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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Mon, 2 Jun 2025 09:56:54 +0300
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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 only matters whether whether the
beahaviour specified by the input (which in this case is DDD) will
reach its own "return", and it does.

-- 
Mikko