Kolmogorov complexity with weak description languages
Let's assume there exists some "decidable" complexity $D(s)$ differs from Kolmogorov complexity $K(s)$ by shift, by factor or, more generally, by any decidable monotonic unbounded numerical function $f(n)$ such that $K(s) &gt; f(D(s))$.

As $D(s)$ is decidable, it is possible to choose (effectively) a sequence of strings $s_n$ such  that $f(D(s_n))&gt; \mathrm{vff}(n)$ where $\mathrm{vff}$ is some "very very fast growing function" such as $\exp(\exp(\exp(n)))$. 

Suppose that we have $K(s_n) &gt; \mathrm{vff}(n)$, i.e. Kolmogorov complexity of string $s(n)$ grows fast with $n$. But index $n$ also identifies the string $s(n)$ and, therefore, may be treated as upper bound of $K(s_n)$ (with some const shift). Any number $n$ needs only $\log(n)$ bits to represent it, and this contradicts with fast growing of complexity of $K(s_n)$. 

Thus for any decidable monotonic unbounded numerical function $f$, there exists strings $s$ such that $K(s) \not&gt; f(D(s))$.