What is the maximum theoretically possible compression rate?

Question

This is a theoretical question, so expect that many details here are not computable in practice or even in theory.

Let\'s say I have a string s that I w

Answer 1

This is Kolmogorov complexity, and you are correct that it's not computable. If it were, you could create a paradoxical program of length n that printed a string with Kolmogorov complexity m > n.

Clearly, you can bound b_min_s for given inputs. However, as far as I know most of the efforts to do so have been existence proofs. For instance, there is an ongoing competition to compress English Wikipedia.