Re: DDD specifies recursive emulation to HHH and halting to HHH1

Op 29.mrt.2025 om 22:07 schreef olcott:

On 3/29/2025 3:45 PM, Fred. Zwarts wrote:

Op 29.mrt.2025 om 20:03 schreef olcott:

On 3/29/2025 10:23 AM, dbush wrote:

On 3/29/2025 11:12 AM, olcott wrote:

On 3/28/2025 11:00 PM, dbush wrote:

On 3/28/2025 11:45 PM, olcott wrote:

>
It defines that it must compute the mapping from
the direct execution of a Turing Machine

>
Which does not require tracing an actual running TM, only mapping properties of the TM described.

>
The key fact that you continue to dishonestly ignore
is the concrete counter-example that I provided that
conclusively proves that the finite string of machine
code input is not always a valid proxy for the behavior
of the underlying virtual machine.

>
In other words, you deny the concept of a UTM, which can take a description of any Turing machine and exactly reproduce the behavior of the direct execution.

>
I deny that a pathological relationship between a UTM and
its input can be correctly ignored.
>
When this pathological relationship changes this behavior
we cannot simply pretend that the behavior is not changed.
>
>

>
When solving a problem, it is stupid to choose a tool that has a pathological relation with the problem.

 A termination analyzer cannot reject itself, yet it can
reject an input. This input was intentionally defined
to try to fool this termination analyzer.
 int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
 On the other hand when this same input DD is simulated
by the termination analyzer that DD defined a pathological
relationship to IT DOES SPECIFY NON-TERMINATING BEHAVIOR.
 

We can ask whether we can create a hammer that can hit all possible nails on the head. It can be proven that no such hammer exists, because we can always attach a nail to the hammer upside down, so that the hammer cannot hit it on its head.
Olcott would call that a 'pathological relationship' between hammer and nail. I think he would argue that for such a pathological relationship between hammer and nail we need another definition of 'hitting behaviour', because the original requirement ignores the pathological relationship. So, when we define a 'hitting behaviour' as when the hammer is halfway down in an attempt to reach the nail, we see that he can construct a hammer and say that it correctly shows 'hitting behaviour' to the nail when it is halfway down, because the requirement to hit it on the head is logically impossible. :-)