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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Tue, 3 Jun 2025 10:13:14 +0200
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Op 02.jun.2025 om 18:01 schreef olcott:
> On 6/2/2025 10:23 AM, Fred. Zwarts wrote:
>> Op 02.jun.2025 om 16:36 schreef olcott:
>>> On 6/2/2025 6:13 AM, Richard Damon wrote:
>>>> On 6/1/25 11:32 PM, olcott wrote:
>>>>> On 6/1/2025 8:19 PM, Richard Damon wrote:
>>>>>> On 6/1/25 5:41 PM, olcott wrote:
>>>>>>> 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*
>>>>>>>
>>>>>>> *Every rebuttal to this changes the words*
>>>>>>>
>>>>>>
>>>>>> No it doesn't, as HHH is defined to abort and simulation after 
>>>>>> finite time, and thus only does finite simulation.
>>>>>>
>>>>>
>>>>> See right there you changed the words.
>>>>> I said nothing about finite or infinite simulation.
>>>>> You said that I am wrong about something that I didn't even say.
>>>>>
>>>>
>>>> But you mean infinitly recursive, or you have no evidence of non- 
>>>> halting.
>>>>
>>>
>>> That is not the way that the computer science works.
>>> Can't possibly reach final halt state *is* non-halting.
>>>
>>
>> No, a premature end of the simulation, does not say anything about the 
>> halting property of the program being simulated.
> 
> As soon as HHH emulates itself emulating DDD
> it can see that DDD cannot possibly reach its
> own final halt state no matter how many steps
> of DDD are correctly emulated.
> 

Wrong. It should be:
When HHH emulates itself emulating DDD it does not see that DDD could 
reach its own final halt state when simulating one more cycle, due to a 
premature abort.
Things that HHH does not see, leave the specification of an aborting and 
halting program unchanged.