How Incomputable Is Kolmogorov Complexity?

Paul M.B. Vitányi
2020 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.
doi:10.3390/e22040408 pmid:33286182 fatcat:imcanhdpnval5i5dj5wejyrj2m