Validating the notion of a simulating halt decider

[olcott]

MIT Professor Michael Sipser has agreed that the following verbatim
paragraph is correct (he has not agreed to anything else):

If simulating halt decider H correctly simulates its input D until H
correctly determines that its simulated D would never stop running
unless aborted then H can abort its simulation of D and correctly report
that D specifies a non-halting sequence of configurations.

void D(void (*x)())
{
int Halt_Status = H(x, x);
if (Halt_Status)
HERE: goto HERE;
return;
}

int main()
{
Output("Input_Halts = ", H(D, D));
}

Unless one rejects the notion of a universal Turing machine (UTM) then
they already know that H can base its halt status decision on the
behavior of D correctly simulated by H.

That theory of computation textbooks do not bother to mention this is
only because they never considered the notion of a simulating halt decider.

void D(void (*x)())
{
H(x, x);
}

It is dead obvious that (ignoring stack overflow) D correctly simulated
by H will never stop running unless H aborts its simulation of D.


--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer