On 11/13/2021 8:25 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.

I brought up the idea that the halting theorem counter-examples specify
infinite recursion in this forum Mar 11, 2017, 3:13:03 PM

The problem is that every H-Hat needs a pair of inputs.

H-Hat takes an H-Hat as input and copies it so that it
can analyze how its input H-hat would analyze the copy
of H-Hat that it just made.

The input H-Hat would have to copy its own input H-Hat
so that it can analyze what its own input H-Hat would
do on its own input, on and on forever...

https://groups.google.com/g/comp.theory/c/NcFS02hKs1U/m/PlBF-1LRBAAJ

>
> 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

I would not say that it is invalid although that is what I did say in
2004. Sep 5, 2004, 11:21:57 AM comp.theory

The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.

The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error.

https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ

> 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
>

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