Problem in solution of ex. 4

Problem in solution of ex. 4

Guest (guest) 17 Jul 2014 06:45

in the solution of exercise 4 question 1b you say:
Halt^* <=_m ALL_TM ( f(<M>)=<M₀> where M₀ on input y simulates M on input y moving q_r when M moves to q_a.

shouldn't q_r and q_a be replaced?

because in this form:
M halts on all inputs »> M₀ does not accept anything
M does not halt on all inputs »> M₀ don't halts on all inputs and if it halts it rejects.

and in the replaced form:
M halts on all inputs »> M₀ accepts anything ( its language is sigma star)
M does not halt on all inputs »> M₀ don't halts on all inputs and if it halts it accepts.(its language is not sigma star)