  The zero-error capacity of a discrete classical channel was first defined by
Shannon as the least upper bound of rates for which one transmits information
with zero probability of error. The problem of finding the zero-error capacity
$C_0$, which assigns a capacity to each channel as a function, was reformulated
in terms of graph theory as a function $\Theta$, which assigns a value to each
simple graph. This paper studies the computability of the zero-error capacity.
For the computability, the concept of a Turing machine and a Kolmogorov oracle
is used. It is unknown if the zero-error capacity is computable in general. We
show that in general the zero-error capacity is semi computable with the help
of a Kolmogorov Oracle. Furthermore, we show that $C_0$ and $\Theta$ are
computable functions if and only if there is a computable sequence of
computable functions of upper bounds, i.e. the converse exist in the sense of
information theory, which pointwise converge to $C_0$ or $\Theta$. Finally, we
examine Zuiddam's characterization of $C_0$ and $\Theta$ in terms of
algorithmic computability.
