Decidability (6 + 6 + 6 + 6 credits) For each of the following problems, state whether it is decidable. If it is decidable, outline a decision procedure for it. If not, prove that it is undecidable. In each case, the input is the code (M) of a Turing machine M = (0,2,1, 8,90, B, F).
(a) Is there an input x € * of length < 10 such that M halts in < 100 steps when run on x?
(b) Is there an input 2 € * of length > 10 such that M halts in <100 steps when run on x?
(c) Is there an input x € * of length < 10 such that M runs for > 100 on input x?
(d) Is there an input x * of length > 10 such that M halts in > 100 steps when run on z?
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