# DFA String Examples

Design a DFA such a way that

Let string is w, Number of a(w) mod 2 != 0

**and**Number of b(w) mod 2 != 0. This means number of a should not be divisible by 2 as well as number of b should also not be divisible by 2.

**Answer**

If you see this question it is also just a bit variation of the above question.

The notations which we have used, we can choose which will be final state.

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State Name | State Notation | Final State |

A | No | |

B | No | |

C | Yes | |

D | No |

**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

- Take string ababbbbabb and traverse from left to right, here #a = 3 and #b = 7
- from left first input is ‘a’ and start state ‘A’
- so from state A we will go to state D
- second input is ‘b’ and from D on b we will go to C
- third input is ‘a’ and from C on a we will go state B
- fourth input is ‘b’ and from B on b we will go to state A
- fifth input is ‘b’ and from A on b we will go to state B
- sixth input is ‘b’ and from B on b we will go to state A
- seventh input is ‘b’ and from A we will go state B
- eighth input is ‘a’ and from B we will go state C
- ninth input is ‘b’ and from state C we will go to state D
- tenth input is ‘b’ and from state D we will go to state B

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

**There could be many variations of the above question, try to figure out them**