Re: The halting problem as defined is a category error

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:

I am either going to go by the Linz proof or my own code

>

Your decision. Anyway the hypothetical halting decider obviously only
takes descriptions of TMs as input, with the OUTput required to be
what the universal simulation or direct execution *of that input*
(namely, DDD *not* calling a UTM) does.
>

That is incorrect in the case where DD calls its own simulating
termination analyzer or the Linz Ĥ contains its own simulating halt
decider.

Yes, HHH does not meet the requirement.
 

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.

When an input calls its own decider in recursive emulation this must
be modeled. The best way to determine the behavior that the input
specifies is for DD to be emulated by HHH according to the semantics
of the x86 language. That does cause recursive emulation.

>
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.

--
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.