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How Incomputable Is Kolmogorov Complexity?

The National Research Center for Mathematics and Computer Science in the Netherlands (CWI), 1098XG Amsterdam, The Netherlands
Department of Computer Science, University of Amsterdam, 1012 WX Amsterdam, The Netherlands
Entropy 2020, 22(4), 408;
Received: 19 February 2020 / Revised: 4 March 2020 / Accepted: 29 March 2020 / Published: 3 April 2020
(This article belongs to the Special Issue Review Papers for Entropy)
Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the incomputability of Kolmogorov complexity, which formal loopholes this leaves us with, recent approaches to compute or approximate Kolmogorov complexity, which approaches are problematic, and which approaches are viable. View Full-Text
Keywords: Kolmogorov complexity; incomputability; feasibility Kolmogorov complexity; incomputability; feasibility
MDPI and ACS Style

Vitányi, P.M. How Incomputable Is Kolmogorov Complexity? Entropy 2020, 22, 408.

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