If $U$ is a universal prefix Turing machine, $U(p)=x$ for some program $p$ and string $x$, is it true that $K(x)=K(p)+O(1)$, with $K$ being the prefix Kolmogorov complexity?
Does the Kolmogorov complexity of a program $p$ generating a string $x$ equal the complexity of $x$ up to constant?
turing machines;kolmogorov complexity