Re: Defining a correct halt decider

Am Thu, 05 Sep 2024 08:39:14 -0500 schrieb olcott:

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.

What is that assumption?

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.

Namely, that DDD halts.

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.

The wrinkle being that it is selfreferential. We are only interested
in the case where the DDD that calls an aborting HHH is simulated
by that same 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.

HHH cannot simulate something that calls itself; yet it halts.

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.

That is exactly your mistake, that you believe the simulation of a
different program somehow has the same behaviour.
--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.