While researching this topic of approximating K complexity with the concept
of similarity you run into such things as the Normalized Information
Distance (NID), compression distance, Normalized Compression Distance (NCD),
Normalized Conditional Compression Distance (NCCD), etc. as well as various
methods people try in in approximating along with various redefinition
attempts and extensions with stuff like the "Complexity Approximation
Principle" (CAP). all kinds of neat stuff.

 

I did run into this interesting paper for those interested worth reading
that gives some empirical confidence on my intuitions of this subject:

http://arxiv.org/pdf/1306.0322.pdf

 

John




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