# A Turing Machine with undecideable Halting Status not relying on Open Problems

Is there any turing machine that it is proovably known to be undecideable, it has to fullfit the following characteristics:

• Not rely on Open Problems/ Conjectures
• Should not use the same machine used in diagonalization proof

In other words, is there an alternative proof that Halting problem is undecideable (other than diagonalization)?

• "known to be undecidable" in a particular formal theory, or in the sense that [the set on inputs on which the machine halts] is non-computable? ​ ​ – user12859 Sep 14 '16 at 14:03
• Is it relevant to say here that $L(M)= \sum^*$ is undecidable, because we do not have a general algorithm that can be applied to this machine to decide whether it is decidable (halts)? If yes, does this support the argument of the halting problem being undecidable? – px06 Sep 14 '16 at 15:20
• But does the proof of that rely on the diagonalization? – CoffeDeveloper Sep 14 '16 at 16:12
• Let M be TM that decides $A_{tm}$. Take M as subroutine to decide language $S_{tm}$ but since that language is not recursive this leads to contradiction (without diagonalization). – Evil Sep 14 '16 at 20:37
• Would accept it if added with some explaination so that also who don't know what Atm is can understand it – CoffeDeveloper Sep 15 '16 at 11:15