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

On 3/29/25 5:37 PM, olcott wrote:

On 3/29/2025 3:11 PM, dbush wrote:

On 3/29/2025 3:46 PM, olcott wrote:

On 3/29/2025 2:25 PM, dbush wrote:

On 3/29/2025 3:19 PM, olcott wrote:

On 3/29/2025 2:01 PM, dbush wrote:

On 3/29/2025 2:58 PM, olcott wrote:

On 3/29/2025 1:37 PM, dbush wrote:

On 3/29/2025 2:15 PM, olcott wrote:

On 3/29/2025 4:31 AM, joes wrote:

Am Fri, 28 Mar 2025 14:27:36 -0500 schrieb olcott:

On 3/28/2025 2:17 PM, dbush wrote:

On 3/28/2025 3:02 PM, olcott wrote:

On 3/28/2025 1:12 PM, dbush wrote:

On 3/28/2025 1:57 PM, olcott wrote:

On 3/27/2025 9:33 PM, dbush wrote:

On 3/27/2025 10:10 PM, olcott wrote:

On 3/27/2025 8:24 PM, dbush wrote:

On 3/27/2025 9:21 PM, olcott wrote:

On 3/27/2025 8:09 PM, dbush wrote:

On 3/27/2025 9:07 PM, olcott wrote:

On 3/27/2025 7:38 PM, dbush wrote:

>

Good, because that's all that's required for a solution to the
halting problem:
>

There are sometimes when the behavior of TM Description D
correctly simulated by UTM1 does not match the behavior correctly
simulated by UTM2.

>
Irrelevant, because to satisfy the requirements, the behavior of
the described machine when executed directly must be reported.

>
I HAVE PROVED THAT THE REQUIREMENT IS WRONG NITWIT.

According to what? WE require it. YOU are answering a different question.
>

Category error.
I want to know if any arbitrary algorithm X with input Y will halt
when executed directly.

>
It is 100% impossible for any TM to take another executing TM as its
input.

Quit that.
>

But it can take a complete description of a TM that

>
Is not always a perfect proxy for the behavior of the direct execution
of the underlying machine.

>

Uh yes it is.
>

>
That my proof that I am correct
is over your head is less than
no rebuttal what-so-ever.

>
The fact that such TM description can be given to a UTM which will exactly replicate the behavior of the described TM when executed directly proves otherwise is apparently over your head.
>

>
One cannot correctly ignore the effect that a specified
pathological relationship has between its simulator
and its input on the behavior of this input.
>

>
All it means is that HHH does not correctly map DDD to 1 as per the requirements:
>

>
int sum(int x, int y) { return x + y; }
In the same way that sum(2,3) cannot be mapped to 7.

>
It can, it just wouldn't meet the requirements of the mathematical "sum" function.
>

>
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
>
Likewise if HHH reported on the behavior of the
directly executed DD

>
It would be behaving as required:
>

 Requiring a halt decider to not be able to return
is an incorrect requirement. It is required to outsmart
such attempts.
 

Only if it is able to do so correctly.
There is no requirement that a correct Halt Decider must exist.
That seems to be one of your fundamental problems, you don't understand that some natural problems can not be solved, because the problem space grows faster than the solution space.