Turing machine interaction problem

TL;DR

This paper explores the problem of designing a Turing machine that interacts with another to produce a specific output after a fixed number of steps, addressing a generalized problem posed by Marcus Hutter.

Contribution

It proposes ideas for solving special cases of the Turing machine interaction problem, extending the understanding of machine interactions in computational theory.

Findings

Identifies conditions under which a Turing machine B can be constructed.

Provides partial solutions for specific interaction scenarios.

Advances the theoretical framework for machine interaction problems.

Abstract

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.