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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How do simulating termination analyzers work? ---Truth Maker
 Maximalism FULL_TRACE
Date: Mon, 14 Jul 2025 22:20:38 -0500
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On 7/14/2025 9:57 PM, Richard Damon wrote:
> On 7/14/25 11:53 AM, olcott wrote:
>> On 7/14/2025 6:37 AM, Richard Damon wrote:
>>> On 7/13/25 10:46 PM, olcott wrote:
>>>> On 7/13/2025 8:33 PM, Richard Damon wrote:
>>>>> On 7/13/25 4:43 PM, olcott wrote:
>>>>>> On 7/7/2025 9:07 AM, Alan Mackenzie wrote:
>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>> On 7/6/2025 4:23 PM, Alan Mackenzie wrote:
>>>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>>>> On 7/6/2025 12:52 PM, Alan Mackenzie wrote:
>>>>>>>>>>> olcott <polcott333@gmail.com> wrote:
>>>>>>>>>>>> On 7/6/2025 11:02 AM, Alan Mackenzie wrote:
>>>>>>>
>>>>>>>>> [ .... ]
>>>>>>>
>>>>>>>>>>>> int DD()
>>>>>>>>>>>> {
>>>>>>>>>>>>      int Halt_Status = HHH(DD);
>>>>>>>>>>>>      if (Halt_Status)
>>>>>>>>>>>>        HERE: goto HERE;
>>>>>>>>>>>>      return Halt_Status;
>>>>>>>>>>>> }
>>>>>>>
>>>>>>>>>>>> Then you should know that DD simulated by HHH
>>>>>>>>>>>> according to the semantics of the C programming
>>>>>>>>>>>> language cannot possibly reach its own "return"
>>>>>>>>>>>> statement final halt state.
>>>>>>>
>>>>>>>>>>> An argument like this is at such a low level of abstraction 
>>>>>>>>>>> as to be near
>>>>>>>>>>> valuless.
>>>>>>>
>>>>>>>>>> It is really weird that you are calling a 100% complete
>>>>>>>>>> concrete specification "a low level of abstraction".
>>>>>>>>>> That HHH(DD) correctly determines that DD simulated by
>>>>>>>>>> HHH cannot possibly halt is a proven fact.
>>>>>>>
>>>>>>>>> A complete concrete specification would necessarily include a 
>>>>>>>>> description
>>>>>>>>> of what you mean by "simulation".
>>>>>>>
>>>>>>>> I specifically mean that this x86 machine code
>>>>>>> [ .... ]
>>>>>>>> Is emulated by an x86 emulator named HHH.
>>>>>>>
>>>>>>> That's no adequate description.  To make it so, you'd have to say 
>>>>>>> what
>>>>>>> you mean by an "x86 emulator".  The name you give it is irrelevant
>>>>>>>
>>>>>>>>>   But my point was that rather than
>>>>>>>>> sticking to the abstract nature of the proof, you're chipping 
>>>>>>>>> tiny pieces
>>>>>>>>> out of it and dealing with those.  The proof you claim to 
>>>>>>>>> refute has no
>>>>>>>>> notion of simulation, for example; it doesn't need it.
>>>>>>>
>>>>>>>
>>>>>>>> *Not at all there are two pieces*
>>>>>>>> (1) HHH(DD) does correctly determine that its input
>>>>>>>>      specifies non halting behavior.
>>>>>>>> (2) The directly executed DD() does not contradict this.
>>>>>>>
>>>>>>> The word "correctly" is fully redundant there.
>>>>>>>
>>>>>>> The proof does not state whether the constructed function returns 
>>>>>>> true or
>>>>>>> false, i.e. whether it specifies non halting behaviour. 
>>>>>>
>>>>>> The proof is purported to prove THAT DD is an undecidable
>>>>>> input for HHH. This is its counter example refuting the
>>>>>> claim that a universal halt decider can exist.
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>> But since your DD by your own admission is a category error for a 
>>>>> halt decider, as you have specifically stated it isn't a program as 
>>>>> the input doesn't include the code of the specific HHH that it 
>>>>> calls, you proof is just invalid.
>>>>>
>>>>> Sorry, all you proved is that you don't know what you are talking 
>>>>> about.
>>>>
>>>> That you keep trying to get away with refuting
>>>> this easily verified fact says a about about you
>>>>
>>>> _DDD()
>>>> [00002192] 55             push ebp
>>>> [00002193] 8bec           mov ebp,esp
>>>> [00002195] 6892210000     push 00002192  // push DDD
>>>> [0000219a] e833f4ffff     call 000015d2  // call HHH
>>>> [0000219f] 83c404         add esp,+04
>>>> [000021a2] 5d             pop ebp
>>>> [000021a3] c3             ret
>>>> Size in bytes:(0018) [000021a3]
>>>>
>>>> When one or more instructions of DDD are emulated
>>>> according to the semantics of the x86 language by
>>>> some HHH, no DDD ever reaches its "ret" instruction.
>>>>
>>>
>>> Which isn't the definition of Non-Halting, 
>> Reaching a final halt state <is> the definition of halting.
>>
> 
> Right, but the OBJECT that measures that it the exectution of the 
> Program, or a complete simulation.
> 

_DDD()
[00002192] 55             push ebp
[00002193] 8bec           mov ebp,esp
[00002195] 6892210000     push 00002192  // push DDD
[0000219a] e833f4ffff     call 000015d2  // call HHH
[0000219f] 83c404         add esp,+04
[000021a2] 5d             pop ebp
[000021a3] c3             ret
Size in bytes:(0018) [000021a3]

When one or more instructions of DDD are emulated
according to the semantics of the x86 language by
some HHH, no DDD ever reaches its "ret" instruction.

Do you really think that you can get away with
disagreeing with the x86 language?

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer