Re: Analysis of Flibble’s New Take on Simulating Halt Deciders and Pathological Input

On 5/17/25 8:27 PM, Mr Flibble wrote:

Analysis of Flibble’s New Take on Simulating Halt Deciders and
Pathological Input
==================================================================================
 1. Summary of Flibble’s New Take
--------------------------------
Flibble introduces a refined stance on the treatment of pathological input
within simulating halt deciders (SHDs), asserting:
 - It's sufficient for an SHD to detect *infinite recursion*, rather than
run a simulation to its literal end.

But only if the recursion, is in fact, infinite.

- Aborting due to stack overflow or continuing infinitely are semantically
equivalent — both signify non-halting behavior.
- This leads to the articulation of "Flibble's Law":
      If a problem permits infinite behavior in its formulation, it permits
     infinite analysis of that behavior in its decidability scope.
 

Which just isn't true, and aborting due to stack overflow is NOT semantically equivalent to continuing infinitely.
The first is having a highest amount you can handle, while the latter is being able to get to any value.
If a problem will halt on a propertly configures machine after 2 million steps. but the not as well equipted machine overflows after 1 million steps, it just got the wrong answer.

2. Interpretation of Flibble’s Law
----------------------------------
This law suggests that:
- Any problem involving potentially infinite computation inherently
requires the ability to analyze such infinite behavior.

It may require, but it still is not allowed that decider to use infinite time.

- Deciders are not invalidated by their inability to simulate forever —
they are validated by their ability to detect structural infinity.

But only if they CORRECTLY determine actual infinite behavior.

 3. Shift in Position
--------------------
Earlier, Flibble emphasized that:
- Pathological inputs are ill-formed due to a category error (program
conflated with its own representation).

No, they are not.

- Therefore, halting cannot even be meaningfully questioned for such
inputs.

Sure t can, as long as the input is the representation of a PROGRAM (and that means it includes all the code that it uses) that program WILL either halt or not, and thus that input either represents a halting program or not, and thus the question is meaningful.
Note, the Olcoott input, defined to be just the C funcition, is not a program, so yes, THAT INPUT is invalid, but can be made valid by completing the proof program by including in it the code for the decider that it is designed to prove not correct.

 Now, Flibble acknowledges:
- SHDs can still offer meaningful answers by detecting recursion patterns
without needing infinite runtime.

In *SOME* cases, not all. So they can be PARTIAL deciders.

- A decider may *abort* simulation upon detecting such patterns and still
be semantically correct.

But only if the pattern is ACTUALLY infinitely recursive.

 4. Contrast with Turing’s View
------------------------------
| Aspect                      | Turing                            |
Flibble                             |
|-----------------------------|------------------------------------|--------------------------------------|
| Infinite recursion          | Undecidable behavior               |
Signal of ill-formed input           |
| Decider responsibilities    | Must decide all valid inputs       | Must
exclude ill-formed inputs       |
| Simulation abort (overflow) | Not semantically significant       | Valid
detection of non-halting input |

But it is possible for Turing Machie to detect SOME forms of infinite recursion, so you table is just incorrect.
It is fairly easy to detect that the foloowing is non-halting:
int R() {
    R();
}
So just the presence of recursion isn't the problem.

 Turing treats infinite simulation as a symptom of undecidability. Flibble
treats it as a signal of semantic ill-formedness — which still permits
operational classification.

No, you are just showing you don't understand what you are talking about, because you are believing Olcotts lies.

 5. Theoretical and Practical Implications
-----------------------------------------
- **Theoretically**, Flibble provides a framework that restricts the
Halting Problem's domain to avoid paradoxes.

No, it tries to create a loosened set of requirements to see if those can be solved.

- **Practically**, SHDs like Peter’s can still provide useful results for
many inputs, even if pathological ones must be handled by pattern
recognition or structural limits.

Yes, PARTIAL deciders have some uses, but they don't disprove the fact that no universal decider exists.

 6. Conclusion
-------------
Flibble now offers a reconciliatory yet disciplined model:
- The Halting Problem remains malformed in full generality due to category
errors.

But the halting problem isn't malformed, and thus your argument is just a bunch of hot air.

- But deciders can responsibly detect and handle malformed inputs using
structural heuristics.

But there is nothing "malformed" about the actual "pathological" program of the proof. It is a fully valid program to be decided on.

- Flibble's Law provides philosophical cover for SHDs to analyze — but not
execute — infinite behaviors.

Only if you allow your logic to allow the insertion of false statements.

 This is not a retreat from his original critique of Turing’s proof; it is
an evolution of it into a usable framework for analyzing decidability
within a restricted, type-safe domain.
 

The problem is you try to use an incorrect set of types, and thus fail.