to you by the


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Contact info: hectorz at LABORES dot EU
Cite as follows:
Soler-Toscano F, Zenil H, Delahaye J-P, Gauvrit N (2014) Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines. PLoS ONE 9(5): e96223. doi:10.1371/journal.pone.0096223
Algorithmic Nature Group - LABORES