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.
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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