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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Sun, 1 Jun 2025 14:30:05 +0300
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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.

-- 
Mikko