It would be really nice if I could provably construct a third program, , which in some sense “combines the internal structure” of the two programs and , while still achieving approximately the same compression.
I don’t think that would fit the definition, since it would be over 2x as complex as either of the original programs. It doesn’t seem like it would solve the spirit of the problem either.
I’m not talking about the spirit of the problem, I’m talking about the actual program corresponding to the derivation in this article. I’m not super familiar with the field though, so I could be wrong.
The math you’re doing here implies that if 0 ≈ K(A) then 0 ≈ K(A) + K(A) = 2K(A), so constant multipliers seem to be allowed in your approximations.
I don’t think that would fit the definition, since it would be over 2x as complex as either of the original programs. It doesn’t seem like it would solve the spirit of the problem either.
I’m not talking about the spirit of the problem, I’m talking about the actual program corresponding to the derivation in this article. I’m not super familiar with the field though, so I could be wrong.
The math you’re doing here implies that if 0 ≈ K(A) then 0 ≈ K(A) + K(A) = 2K(A), so constant multipliers seem to be allowed in your approximations.