I am interested in computation and I am lost on undecidability and reductions. I have the following two problems I am stuck on.
Let us call 2 Turing machines related if there is an input $w$ on which both halt (after finitely many steps). Let $h(M )$ be the set of inputs on which the TM $M$ halts.
Show that the problem $\text{RELATED} = \{\langle M1, M2\rangle \mid h(M1) \cap h(M2) \neq \emptyset\}$ is Turing recognizable.
Assume, you know that the halting problem $H$ is undecidable. Show that the problem $\text{RELATED}$ is undecidable. Show this result by defining an appropriate mapping reduction $g$.