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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Wed, 4 Jun 2025 10:28:36 +0300
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On 2025-06-03 21:00:20 +0000, olcott said:

> On 6/3/2025 3:47 PM, Mr Flibble wrote:
>> On Tue, 03 Jun 2025 15:25:51 -0500, olcott wrote:
>> 
>>> On 6/3/2025 2:50 AM, Mikko wrote:
>>>> On 2025-06-02 15:55:00 +0000, olcott said:
>>>> 
>>>>> On 6/2/2025 2:02 AM, Mikko wrote:
>>>>>> On 2025-06-02 03:32:28 +0000, olcott said:
>>>>>> 
>>>>>>> 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.
>>>>>> 
>>>>>> Again you are trying a sraw man deception. RIchard Damon did not
>>>>>> change your words, he only wrote his own. He did not claim that you
>>>>>> said anything about "finite" or "infinite" but that you should
>>>>>> understand the difference.
>>>>> 
>>>>> Unlike most people here I do understand that not possibly reaching a
>>>>> final halt state *is* non-halting behavior.
>>>> 
>>>> You don't understand it correctly. Whether a computation is halting is
>>>> a feature of the computation, not a particular exectuion of that
>>>> coputation.
>>>> A halting computation is a halting computation even if its execution is
>>>> discontinued before reaching the final halt state.
>>>> 
>>>> 
>>> int main()
>>> {
>>> DDD(); // Do you understand that the HHH(DDD) that this DDD
>>> }        // calls is only accountable for the behavior of its
>>> // input, and thus NOT accountable for the behavior // of its
>>> caller?
>> 
>> We have been over this before.
>> 
>> This is incorrect as it is a category (type) error in the form of
>> conflation of the EXECUTION of DDD with the SIMULATION of DDD: to
>> completely and correctly simulate/analyse DDD there must be no execution
>> of DDD prior to the simulation of DDD.
>> 
> 
> I know that, you know that:
> 80 other people don't know that.
> All the textbooks don't know that.
> 
> All the textbooks expect HHH to report on the
> behavior of its caller.

Can you quote even one textbook saying "HHH shall report on the behaviour
of its caller" ?

-- 
Mikko