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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Thu, 12 Jun 2025 11:19:41 +0300
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On 2025-06-11 14:24:57 +0000, olcott said:

> On 6/11/2025 4:06 AM, Mikko wrote:
>> On 2025-06-10 17:12:24 +0000, olcott said:
>> 
>>> On 6/10/2025 2:25 AM, Mikko wrote:
>>>> On 2025-06-08 06:00:50 +0000, olcott said:
>>>> 
>>>>> 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.
>>>> 
>>>> No, it is not. It was an attempt to deceive with a false ad hominem.
>>> 
>>> When self-evident truth are not understood they remain
>>> self-evident.
>> 
>> Likewise, what is not a self-evident truth does not become one
>> when falsely claimed to be a self-evindet truth.
>> 
>> For example, "what I don't understand is not a proof" is not self-evident.
>> It depends on the additional information "I can understand proofs" that
>> you can't have.
> 
> If I show the steps of solving for X in an algebra
> problem and you do not know as much as how to count
> to five this does not mean that my proof is incorrect.

Most likely I wouldn't say so but hard to be sure as you never show
the steps of any proof and I can count to five.

>> Likewse, "When I provide proof that you cannot understand this does not
>> mean that I did not provide proof" is not self-evident as it assumes
>> there are proofs that I cannot understand at least to the extent that I
>> can recognise them as proofs. But that assumption is not self-evident
>> and not true.
> 
> Most every rebuttal of my work changes the words that
> I actually said and then rebuts these changed words.

Doesn't matter as long as you have no counter-arguments.

-- 
Mikko