DFA String Examples

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Design a DFA such a way that
Let string is w, Number of a(w) mod 2 = 0 or Number of b(w) mod 2 = 0. This means number of a should be divisible by 2 as well as number of b should also be divisible by 2.

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Answer
If you see this question it just a bit variation of the above question.
The notations which we have used, we can choose which will be final state.

State Name	State Notation	Final State
A	ee	Yes
B	eo	Yes
C	oo	No
D	oe	Yes

Note As the requirement is either number_of_a(w) mod 2 = 0 or number_of_b(w) mod 2=0 or both.
That is the reason we are assigning multiple final states.

Testing

1. Take string ababbbb and traverse from left to right, here #a = 2 and #b = 5
2. from left first input is ‘a’ and start state ‘A’
3. so from state A we will go to state D
4. second input is ‘b’ and from D on b we will go to C
5. third input is ‘a’ and from C on a we will go state B
6. fourth input is ‘b’ and from B on b we will go to state A
7. fifth input is ‘b’ and from A on b we will go to state B
8. sixth input is ‘b’ and from B on b we will go to state A
9. seventh input is ‘b’ and from A we will go state B

After end of the string we are standing at state B, which is final state. So we say that string got accepted.

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