1)

In the general halting problem, we ask for an algorithm that gives the correct answer for any M and w. We

can relax this generality, for example, by looking for an algorithm that works for all M but only a single w.

We say that such a problem is decidable if for every wthere exists a (possibly different) algorithm that

determines whether or not (M, w) halts. Show that even in this restricted setting the problem is undecidable.

2)

Consider the question: "Does a Turing machine in the course of a computation revisit the starting cell (i.e.,

the cell under the read-write head at the beginning of the computation)?" Is this a decidable question?

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