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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Wed, 4 Jun 2025 11:27:48 -0500
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On 6/4/2025 2:32 AM, Mikko wrote:
> On 2025-06-03 20:28:36 +0000, olcott said:
> 
>> On 6/3/2025 2:55 AM, Mikko wrote:
>>> On 2025-06-02 15:23:15 +0000, olcott said:
>>>
>>>> On 6/2/2025 1:56 AM, Mikko wrote:
>>>>> On 2025-06-01 21:41:36 +0000, olcott said:
>>>>>
>>>>>> On 6/1/2025 6:30 AM, Mikko wrote:
>>>>>>> On 2025-05-30 15:41:59 +0000, olcott said:
>>>>>>>
>>>>>>>> On 5/30/2025 3:45 AM, Mikko wrote:
>>>>>>>>> On 2025-05-29 18:10:39 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 5/29/2025 12:34 PM, Mr Flibble wrote:
>>>>>>>>>>>
>>>>>>>>>>> 🧠 Simulation vs. Execution in the Halting Problem
>>>>>>>>>>>
>>>>>>>>>>> In the classical framework of computation theory (Turing 
>>>>>>>>>>> machines),
>>>>>>>>>>> simulation is not equivalent to execution, though they can 
>>>>>>>>>>> approximate one
>>>>>>>>>>> another.
>>>>>>>>>>
>>>>>>>>>> To the best of my knowledge a simulated input
>>>>>>>>>> always has the exact same behavior as the directly
>>>>>>>>>> executed input unless this simulated input calls
>>>>>>>>>> its own simulator.
>>>>>>>>>
>>>>>>>>> The simulation of the behaviour should be equivalent to the real
>>>>>>>>> behaviour.
>>>>>>>>
>>>>>>>> That is the same as saying a function with infinite
>>>>>>>> recursion must have the same behavior as a function
>>>>>>>> without infinite recursion.
>>>>>>>
>>>>>>> A function does not have a behaviour. A function has a value for
>>>>>>> every argument in its domain.
>>>>>>>
>>>>>>> A function is not recursive. A definition of a function can be
>>>>>>> recursive. There may be another way to define the same function
>>>>>>> without recursion.
>>>>>>>
>>>>>>> A definition of a function may use infinite recursion if it is also
>>>>>>> defined how that infinite recursion defines a value.
>>>>>>>
>>>>>>> Anyway, from the meaning of "simulation" follows that a simulation
>>>>>>> of a behaviour is (at least in some sense) similar to the real
>>>>>>> behaviour. Otherwise no simulation has happened.
>>>>>>>
>>>>>>
>>>>>> void DDD()
>>>>>> {
>>>>>>    HHH(DDD);
>>>>>>    return;
>>>>>> }
>>>>>>
>>>>>> The *input* to simulating termination analyzer HHH(DDD)
>>>>>> specifies recursive simulation that can never reach its
>>>>>> *simulated "return" instruction final halt state*
>>>>>
>>>>> It does not matter whether a particular simulation does or does not
>>>>> reach its "return" instruction.
>>>>
>>>> It completely matters. DDD correctly simulated by HHH
>>>> proves the exact behavior that the input to HHH(DDD)
>>>> actually specifies.
>>>
>>> It proves nothing without a proof that DDD is correctly simulated by 
>>> HHH.
>>
>> I have shown that proof too many times and people
>> denied the very obvious verified facts of it.
> 
> You have never shown any proof of anything. But a verifiable and verified
> fact is that DDD halts. An obvious conseqence of that fact is that every
> report that means 'DDD does not halt' is wrong.
> 

When I provide proof that you cannot understand
this does not mean that I did not provide proof.

_DDD()
[00002183] 55             push ebp
[00002184] 8bec           mov ebp,esp
[00002186] 6883210000     push 00002183 ; push DDD
[0000218b] e833f4ffff     call 000015c3 ; call HHH
[00002190] 83c404         add esp,+04
[00002193] 5d             pop ebp
[00002194] c3             ret
Size in bytes:(0018) [00002194]

_main()
[000021a3] 55             push ebp
[000021a4] 8bec           mov ebp,esp
[000021a6] 6883210000     push 00002183 ; push DDD
[000021ab] e843f3ffff     call 000014f3 ; call HHH1
[000021b0] 83c404         add esp,+04
[000021b3] 33c0           xor eax,eax
[000021b5] 5d             pop ebp
[000021b6] c3             ret
Size in bytes:(0020) [000021b6]

  machine   stack     stack     machine    assembly
  address   address   data      code       language
  ========  ========  ========  ========== =============
[000021a3][0010382d][00000000] 55         push ebp      ; main()
[000021a4][0010382d][00000000] 8bec       mov ebp,esp   ; main()
[000021a6][00103829][00002183] 6883210000 push 00002183 ; push DDD
[000021ab][00103825][000021b0] e843f3ffff call 000014f3 ; call HHH1
New slave_stack at:1038d1

Begin Local Halt Decider Simulation   Execution Trace Stored at:1138d9
[00002183][001138c9][001138cd] 55         push ebp      ; DDD of HHH1
[00002184][001138c9][001138cd] 8bec       mov ebp,esp   ; DDD of HHH1
[00002186][001138c5][00002183] 6883210000 push 00002183 ; push DDD
[0000218b][001138c1][00002190] e833f4ffff call 000015c3 ; call HHH
New slave_stack at:14e2f9

Begin Local Halt Decider Simulation   Execution Trace Stored at:15e301
[00002183][0015e2f1][0015e2f5] 55         push ebp      ; DDD of HHH[0]
[00002184][0015e2f1][0015e2f5] 8bec       mov ebp,esp   ; DDD of HHH[0]
[00002186][0015e2ed][00002183] 6883210000 push 00002183 ; push DDD
[0000218b][0015e2e9][00002190] e833f4ffff call 000015c3 ; call HHH
New slave_stack at:198d21

*The above DDD emulated by HHH1 and DDD emulated by HHH exactly match*

*The below DDD emulated by HHH a second time that HHH1 never does*

[00002183][001a8d19][001a8d1d] 55         push ebp      ; DDD of HHH[1]
[00002184][001a8d19][001a8d1d] 8bec       mov ebp,esp   ; DDD of HHH[1]
[00002186][001a8d15][00002183] 6883210000 push 00002183 ; push DDD
[0000218b][001a8d11][00002190] e833f4ffff call 000015c3 ; call HHH
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

[00002190][001138c9][001138cd] 83c404     add esp,+04 ; DDD of HHH1
[00002193][001138cd][000015a8] 5d         pop ebp     ; DDD of HHH1
[00002194][001138d1][0003a980] c3         ret         ; DDD of HHH1
[000021b0][0010382d][00000000] 83c404     add esp,+04 ; main()
[000021b3][0010382d][00000000] 33c0       xor eax,eax ; main()
[000021b5][00103831][00000018] 5d         pop ebp     ; main()
[000021b6][00103835][00000000] c3         ret         ; main()
Number of Instructions Executed(352831) == 5266 Pages


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