Re: Halting Problem: What Constitutes Pathological Input

On 2025-05-06 17:26:11 +0000, Mr Flibble said:

On Tue, 06 May 2025 11:41:21 +0300, Mikko wrote:
 

On 2025-05-05 15:17:58 +0000, Mr Flibble said:
 

What constitutes halting problem pathological input:
 Input that would cause infinite recursion when using a decider of the
simulating kind.

 The "decider" is not a decider if there is an infinite recursion. Every
input causes an infinite exectuion on some non-decider.
It does not make sense to call every input "pathological".
It may make some sense to say that no input is "pathological" but that
does not make the word "pathological" useful.
 

Such input forms a category error which results in the halting problem
being ill-formed as currently defined.

 Every question whether a particluar Turing machine with a particular
input halts is a valid halting question. That the question may be too
hard for some does notmake it a category error.
 Besides, if there were a category error you would already have said
which word was of which category instead of which category.

 The two categories (types) in the category error are:
1) The decider.
2) The self-referencial (wrt the decider) input passed to the decider.

Where that error is? Which is the wrong type and which is the right one?
What makes the wrong type wrong in that particular context?
--
Mikko