Re: HHH(DD) --- COMPUTE ACTUAL MAPPING FROM INPUT TO OUTPUT

On 4/16/2025 4:01 PM, Mr Flibble wrote:

On Wed, 16 Apr 2025 21:21:52 +0100, Richard Heathfield wrote:
 

On 16/04/2025 21:10, Mr Flibble wrote:

On Wed, 16 Apr 2025 20:56:13 +0100, Richard Heathfield wrote:
>

On 16/04/2025 20:42, Mr Flibble wrote:

>
<snip>
>

the category error associated with pathological input.  One simply
has to add a third halting result of "pathological input" and we are
fine.

>
That's just another way of saying that the universal termination
analyser as specified (determining whether P(D) does or does not
eventually halt) can't be written. If it can't determine whether P(D)
halts, no matter how pathological, it isn't universal.

>
You forget that I have already solved this problem:

>
You forget that Turing has already proved otherwise.
>
<snip>
>

Obviously my idea necessitates extending the definition of a halt
decider:
>
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP.

>
And equally obviously you have answered a different question. The
Halting Problem requires a universal termination analyser that correctly
classifies all P(D) as halting or non-halting, and those are your only
choices. You don't have a solution to the Halting Problem; you have
solved the Flibble Problem.
>

Thoughts?  I am probably missing something obvious as my idea appears
to refute [Strachey 1965] and associated HP proofs which great minds
have mulled over for decades.

>
What you are missing is a program that meets the spec. Yeah, that's
pretty obvious.

  From Wikipedia, a definition of the halting problem:
 "In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and an
input, whether the program will finish running, or continue to run
forever. Alan Turing proved in 1936 that a general algorithm to solve the
halting problem for all possible program–input pairs cannot exist.
 For any program f that might determine whether 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. A key part of
the proof is a mathematical definition of a computer and program, which is
known as a Turing machine; the halting problem is undecidable over Turing
machines. It is one of the first cases of decision problems proven to be
unsolvable. This proof is significant to practical computing efforts,
defining a class of applications which no programming invention can
possibly perform perfectly."
 It is a category error for the pathological program (or any program) to
pass itself (either as source code or function address) and its input to a
halt decider from within the program itself (the two categories in the
error being the program/input pair and the halt decider). This category
error would manifest as infinite recursion if the halt decider was of the
simulating type.
 

Yes, then we three agree including PhD computer science professor
Eric Hehner PhD (see page 2 and references). publication/369971402_Simulating_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D

I, aka Mr Flibble, have uniquely identified this category error and have
thus solved the halting problem: halting and non-halting can be detected
by a simulating halting decider which can also reject self referencial
input as "not a program" due to such input being a manifestation of the
category error.
 Some f**ktards in this forum claim that the second paragraph in the
problem definition above is not actually a part of the problem but simply
a proof: this claim would be credible if not for the words "A key part of
THE proof ..." in the second paragraph.
 I, aka Mr Flibble, have thus won the Halting Problem Prize of $1,000,000.
 /Flibble

https://www.researchgate.net/publication/369971402_Simulating_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D --
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer