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-1

-00:00:00,025 --> 00:00:02,900

-Okay, so now we're going to answer the question. So if we want

-

-2

-00:00:02,900 --> 00:00:06,520

-to consider all these inputs, and run them all on the software,

-

-3

-00:00:06,520 --> 00:00:09,490

-let's see how it will work. Let's assume that these are, 32

-

-4

-00:00:09,490 --> 00:00:12,280

-bit integers. So at this point what we will have is, a

-

-5

-00:00:12,280 --> 00:00:15,130

-number of combination, which is 2 to the 32, times 2 to

-

-6

-00:00:15,130 --> 00:00:18,390

-the 32. They're two integers. This is equal to 2 to the

-

-7

-00:00:18,390 --> 00:00:21,910

-64, which in turn, is more or less equal, to 10 to

-

-8

-00:00:21,910 --> 00:00:25,110

-the 19. So 10 to the 19 is the number of tests that

-

-9

-00:00:25,110 --> 00:00:27,960

-we need to run to cover the whole domain. Now let's assume

-

-10

-00:00:27,960 --> 00:00:31,400

-that we can run one test per nanosecond. So what that means

-

-11

-00:00:31,400 --> 00:00:34,290

-is that we can run 10 to the 9 tests per second,

-

-12

-00:00:34,290 --> 00:00:37,240

-and that's a lot. If we do the math, that results in 10

-

-13

-00:00:37,240 --> 00:00:40,750

-to the 10 seconds over all, because we have 10 to the

-

-14

-00:00:40,750 --> 00:00:43,760

-19 tests, we could run 10 to the 9 tests per second

-

-15

-00:00:43,760 --> 00:00:46,630

-so, we do the math, and we can run all these tests

-

-16

-00:00:46,630 --> 00:00:50,340

-in 10 to the 10 seconds. And what that corresponds to, it's about

-

-17

-00:00:50,340 --> 00:00:54,470

-600 years, so a lot of time. So even for such

-

-18

-00:00:54,470 --> 00:00:57,710

-a simple problem, a problem that takes two integers and adds them,

-

-19

-00:00:57,710 --> 00:01:00,990

-it will take more than 500 years to test it exhaustively. So

-

-20

-00:01:00,990 --> 00:01:04,690

-the bottom line here is that we just can't do exhaustive testing.