Re: Simulation vs. Execution in the Halting Problem

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.

✅ What’s True:
Running a simulation of a program—even partially—is meant to reflect its
execution behavior.
Simulators, emulators, or analyzers aim to predict how a program would
behave if actually run.
 ⚠️ Where the Divergence Happens:
 1. Simulation May Not Be Complete
Even if the simulator detects what it believes to be infinite recursion,
it:
- Has not observed it to infinity
- Has inferred it based on structure or partial behavior
 2. Execution Is Definitive, Simulation Is Predictive
- Execution is actual: the program runs on hardware (real or virtual) and
either halts or doesn’t.
- Simulation is analytic: a model tries to deduce the result without fully
committing to it.
 🔄 What SHDs Claim (Flibble/Olcott):
If the SHD halts its simulation due to detecting a provable infinite
recursion, then that should be considered a correct determination of non-
halting for the input program.
 This leads to their argument:
- SHD's halting ≠ the program’s halting
- But SHD's halting due to detection of infinite recursion ⇒ program’s
non-halting
 🧩 The Problem:
In classical computability theory:
- You can’t always know that a structure will cause non-halting.
- Many programs appear recursive but halt (e.g., bounded recursion).
- There’s no general algorithm that can always correctly detect infinite
recursion in all programs.
 Thus:
Simulation that halts does not conclusively determine that the simulated
program would or would not halt — unless the simulation is exhaustive and
faithful, which isn't always possible.
 ✅ Conclusion:
Partial simulation provides strong hints but not definitive proof of
halting or non-halting — unless the analysis itself is provably sound and
complete within a restricted system (e.g., total languages).

HHH never rejects any input unless it has proven:
*would never stop running unless aborted*
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer