### Algorithmic Complexity for Short Strings

Use space to separate strings.

The length of each string must be shorter than 13 characters.

### Result of Evaluation

$$\textit{BDM} = \sum_{i=1}^{n} \textit{K}(\textit{block}_{i}) +\textit{log}_{2}(|\textit{block}_{i}|)$$

Strings that don't appear in the $$D(\#\textit{of states}, \#\textit{ of symbols})$$ distribution have their $$\textit{K}$$ value estimated as

$$\textit{Max}(K(\#\textit{ of states}, \#\textit{ of symbols})) + 1$$

### Result of Evaluation

$$BDM = \sum_{i=1}^{n} K(block_{i})+log_{2}(|block_{i}|)$$

### Result of Evaluation

$$K(\#\textit{ of states}, \#\textit{ of symbols}) = -log_{2}(D(\#\textit{of states}, \textit{# of symbols})$$

$$\textit{}~$$$$K(\#\textit{ of states}, \#\textit{ of symbols})$$ indicates the estimated Kolmogorov complexity of the string by the Coding Theorem Method.

$$D(\#\textit{of states}, \#\textit{ of symbols})$$ indicates the estimated algorithmic probability, which is the output frequency of the string by Turing machines with the same alphabet.

Strings that don't appear in the $$D(\#\textit{of states}, \#\textit{ of symbols})$$ distribution have their $$\textit{K}$$ value estimated as

$$\textit{Max}(K(\#\textit{ of states}, \#\textit{ of symbols})) + 1$$

More information on the other complexity functions is available in the documentation of the ACSS package @ CRAN.