kolmogorov complexity

yonatan vainer 07 Aug 2017 11:33

We claimed that for every string x:

(1)\begin{align} K_{U}(x)\leq K_{M}(x) + c_{M} \end{align}

But in lecture 10 slide 15 we want to prove that

(2)\begin{align} K(x)\leq |x| + c \end{align}

So we use TM M that computes the identity, but suddenly the constant c loses the dependency in the TM M. Can you please explain why it is valid and is the constant c really not dependent in any TM?