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Dynamics and Complexity of Computrons
Open AccessFeature PaperReview

A Review of Methods for Estimating Algorithmic Complexity: Options, Challenges, and New Directions

by Hector Zenil 1,2,3
1
Algorithmic Dynamics Lab, Karolinska Institute, 171 77 Stockholm, Sweden
2
Oxford Immune Algorithmics, Reading RG1 3EU, UK
3
Algorithmic Nature Group, LABORES, 75006 Paris, France
This review is based on an invited talk for MORCOM (Morphological, Natural, Analog and Other Unconventional Forms of Computing for Cognition and Intelligence) Delivered at the International Society for Information Studies (IS4IS) Summit at the University of California, Berkeley, CA, USA, 2–6 June 2019.
Entropy 2020, 22(6), 612; https://doi.org/10.3390/e22060612
Received: 30 April 2020 / Revised: 17 May 2020 / Accepted: 23 May 2020 / Published: 30 May 2020
(This article belongs to the Special Issue Shannon Information and Kolmogorov Complexity)
Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression to newer approaches that advance, complement and also pose new challenges and may exhibit their own limitations. Evidence suggesting that these different methods complement each other for different regimes is presented and despite their many challenges, some of these methods can be better motivated by and better grounded in the principles of algorithmic information theory. It will be explained how different approaches to algorithmic complexity can explore the relaxation of different necessary and sufficient conditions in their pursuit of numerical applicability, with some of these approaches entailing greater risks than others in exchange for greater relevance. We conclude with a discussion of possible directions that may or should be taken into consideration to advance the field and encourage methodological innovation, but more importantly, to contribute to scientific discovery. This paper also serves as a rebuttal of claims made in a previously published minireview by another author, and offers an alternative account. View Full-Text
Keywords: algorithmic complexity; Kolmogorov complexity; practical feasibility; Lempel–Ziv–Welch (LZW); Shannon entropy; lossless compression; coding theorem method; causality v correlation; block decomposition method; rebuttal to Paul Vitányi’s review algorithmic complexity; Kolmogorov complexity; practical feasibility; Lempel–Ziv–Welch (LZW); Shannon entropy; lossless compression; coding theorem method; causality v correlation; block decomposition method; rebuttal to Paul Vitányi’s review
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Zenil, H. A Review of Methods for Estimating Algorithmic Complexity: Options, Challenges, and New Directions. Entropy 2020, 22, 612.

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