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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: DDD simulated by HHH cannot possibly halt (Halting Problem) ---
 mindless robots
Date: Wed, 23 Apr 2025 19:23:53 +0200
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Op 23.apr.2025 om 17:53 schreef olcott:
> On 4/23/2025 3:59 AM, Fred. Zwarts wrote:
>> Op 22.apr.2025 om 21:24 schreef olcott:
>>> On 4/22/2025 7:42 AM, joes wrote:
>>>> Am Mon, 14 Apr 2025 17:48:36 -0500 schrieb olcott:
>>>>> On 4/14/2025 4:29 AM, joes wrote:
>>>>>> Am Sun, 13 Apr 2025 16:00:43 -0500 schrieb olcott:
>>>>>>> On 4/13/2025 3:00 PM, dbush wrote:
>>>>>>>> On 4/13/2025 3:59 PM, olcott wrote:
>>>>>>>>> On 4/13/2025 3:54 AM, joes wrote:
>>>>>>>>>> Am Fri, 11 Apr 2025 10:56:32 -0500 schrieb olcott:
>>>>>>>>>>> On 4/11/2025 3:24 AM, Richard Heathfield wrote:
>>>>>>>>>>>> On 11/04/2025 08:57, Mikko wrote:
>>>>>>>>>>
>>>>>>>>>>>>> No proof of this principle has been shown so its use is not
>>>>>>>>>>>>> valid.
>>>>>>>>>>>> No proof of Peano's axioms or Euclid's fifth postulate has been
>>>>>>>>>>>> shown.
>>>>>>>>>>>> That doesn't mean we can't use them.
>>>>>>>>>>>> Mr Olcott can have his principle if he likes, but only by 
>>>>>>>>>>>> EITHER
>>>>>>>>>>>> proving it (which, as you say, he has not yet done) OR by 
>>>>>>>>>>>> taking
>>>>>>>>>>>> it as axiomatic, leaving the world of mainstream computer 
>>>>>>>>>>>> science
>>>>>>>>>>>> behind him,
>>>>>>>>>>>> constructing his own computational 'geometry' so to speak, and
>>>>>>>>>>>> abandoning any claim to having overturned the Halting Problem.
>>>>>>>>>>>> Navel contemplation beckons.
>>>>>>>>>>>> Axioms are all very well, and he's free to invent as many as he
>>>>>>>>>>>> wishes,
>>>>>>>>>>>> but nobody else is obliged to accept them.
>>>>>>>>>>> *Simulating termination analyzer Principle*
>>>>>>>>>>> It is always correct for any simulating termination analyzer to
>>>>>>>>>>> stop simulating and reject any input that would otherwise 
>>>>>>>>>>> prevent
>>>>>>>>>>> its own termination.
>>>>>>>>>> Sure. Why doesn’t the STA simulate itself rejecting its input?
>>>>>>>>> Because that is a STUPID idea and categorically impossible because
>>>>>>>>> the outermost HHH sees its needs to stop simulating before any 
>>>>>>>>> inner
>>>>>>>>> HHH can possibly see this.
>>>>>>>> In other words, you agree that Linz and others are correct that 
>>>>>>>> no H
>>>>>>>> exists that satisfies these requirements:
>>>>>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>>>>>> instructions)
>>>>>>>> X described as <X> with input Y:
>>>>>>>> A solution to the halting problem is an algorithm H that 
>>>>>>>> computes the
>>>>>>>> following mapping:
>>>>>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>>>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
>>>>>>>> directly
>>>>>>> No stupid! Those freaking requirements are wrong and anchored in the
>>>>>>> ignorance  of rejecting the notion of a simulating termination
>>>>>>> analyzer OUT-OF-HAND WITHOUT REVIEW.
>>>>>>> As anyone can see HHH MUST REJECT ITS INPUT OR GET STUPIDLY STUCK IN
>>>>>>> NON-TERMINATION. If people were not mindless robots they would have
>>>>>>> immediately acknowledged this years ago.
>>>>>> But why does it not return „I know this halts, but I can’t simulate
>>>>>> it”?
>>>>> Because it is not a liar and tells the truth for every input in its
>>>>> domain.
>>>> Aha. Then why does it not simulate it and say that it halts?
>>>>
>>>
>>> I have proven that the directly executed DD and DD
>>> emulated by HHH according to the semantics of the
>>> x86 language have a different set of state changes
>>> many hundreds of times for several years.
>>>
>>
>> You did not prove it, you dreamed about it for many years, but you 
>> failed to show the first state change were the simulation differs from 
>> the simulation. You only showed that HHH failed to complete the 
>> simulation.
> 
> _DD()
> [00002133] 55         push ebp      ; housekeeping
> [00002134] 8bec       mov ebp,esp   ; housekeeping
> [00002136] 51         push ecx      ; make space for local
> [00002137] 6833210000 push 00002133 ; push DD
> [0000213c] e882f4ffff call 000015c3 ; call HHH(DD)
> [00002141] 83c404     add esp,+04
> [00002144] 8945fc     mov [ebp-04],eax
> [00002147] 837dfc00   cmp dword [ebp-04],+00
> [0000214b] 7402       jz 0000214f
> [0000214d] ebfe       jmp 0000214d
> [0000214f] 8b45fc     mov eax,[ebp-04]
> [00002152] 8be5       mov esp,ebp
> [00002154] 5d         pop ebp
> [00002155] c3         ret
> Size in bytes:(0035) [00002155]
> 
> By merely knowing that HHH emulates DD until it
> sees itself about to emulate DD a third time
> (mathematical induction proof that DD is stuck in
> recursive emulation) we can know that

We know that the simulating HHH fails to see that the recursion is 
finite and that the next time the simulated HHH would abort and halt, 
which makes the abort of the simulating HHH unneeded.

> 
> The call to HHH(DD) from the directly executed DD returns.
> The call to HHH(DD) from DD emulated by HHH cannot possibly return.
Yes, HHH fails to simulate itself up to the end.
You still did not show which state change in the simulation is different 
from the direct execution. The only difference is that HHH aborts 
prematurely and the direct execution does not abort.