Turing machine interaction problem

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.