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The Online Algorithmic Complexity Calculator

Full Code for the Online Algorithmic Complexity Calculator

Source files for the R Shiny web server are available at Github.

After installing Git, all files can be downloaded from a terminal calling:

git clone https://github.com/algorithmicnaturelab/OACC.git

With RStudio and Shiny installed, the OACC can be run locally by calling runApp() on the server.r or ui.r source files.

Algorithmic Complexity for Short Strings (ACSS) R Package

The acss package can be installed from the Comprehensive R Archive Network (CRAN) via:

install.packages("acss")

require(acss)

It will work right out of the box, without any software other than R.

Usage

acss_data is a data frame with 4590267 values for the following 5 columns:

K.2 acss with 2 symbols
K.4 acss with 4 symbols
K.5 acss with 5 symbols
K.6 acss with 6 symbols
K.9 acss with 9 symbols

Each representing a set of strings with CTM values K.x estimated by algorithmic probability D.x. in the alphabet of size x.

Calling

acss(string = "ATATATATATAT", alphabet = 2)

will output the CTM value (K) and the algorithmic probability (D) for the string considering only 2 possible symbols in the algorithmic probability distribution.

 K.2 D.2 ATATATATATAT 26.99073 7.498626e-09

While calling

acss(string = "ATATATATATAT", alphabet = 4)

will output the CTM value (K) and the algorithmic probability (D) for the string
considering 4 possible symbols in the algorithmic probability distribution.

 K.4 D.4 ATATATATATAT 27.81547 4.233589e-09

$K.x$ is always equal to $-\log_{2}(D.x)$

Running example(acss) will give plenty of usage examples.

Full documentation is available at the Comprehensive R Archive Network (CRAN).

For technical details on the Coding Theorem Method, please visit How It Works.

Universal Distribution Approximations

You can download the known algorithmic probability datasets from the Algorithmic Nature Dataverse Repository or you can click on the Download icon below directly.

 $D(4,2)$ dataset in CSV format $D(5,2)$ dataset in CSV format $D(4,2)_{2D}$ dataset in CSV format see R package $D(5,2)_{2D}$ dataset in CSV format see R package $D(4,4)$ dataset in CSV format see R package $D(4,6)$ dataset in CSV format see R package $D(4,9)$ dataset in CSV format see R package $D(4,10)$ dataset in CSV format see R package

Mining and Exploitation Tools

 Mathematica API notebook