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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Unpartial Halt Deciders
Date: Fri, 18 Apr 2025 17:08:12 -0400
Organization: i2pn2 (i2pn.org)
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On 4/18/25 3:52 PM, Mr Flibble wrote:
> On Fri, 18 Apr 2025 12:32:41 -0700, Keith Thompson wrote:
> 
>> Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
>>> On Fri, 18 Apr 2025 12:25:36 -0700, Keith Thompson wrote:
>>>> Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
>>>>> I, aka Mr Flibble, have created a new computer science term, the
>>>>> "Unpartial Halt Decider".  It is a Halt Decider over the domain of
>>>>> all program-input pairs excluding pathological input (a manifestation
>>>>> of the self referencial category error).
>>>> [...]
>>>>
>>>> Do you have a rigorous definition of "pathological input"?
>>>>
>>>> Is there an algorithm to determine whether a given input is
>>>> "pathological" or not?
>>>>
>>>> I could define an is_prime() function like this:
>>>>
>>>>      bool is_prime(int n) {
>>>>          return n >= 3 && n % 2 == 1;
>>>>          // returns true for odd numbers >= 3, false for all others
>>>>      }
>>>>
>>>> I'll just say that odd numbers that are not prime are pathological
>>>> input, so I don't have to deal with them.
>>>
>>> Pathological input:
>>>
>>> Self-referencial to the decider.
>>
>> OK.
>>
>> Do you have a *rigorous* definition of "pathological input"?
>>
>> Is there an algorithm to determine whether a given input is
>> "pathological" or not?
> 
> In the general case pathological input is not computable as it is a
> category/type error (ergo not logically sound) so there is no algorithm
> that can detect it.  Specific forms of it can however be detected by a
> Simulating Halt Decider given certain constraints - see Mr Olcott for
> details.
> 
> /Flibble

In other words, you admit it is an undefined term, and even maybe 
undefinable term.

As I asked, how much do you need to change the copy of the decider used 
by the pathological input to make it not pathological.

Note, PO's restriction that the input must be a non-program by refering 
to the copy of the decider outside of itself just shows that you has no 
idea of what he is talking about, and that he isn't doing Computation 
Theory at all, just his own POOP.