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Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines

Figure 1

A flow chart illustrating the Coding Theorem Method, a never-ending algorithm for evaluating the (Kolmogorov) complexity of a (short) string making use of several concepts and results from theoretical computer science, in particular the halting probability, the Busy Beaver problem, Levin's semi-measure and the Coding theorem.

The Busy Beaver values can be used up to 4 states for which they are known, for more than 4 states an informed maximum runtime is used as described in this paper, informed by theoretical [3] and experimental (Busy Beaver values) results. Notice that are the probability values calculated dynamically by running an increasing number of Turing machines. is intended to be an approximation to out of which we build after application of the Coding theorem.

Figure 1

doi: https://doi.org/10.1371/journal.pone.0096223.g001