acss_data: acss_data: algorithmic complexity of short strings

Description Usage Format Author(s) Source References


Contains the algorithmic complexity for short string, an approximation of the Kolmogorov Complexity of a short string using the coding theorem method. For a given set of symbols in a string, all possible or a large number of random samples of Turing machines (TM) with a given number of states and number of symbols corresponding to the number of symbols in the strings were simulated until they reached a halting state or failed to end. The complexity of the string corresponds to the distribution of the halting states of the TMs.

See for more information or references below.

This dataset shouldn't be called directly but rather through the accessor functions in package acss.




A data frame with 4590267 observations on the following 5 variables.


acss with 2 symbols, computed on all possible Turing machines (TM) with 5 states and 2 symbols.


acss with 4 symbols, computed on a large number of TMs with 4 states and 4 symbols.


acss with 5 symbols, computed on a large number of TMs with 4 states and 5 symbols.


acss with 6 symbols, computed on a large number of TMs with 4 states and 6 symbols.


acss with 9 symbols, computed on a large number of TMs with 4 states and 9 symbols.


Fernando Soler Toscano, Nicolas Gauvrit, and Hector Zenil.
Ported to R by Henrik Singmann.



Delahaye, J.-P., & Zenil, H. (2012). Numerical evaluation of algorithmic complexity for short strings: A glance into the innermost structure of randomness. Applied Mathematics and Computation, 219(1), 63-77. doi:10.1016/j.amc.2011.10.006

Gauvrit, N., Zenil, H., Delahaye, J.-P., & Soler-Toscano, F. (2014). Algorithmic complexity for short binary strings applied to psychology: a primer. Behavior Research Methods. doi:10.3758/s13428-013-0416-0

Soler-Toscano, F., Zenil, H., Delahaye, J.-P., & Gauvrit, N. (2012). Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines. arXiv:1211.1302 [].

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