What is the ultimate compression of enwik8?
By definition, the Kolmogorov complexity K of a string x is defined as the length of the shortest program (self-extracting archive) computing x. K(x) itself cannot be computed, only approximated from above, namely by finding better and better compressions, but even if we reach K(x) will never know whether we have done so. For a text string like enwik8, Shannon’s estimate suggests that enwik8 should be compressible down to 12MB.
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