On 5/5/2025 1:37 PM, olcott wrote:Self-contradiction is semantically ill-formed and hasOn 5/5/2025 11:13 AM, Mr Flibble wrote:In other words, you're demonstrating that you don't understand proof by contradiction, a concept taught to and understood by high school students more than 50 years your junior.On Mon, 05 May 2025 11:58:50 -0400, dbush wrote:>
>On 5/5/2025 11:51 AM, olcott wrote:>On 5/5/2025 10:17 AM, Mr Flibble wrote:>What constitutes halting problem pathological input:>
>
Input that would cause infinite recursion when using a decider of the
simulating kind.
>
Such input forms a category error which results in the halting problem
being ill-formed as currently defined.
>
/Flibble
I prefer to look at it as a counter-example that refutes all of the
halting problem proofs.
Which start with the assumption that the following mapping is computable
and that (in this case) HHH computes it:
>
>
Given any algorithm (i.e. a fixed immutable sequence of instructions) X
described as <X> with input Y:
>
A solution to the halting problem is an algorithm H that computes the
following mapping:
>
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed
directly
>
>
>int DD()>
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
>
https://github.com/plolcott/x86utm
>
The x86utm operating system includes fully operational HHH and DD.
https://github.com/plolcott/x86utm/blob/master/Halt7.c
>
When HHH computes the mapping from *its input* to the behavior of DD
emulated by HHH this includes HHH emulating itself emulating DD. This
matches the infinite recursion behavior pattern.
>
Thus the Halting Problem's "impossible" input is correctly determined
to be non-halting.
>
>
Which is a contradiction. Therefore the assumption that the above
mapping is computable is proven false, as Linz and others have proved
and as you have *explicitly* agreed is correct.
The category (type) error manifests in all extant halting problem proofs
including Linz. It is impossible to prove something which is ill-formed
in the first place.
>
/Flibble
The above example is category error because it asks
HHH(DD) to report on the direct execution of DD() and
the input to HHH specifies a different sequence of steps.
>
nothing to do with proof by contradiction.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
| Date | Sujet | # | Auteur | |
| 3 May 26 |  … |
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