On 7/3/2026 9:43 PM, dbush wrote:One such example is shown below where algorithm H1 does not correctly report the halt status of algorithm D1 which is built using the counter-example template.On 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.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.
>
void D(ptr *I)
{
// algorithm D1; input: I
ptr *X = D;
ptr *Y = I;
int result;
{
// algorithm H1; inputs: X,Y
result = 0 + (X-X) + (Y-Y);
}
if (result == 1) {
while (1);
}
}
int H(ptr *X, ptr *Y)
{
int result;
{
// algorithm H1; inputs: X,Y
result = 0 + (X-X) + (Y-Y);
}
return result;
}
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