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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Sun, 8 Jun 2025 01:00:50 -0500
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On 6/8/2025 12:49 AM, Mikko wrote:
> On 2025-06-04 16:27:48 +0000, olcott said:
> 
>> 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.
> 
> Yes, it does. 

What I just said is a truism, tautology, self-evident truth.

In epistemology (theory of knowledge), a self-evident
proposition is a proposition that is known to be true
by understanding its meaning without proof...
https://en.wikipedia.org/wiki/Self-evidence



> To understand a proof does not require any skills other
> than proof checking, which is a Turing computable function.
> 


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