We will show a reduction from Halt: f:<M,w> —> <M',0>

M' for input x:

1. run M on w for |x| steps

2. if M halts on w in |x| steps - loop, otherwise - halt.

If M does not halt on w, then for any x M will not halt on w in |x| steps and so M' will always halt and so M',0 is not in D(halt)

If M halts on w, then for "very long" x's M will halt on w after running for |x| steps and then M' will loop on that x, and so there is a y, such that if we concatenate it and get <M',0y>, M' will not halt on 0y and so <M',0> is in D(Halt).

which of the following is true:

1. D(halt) is in R.E

2. D(halt) is in coR.E

3. Halt (intersection with) D(halt) is in coR.E

4. Halt <=m (mapping reduction) D(halt)

reminder: halt- is the Htm problem we saw at class

Please help.

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