0:00:00.000,0:00:04.680
So the first statement here is obviously not true. We have not even talked about time.
0:00:04.680,0:00:08.460
We have just pondered the existence of an algorithm for the halting problem
0:00:08.460,0:00:13.180
or more specifically, the non-existence of such an algorithm, and that is exactly what we have shown.
0:00:13.180,0:00:16.300
We have shown that there's no algorithm that solves the halting problem
0:00:16.300,0:00:21.490
if we allow that algorithm to be given any program and any input, but of course,
0:00:21.490,0:00:28.560
there are specific programs for which we can use algorithms to decide if they will go into loops or not
0:00:28.560,0:00:32.509
and this is for example one technique that is used in automated software testing.
0:00:32.509,0:00:36.260
It's not that there can be an algorithm that solves the halting problem
0:00:36.260,0:00:42.390
for specific cases or specific programs, the halting problem cannot be solved for the general case.
0:00:42.390,0:00:46.950
So if say you have an algorithm that can solve the halting problem for any program,
0:00:46.950,0:00:51.700
any input that you throw at it, that cannot be the case, but for specific,
0:00:51.700,9:59:59.000
special cases, we haven't shown anything so far.