As Atm is recognizable, its complement cannot be recognizable, due to being so Atm would be decidable.I am trying to clarify if the problem P is the complement to Atm.If so, how could i approach the problem without looking at Atm to prove undecidability?My first thought was:H is a machine which solves P:H halts and accepts when M rejects w.H halts and rejects when M accepts w.And from then on contradict the construct like in the proof of Atm.
Is P = {  | M rejects w} the complement to Atm = {  | M accepts w}?
turing machines