00:01
In this question, we have to design a dfa that will accept the language that is given to us in the question.
00:07
So let us see.
00:24
So this will be accepting this which is given to us in the question.
00:29
X then x belongs to 0 to 1.
00:43
Then there is star.
00:44
And then this is the summation that is 3 .hashtag 0 and it has x plus 2 .hashtag.
01:04
This is given to us in the question in the same way we are writing it here.
01:09
So it is divisible by 5.
01:14
So there are these steps that we have to follow for this.
01:25
So first we have to define the states.
01:35
So as you can see, we have there are in this we have to see the remainder 1, 2, 3, 4.
01:43
So for remainder 1 that is there that is for remainder 0 that is r 0 or we can say 0 of r 0.
01:56
So for remainder 0 the summation 3 dot this entire this thing that is this entire sentence that is there is divisible by 5 with a remainder of 0.
02:13
So with a remainder of 0.
02:18
So this is our first case.
02:20
Then we have to see this for 4.
02:23
So in the same way, we will give that this with r 1 with the remainder of 1.
02:34
So it is telling us that the summation of this is currently divisible by 5 with a remainder of 1.
02:44
So it is same in all the cases.
02:48
Just we have to change the remainder that is there.
02:51
So we will go up till 4 in this case that is r 4.
03:00
So we have to we have given this as the states.
03:03
Now we have to give the transition rules that is there.
03:08
So let us look at the transition rules that are there.
03:13
So from the state r 0 that is there, we if the next input is 0, then the transition to state will be r 0.
03:32
So if the next input.
03:34
So this will be from state r 0.
03:38
So here from state r 0, if the next input is 0, if the next input is 0, then the transition will be to state r 0.
03:55
Then if next will be if the next input that is there, if it is 1, then in this case, the transition will be to state r 1.
04:11
Then we will next see the transition or determine the transition from state r 1.
04:20
So this tells us that if the next input is 0.
04:27
So if the next this is for r 1, if the next input is 0, then the transition will be to state r 0...