For each of the following decision problems, either sketch an algorithm or prove that the problem is undecidable. Recall that w denote the reversal of string w. For each problem, the input is an encoding (M, w) of a Turing machine M and its input string w. (a) Does M either accept w or reject wk? (b) If we run M on input w, does M ever change a symbol on its tape? (c) If we run M on input w, does M ever leave its start state? (d) If we run M on input w, does M ever reenter its start state?

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