Re: Simulation vs. Execution in the Halting Problem

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:
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On 6/1/2025 6:30 AM, Mikko wrote:

On 2025-05-30 15:41:59 +0000, olcott said:
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On 5/30/2025 3:45 AM, Mikko wrote:

On 2025-05-29 18:10:39 +0000, olcott said:
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On 5/29/2025 12:34 PM, Mr Flibble wrote:

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🧠 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.

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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.

But a simple check is just run DDD ahd see that it halts. That is
sufficient to determine the only correct answer.
 

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