Unravelling Complexity: The Life and Work of Gregory Chaitin by Shyam Wuppuluri & Francisco Antonio Doria

Author:Shyam Wuppuluri & Francisco Antonio Doria
Language: eng
Format: epub
Publisher: World Scientific Publishing Co. Pte. Ltd.
Published: 2020-07-16T16:00:00+00:00

In Fig. 3, I showed how the ideas of Chaitin (and Kolmogorov and Solomonoff) can help understand the complexity of ECA by looking at how difficult it is to describe them succinctly from their generating model. The simplified rule shown in Fig. 3 is an upper bound on their Kolmogorov–Chaitin complexity. Such simple estimations already provide a much better characterization than other simplifications, such as that of the so-called Langton’s λ parameter, as they correspond better to the literature on the complexity of ECA. And even better estimations and tighter bounds can be found using more powerful approaches based on Chaitin’s (and Levin’s) work, notably with the help of two methods that I and my team put together called CTM and BDM (as shown in Fig. 3), rooted in a beautiful concept called algorithmic probability, which is deeply related to Chaitin’s own Ω number.

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