Re: Simulation vs. Execution in the Halting Problem

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