On 11/13/2021 8:59 AM, Mr Flibble wrote:
> On Sat, 13 Nov 2021 09:54:33 -0500
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 11/13/21 9:25 AM, Mr Flibble wrote:
>>> Definition of the halting problem (from Wikipedia):
>>>
>>> For any program f that might determine if programs halt, a
>>> "pathological" program g, called with some input, can
>>> pass its own source and its input to f and then
>>> specifically do the opposite of what f predicts g will
>>> do. No f can exist that handles this case.
>>>
>>> The reason no f can exist for the case described is because it
>>> involves an INVALID infinite recursion and NOT because a general
>>> algorithm that can answer the question as to whether a program and
>>> its given input halts or runs for ever cannot exist.
>>>
>>> The key to understanding this is to recognize that the pathological
>>> infinite recursion described above is INVALID for the same reason
>>> that a recursive definition is INVALID; this is NOT the same as
>>> infinite recursion due to normal recursive function calls defined
>>> within a non-pathological program which can be viewed as:
>>>
>>> a) non-halting (infinite stack for recursion)
>>> b) non-halting (tail recursion being optimized into an infinite
>>> loop) c) halting (finite stack exhausted)
>>>
>>> /Flibble
>>>
>>
>> Incorrect.
>>
>> Given a claimed Turing Machine H that is supposed to return the
>> correct halting decision of the computation that is provided as its
>> input, the formation of the H^ Turing Machine is a simple mechanical
>> operation, as is converting the machine into a description <H^> to
>> give to H or H^. Thus there is on INVALID machine creation, given the
>> assumption that the original H was properly provided.
>>
>> There is nothing about the problem statement that requires the H to
>> be infinitely recursive, and there are many examples of partial halt
>> deciders that are most definitely valid.
>>
>> There is nothing INVALID in view here, merely that it has been shown
>> that when we look at the countably infinite number of Turing Machines
>> possible, that NONE of them have the needed property. It isn't that
>> there is something that has outlawed that machine, it just doesn't
>> exist.
>>
>> You miss the fact that infinite behavior is NOT 'INVALID' for Turing
>> Machines, we just require that Turing Machines that are classified as
>> 'Deciders' never have that type of behavior.
>
> You are incorrect. The halting problem as currently defined is basically
> a category error; recursive definitions are bogus.
>
> /Flibble
>

You are the only other person that ever noticed this. As it turns out
this recursive definition is simply decidable as never halting.

My new paper is
(a) much more compelling
(b) much simpler
(c) much shorter
(d) defines both H and P as pure functions thus computable.

Halting problem undecidability and infinitely nested simulation (V2)
November 2021 PL Olcott

https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer