Re: Defining a correct halt decider

On 9/5/2024 2:39 AM, Mikko wrote:

On 2024-09-03 13:17:56 +0000, olcott said:
 

On 9/3/2024 3:44 AM, Mikko wrote:

On 2024-09-02 16:06:11 +0000, olcott said:
>

A correct halt decider is a Turing machine T with one accept state and one reject state such that:
>
If T is executed with initial tape contents equal to an encoding of Turing machine X and its initial tape contents Y, and execution of a real machine X with initial tape contents Y eventually halts, the execution of T eventually ends up in the accept state and then stops.
>
If T is executed with initial tape contents equal to an encoding of Turing machine X and its initial tape contents Y, and execution of a real machine X with initial tape contents Y does not eventually halt, the execution of T eventually ends up in the reject state and then stops.

>
Your "definition" fails to specify "encoding". There is no standard
encoding of Turing machines and tape contents.

>
That is why I made the isomorphic x86utm system.
By failing to have such a concrete system all kinds
of false assumptions cannot be refuted.

 If it were isnomorphic the same false assumtipns would apply to both.

They do yet I cannot provide every single details of
the source-code of the Turing machine because these
details would be too overwhelming.
So instead every author makes a false assumption that
is simply believed to be true with no sufficient basis
to show that it isn't true.
Once I prove my point as the x86 level I show how the
same thing applies to the Peter Linz proof.

 

The behavior of DDD emulated by HHH** <is> different
than the behavior of the directly executed DDD**
**according to the semantics of the x86 language

 The halting problem is not about a string but about a behaviour.

Is is about the behavior that this string specifies.
HHH computes the mapping from its input finite string
to the behavior that this finite string specifies on
the basis of DDD emulated by HHH.
DDD emulated by HHH cannot possibly reach its final halt
state and on this basis alone HHH is correct to reject
DDD and report non-halting.
When there is a pathological relationship to the decider
and its input then this behavior must include DDD calling
HHH to emulated itself again.
That no one bothered to notice that the behavior of an
input DDD to a simulating termination analyzer HHH can
be different than the behavior of a directly executed
DDD when there is a pathological relationship between
HHH and DDD IS NOT MY MISTAKE.

Your decider is not a halt decider if it answers about another
behaviour.
 

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer