Re: The truth about the halting problem counter-example input

On 04/07/2026 06:11, olcott wrote:
> On 7/3/2026 9:43 PM, dbush wrote:
>> On 7/3/2026 10:37 PM, olcott wrote:
>>> On 7/3/2026 9:19 PM, dbush wrote:
>>>> On 7/3/2026 10:05 PM, olcott wrote:
>>>>> On 7/3/2026 8:58 PM, dbush wrote:
>>>>>> On 7/3/2026 9:52 PM, olcott wrote:
>>>>>>> On 7/3/2026 5:51 PM, André G. Isaak wrote:
>>>>>>>> On 2026-07-03 16:37, olcott wrote:
>>>>>>>>> On 7/3/2026 1:47 PM, André G. Isaak wrote:
>>>>>>>>>> On 2026-07-03 12:36, olcott wrote:
>>>>>>>>>>> On 7/3/2026 1:18 PM, dbush wrote:
>>>>>>>>>>
>>>>>>>>>>>> If an algorithm takes an input and produces an output, that 
>>>>>>>>>>>> is by definition a mapping. 
>>>>>>>>>>> That only proves that the definition is incoherent.
>>>>>>>>>>> The coherent way that it actually works is that
>>>>>>>>>>> inputs are transformed into outputs by applying
>>>>>>>>>>> finite string transformation rules to inputs to
>>>>>>>>>>> derive outputs.
>>>>>>>>>>
>>>>>>>>>> Apparently you don't understand the difference between a 
>>>>>>>>>> mapping and an algorithm. They are two different things.
>>>>>>>>>>
>>>>>>>>>> André
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> A function that ignores its input and only returns 0
>>>>>>>>> is not any sort of halt function.
>>>>>>>>
>>>>>>>> He was defining 'mapping', not 'halt function'.
>>>>>>>>
>>>>>>>> André
>>>>>>>>
>>>>>>>
>>>>>>> A actual halt function must compute 
>>>>>> The mathematical halting function:
>>>>>>
>>>>>
>>>>> When you actually implement this concretely 
>>>>
>>>> We find that it is not possible, as Linz and others have proved.
>>>>
>>>
>>> Impossible requirements are incorrect requirements.
>>>
>>
>> Nope.  Requirements are requirements for a reason.  If they can't be 
>> satisfied, then that's just the way it is.
>>
> 
> The halting problem requires a decider that correctly reports the halt 
> status of an input that does the opposite of whatever it reports. The 
> meaning of these words prove that is logically impossible.
> 
>> I would like to have a single algorithm that can tell me whether any 
>> arbitrary algorithm with a given input will halt when executed 
>> directly, but unfortunately no such algorithm exists.
> 
> typedef int (*ptr)();
> int HHH(ptr P);
> 
> 01 int DD()
> 02 {
> 03   int Halt_Status = HHH(DD);
> 04   if (Halt_Status)
> 05     HERE: goto HERE;
> 06   return Halt_Status;
> 07 }
> 08
> 09 void main()
> 10 {
> 11   DD();
> 12   HHH(DD);
> 13 }
> 
> HHH is not accountable to report on the
> behavior of its caller on line 11.

It is if HHH reagards itself as a part of the input. But HHH is not
required to interprete the input that way. It could reject the input
for the undefined symbol HHH.

-- 
Mikko