Re: Unpartial Halt Decider 4.0

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).