Is there a good known algorithm which performs general purpose compression where the target is a given turing complete instruction set? Rather than relying on a fixed general purpose decoder and the associated compressed data.

I’m asking here instead of asking an LLM because that’s what humans used to do and it was pleasant.

A perfect implementation would be a Kolmogorov oracle. https://en.wikipedia.org/wiki/Kolmogorov_complexity#Halting_... suggests this is equivalent to a halting oracle. So, it depends what you mean by "good".

that sounds pretty related to Kolgomorov complexity, which is uncomputable in general. https://en.wikipedia.org/wiki/Kolmogorov_complexity

I too would be interested in approximations or heuristics if anyone has any