Re: Unpartial Halt Deciders

On 4/18/25 9:50 AM, Mr Flibble wrote:

Hi!
 I, aka Mr Flibble, have created a new computer science term, the
"Unpartial Halt Decider".  It is a Halt Decider over the domain of all
program-input pairs excluding pathological input (a manifestation of the
self referencial category error).
 A simulating halt decider of the unpartial type *with infinite resources*
solves the halting problem as corrected to exclude the self referencial
category error.
 Turing’s statement of the problem included logically invalid inputs. Once
we correct the domain to disallow self-reference, the rest is decidable.
 /Flibble

So, how do you define your exclusion?
Does it include a program like D that uses a copy of a slightly modified version of the decider it is designed to defeat, but said modifications don't change the output of that decider?
How much do you need to modify the code for that case to be allowed?
Is your exclusion only for that particular decider, of is a program that has a pathological relationship to one decider not a valid program at all?
How does this not make your whole computation system not fail to be Turing Complete, as there are now program combinations that are just now not allowed to be programs?
Does your new definition handle the busy-beaver problem? (Which could be solved if we actually had halt deciders)
The problem you run into is that while this "pathological" relationship is a simple and obvious way to make an input that can't be decided by a particular decider, it isn't the only input that the decider will get wrong.