Revisit the proof of. Is the reduction of LSA to LA there a map reduction? If not, does there exist such a map reduction? Show that there is no algorithm to determine whether or not a given TM...

Revisit the proof of. Is the reduction of
LSA to
LA there a map reduction? If not, does there exist such a map reduction?

Show that there is no algorithm to determine whether or not a given TM eventually halts with an empty tape given any input.

Is the problem of determining whether or not an arbitrary TM revisits its initial square (the cell with b_ which is followed by the input) solvable?

Using reduction, prove that
L∅ = {ψ(M) :
L(M) = ∅} is not computably enumerable. Also, prove that
Lnot
∅ = {ψ(M) :
L(M) _ ∅} is computably enumerable.