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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How do simulating termination analyzers work? (V2)
Date: Tue, 24 Jun 2025 10:09:32 -0500
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In-Reply-To: <103dpio$1tstq$1@dont-email.me>

On 6/24/2025 4:02 AM, Mikko wrote:
> On 2025-06-23 16:56:21 +0000, olcott said:
> 
>> On 6/23/2025 2:18 AM, Mikko wrote:
>>> On 2025-06-22 16:35:42 +0000, olcott said:
>>>
>>>> On 6/22/2025 4:07 AM, Mikko wrote:
>>>>> On 2025-06-21 12:24:07 +0000, Mr Flibble said:
>>>>>
>>>>>> On Fri, 20 Jun 2025 19:44:50 -0500, olcott wrote:
>>>>>>
>>>>>>> On 6/20/2025 7:01 PM, Richard Damon wrote:
>>>>>>>> On 6/20/25 3:08 PM, olcott wrote:
>>>>>>>>> void Infinite_Recursion()
>>>>>>>>> {
>>>>>>>>>    Infinite_Recursion(); return;
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> void Infinite_Loop()
>>>>>>>>> {
>>>>>>>>>    HERE: goto HERE;
>>>>>>>>>    return;
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> void DDD()
>>>>>>>>> {
>>>>>>>>>    HHH(DDD);
>>>>>>>>>    return;
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> int Sipser_D()
>>>>>>>>> {
>>>>>>>>>    if (HHH(Sipser_D) == 1)
>>>>>>>>>      return 0;
>>>>>>>>>    return 1;
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> int DD()
>>>>>>>>> {
>>>>>>>>>    int Halt_Status = HHH(DD);
>>>>>>>>>    if (Halt_Status)
>>>>>>>>>      HERE: goto HERE;
>>>>>>>>>    return Halt_Status;
>>>>>>>>> }
>>>>>>>>>
>>>>>>>>> My claim is that each of the above functions correctly 
>>>>>>>>> simulated by
>>>>>>>>> any termination analyzer HHH that can possibly exist will never 
>>>>>>>>> stop
>>>>>>>>> running unless aborted by HHH.
>>>>>>>>
>>>>>>>> The problem is that NO "Simulating Halt Decider" HHH, can correctly
>>>>>>>> simulte ANY of those inputs.
>>>>>>>>
>>>>>>>> For the first two, it is possible for a smart enough Simulation 
>>>>>>>> Halt
>>>>>>>> Decider to determine that the correct simulation of the input 
>>>>>>>> will not
>>>>>>>> halt, no matter what HHH actually does, since it doesn't depend 
>>>>>>>> on the
>>>>>>>> decider.
>>>>>>>>
>>>>>>>> For the last 3, it can not prove that they will not halt, as, in 
>>>>>>>> fact,
>>>>>>>
>>>>>>>> the correct simulation of all those inputs *WILL* halt
>>>>>>>
>>>>>>> _DDD()
>>>>>>> [00002192] 55             push ebp [00002193] 8bec           mov 
>>>>>>> ebp,esp
>>>>>>> [00002195] 6892210000     push 00002192 [0000219a] e833f4ffff     
>>>>>>> call
>>>>>>> 000015d2  // call HHH [0000219f] 83c404         add esp,+04 
>>>>>>> [000021a2]
>>>>>>> 5d             pop ebp [000021a3] c3             ret Size in
>>>>>>> bytes:(0018) [000021a3]
>>>>>>>
>>>>>>> Exactly how would N instructions of DDD emulated by HHH according 
>>>>>>> to the
>>>>>>> semantics of the x86 language reach machine address 000021a3 ?
>>>>>>
>>>>>> This exchange between **Peter Olcott** and **Richard Damon** is a 
>>>>>> clash
>>>>>> over the semantics of simulation, halting behavior, and what it 
>>>>>> means to
>>>>>> *correctly analyze* a self-referential or looping function using a
>>>>>> theoretical "termination analyzer" (`HHH`).
>>>>>>
>>>>>> Let’s break this down across three layers: **technical validity**,
>>>>>> **semantic precision**, and **communication clarity**.
>>>>>>
>>>>>> ---
>>>>>>
>>>>>> ## 🔍 1. **Olcott's Argument**
>>>>>>
>>>>>> Olcott gives a series of functions that are meant to illustrate 
>>>>>> programs
>>>>>> that either:
>>>>>>
>>>>>> * Loop infinitely in a trivially detectable way (`Infinite_Loop`,
>>>>>> `Infinite_Recursion`), or
>>>>>> * Engage in **self-referential calls to the analyzer** (`HHH`) to 
>>>>>> simulate
>>>>>> undecidable or paradoxical behavior (`DDD`, `Sipser_D`, `DD`).
>>>>>>
>>>>>> He claims:
>>>>>>
>>>>>>> Any HHH that correctly simulates these programs will never stop 
>>>>>>> running
>>>>>
>>>>> As soon as he writes "any HHH" he falls in the trap called 
>>>>> "equivocation".
>>>>
>>>> Likewise when I say that every integer N > 6 is > 5
>>>
>>> No, that is not the same. Instead that is provable from the transitivity
>>> of >.
>>
>> The semantics of the C programming language conclusively
>> proves that DDD correctly simulated by any STA that can
>> possibly exist cannot possibly reach its own "return"
>> instruction final halt state.
> 
> Not whithout an unambiguous definition of "STA" and a sufficient
> specification of HHH.
> 

*This was all that ChatGPT needed to know about HHH*
Termination Analyzer HHH simulates its input until
it detects a non-terminating behavior pattern. When
HHH detects such a pattern it aborts its simulation
and returns 0.

*Complete analysis of HHH(DDD) == 0 by ChatGPT*
https://chatgpt.com/share/67158ec6-3398-8011-98d1-41198baa29f2


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