Re: Unpartial Halt Decider 4.0

On 4/18/25 3:05 PM, Mr Flibble wrote:

On Fri, 18 Apr 2025 15:00:10 -0400, Richard Damon wrote:
 

On 4/18/25 2:45 PM, Mr Flibble wrote:

Hi!
>
I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider".  It is a Partial Halt Decider over the domain
of all *finite* program-input pairs excluding pathological input (a
manifestation of the self referencial category error).
>
It is a Simulating Halt Decider with *infinite resources*.
>
Turing’s statement of the problem included logically invalid inputs.
Once we correct the domain to disallow self-reference, the rest (of
*finite* size) are decidable.
>
/Flibble

>
If you are trying to say that you machine with infinite resources can
decide on an input that can only use finite resources (that your
definition of a "finite program" is that it has a finite total storage
space) then this is a solved problem from generations before. The
"geared" simulation system, with two simulators, one running two steps
to the others one step, and looking for duplicated state, was well know
known decades ago, and doesn't need unbounded storage, just finite
storage, the two simulators of the finite machines, and what it takes to
compare their state.
>
If you allow your input to represent actual Turing Equivalent machines,
which have finite program state, but unlimited tape storage, then you
haven't shown how you decide on them.
>
You also haven't shown how the inputs you want to exclude are "logically
invalid". They may not be "decided" on by the given halt decider, but
there is nothing "invalid" about them, once you actually require your
decider to be a PROGRAM, and thus fixed and defined code.
>
You still haven't answered how to actually DEFINE this "pathological
input", so your whole system, and the term, is still undefined, so you
haven't "created" a term, but just the idea of a term that you can't yet
figure out how to define (and my guess is actually definable without
just loosing Turing Completeness of your system as even an idea you get
close to).

 Flibble's Law (also known as The Principle of Computational Reciprocity):
 If a problem permits infinite behavior in its formulation, it permits
infinite analysis of that behavior in its decidability scope.
 /Flibble

No it doesn't. You may think it should, but to meet the actual requirements to provide the required knowledge it can't.
The fact that it might require infinite analysis became the answer to the question, that some things are just not knowable, which was the big question at the time, could mathematics create a method to answer all questions, and the result was a clear NO, as mathematics allows us to create problems with unknowable answers.