Re: Termination analyzer defined ---RICHARD IS WRONG !!!

On 5/14/2024 4:34 AM, Mikko wrote:

On 2024-05-13 18:07:37 +0000, Jeff Barnett said:
 

On 5/13/2024 3:06 AM, Mikko wrote:
>

Anyway, if an analyzer can never tell whether a program terminates
with every possible input then it is not a termination analyzer.

>
I don't think the above is true in the way you meant it. Recall that the collection of all Turing machines with blank input tapes is the same set of computations as the collection with arbitrary input tapes. It's always possible to take any specific machine, T, and initial tape, I, and produce machine T' with blank initial input tape that is equivalent: T' initially writes I on its tape (say one character output per state in sequence) then continues with the set of states that comprises T.
>
So it is obvious that a termination analyzer (AKA a halt decider) restricted to blank tape problems will do quite nicely and it is also quite obvious that no such entity exists.

 You only discuss halting decisions with specific inputs. THerefore you say
nothing about termination analyzers and don't show any mistake in my comment.
 

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
*My focus is even more narrow than that*
I only need to show that Linz embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ does correctly
determine the halt status of its input and the halting problem
proofs are refuted.
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