Re: Incorrect requirements --- Computing the mapping from the input to HHH(DD)

On 11/05/2025 13:17, Mr Flibble wrote:

On Sun, 11 May 2025 13:12:14 +0100, Richard Heathfield wrote:
 

On 11/05/2025 13:09, Mr Flibble wrote:

On Sun, 11 May 2025 12:57:21 +0100, Richard Heathfield wrote:
>

On 11/05/2025 12:48, Mr Flibble wrote:

On Sun, 11 May 2025 10:34:18 +0000, Alan Mackenzie wrote:
>

Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:

>
<snip>
>

Nope, I have formally defined the error that doesn't contradict
Peter's work.

>
You don't even understand what "formally" means.

>
Sure I do. I can formally define it again for you if you like? Here
is the formal definition:
>
What constitutes halting problem pathological input:
>
Input that would cause infinite recursion when using a decider of the
simulating kind.

>
When executed directly, such an input would either halt or not,
category error or no.
>
Which is it?

>
Peter's view:
* direct execution results in infinite recursion which is treated as
non-
halting.
>
Flibble's view:
* direct execution results in manifestation of the category error:
which in practice means a crash in the form of a stack fault (debatable
halting equivalance) for a decider with finite resources (stack space)
or non- halting for a decider with infinitie resources (stack space).

>
So what you're saying is that the pair of you can't decide.

 What is that supposed to mean?
 The infinite recursion is a manifestation of the category error; the
halting problem relies on two aspects: self-reference then diagonalization
but that latter can never happen as the former is invalid.
 

>
QED.

 All you have demonstrated is hand waving.

On the contrary, you described a category of decider program as "pathological input" that demonstrated that the Halting Problem proof is flawed.
The Halting Problem proof claims to prove that there are some programs whose termination status we can't know. You have devised a program category which you claim overturns this proof, and you claim that you can even describe the behaviour of at least one program in this category, but you... don't know its termination status.
Got it. :-)
Are you here all week?
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within