  The article introduces some ideas for solving special cases of the following
problem, proposed in a somewhat generalized form by Marcus Hutter in 2000.
Given two Turing machines $A$ and $C$, it is required to build a Turing machine
$B$, such that after interacting of $A$ and $B$ on a shared tape for a fixed
number of iterations, the machine $C$ outputs 1 on the communication protocol
of $A$ and $B$. Details in the introduction.
