A Review of Methods for Estimating Algorithmic Complexity: Options, Challenges, and New Directions
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Established and novel techniques in the field of applications of algorithmic (Kolmogorov) complexity are reviewed, ranging from dominant ones such as statistical lossless compression to newer approaches that advance and complement those other approaches while also posing new challenges and exhibiting 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 mini-review by another author, and offers an alternative account.
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