Re: Unpartial Halt Decider 4.0

On 4/18/25 5:12 PM, Mr Flibble wrote:

On Fri, 18 Apr 2025 17:04:43 -0400, Richard Damon wrote:
 

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.

 Yes it does. Again:
 It is about playing the game by the rules of the game:

And the rules of the game are that deciders must answer in finite time.

 If Busy Beavers are allowed an INFINITE tape in the context of the Halting
Problem then Simulating Halt Deciders are allowed INFINITE resources.
 /Flibble

Yes, the can have unbounded memory, just they still must have finite time (which means they will only use finite memory).
The problem is to try to detect a non-halting and non-repeating program to reject it.