On 7/3/2026 9:43 PM, dbush wrote:It is if HHH reagards itself as a part of the input. But HHH is notOn 7/3/2026 10:37 PM, olcott wrote: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.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:The mathematical halting function: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
>
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.
>
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.
required to interprete the input that way. It could reject the input
for the undefined symbol HHH.
--
Mikko
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