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

Am Fri, 28 Mar 2025 14:16:50 -0500 schrieb olcott:

On 3/28/2025 4:35 AM, Fred. Zwarts wrote:

Op 28.mrt.2025 om 02:21 schreef olcott:

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:

On 3/27/2025 8:34 PM, olcott wrote:

On 3/27/2025 7:12 PM, dbush wrote:

TM's cannot possibly ever report on the behavior of the direct
execution of another TM.

>
False:
>

I did not say that no TM can ever report on behavior that matches the
behavior of a directly executing TM.

Why does HHH report that the directly executed DDD wouldn't halt?

No TM can every directly see the behavior of the direct execution of
any other TM because no TM can take a directly executing TM as an
input.

Wrong:

The best that any TM can ever do to see what the behavior of another
TM might be is to simulate the machine code (TM description) of this
machine.
When this input defines a pathological relationship with its
simulating half decider this does prevent this simulated machine from
reaching its final halt state.
>

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

The pathological construction is always possible. It does not depend
on the specific decider.

The halt decider has always been correct it is the input that cheats.

Now it gets interesting. Given that a halt decider exists, the counter-
input is a perfectly cromulent construction. How do you prove the
assumption correct?

--
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.