Re: The halting problem as defined is a category error

Am Wed, 23 Jul 2025 16:08:51 -0500 schrieb olcott:

On 7/23/2025 3:56 PM, joes wrote:

Am Wed, 23 Jul 2025 15:14:35 -0500 schrieb olcott:

On 7/23/2025 2:06 PM, joes wrote:

Am Wed, 23 Jul 2025 09:24:15 -0500 schrieb olcott:

On 7/23/2025 8:31 AM, joes wrote:

Am Wed, 23 Jul 2025 07:22:55 -0500 schrieb olcott:

The actual behavior that is actually specified must include that in
both of these cases recursive simulation is specified. We can't just
close our eyes and pretend otherwise.

That is what HHH does: close its eyes and pretend that DDD called a
pure simulator instead of recursing. See below.
>

That you don't understand my code is ot a rebuttal. HHH simulate DDD
that calls HHH(DDD) that causes the directly executed HHH to simulate
itself simulating DDD until this simulated simulated DDD calls a
simulated simulated HHH(DDD).

 
Of course, and then it incorrectly assumes that an unaborted simulation
*of this HHH*, which does in fact abort, wouldn't abort.
 

If HHH(DDD) never aborts its simulation then this HHH never stops
running.

If HHH (which aborts) was given to a UTM/pure simulator, it would
stop running.

No, the best way to determine what the input "specifies" is to just
run it or use a UTM - unless you actually mean the behaviour of HHH
simulating DDD, in which case it is always tautologically correct.

>

HHH itself *is itself* a UTM that is smart enough to not get stuck in
non-halting behavior. That is why I named my operating system x86UTM.

 
I.e. not a UTM. Those wouldn't need to halt on inputs that don't halt
*by themselves*, which DDD isn't.

>
I red car *is* a car.
A UTM that is also a halt decider is a UTM.

A car that is also a bicycle is not a car.
The simulation of a non-halting input doesn't halt.

--
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.