DFA String Examples

Clearly the language is infinite because there is infinite number of strings.
The idea behind this approach is very simple, follow the steps below and you will understand.

1. From start either 'a' or 'b' can come so state A and state B
2. Then second input is if 'a' then reach out to final state C
3. On state C(final state) we can accept everything, that's why a loop
4. On state B we if we have input 'b' then reject it as second symbol must be 'a'
5. D is a dead state and on it we can accept everything

Testing

1. Lets take one input string aab
2. Scan string from left to right
3. First input is a, so from state A we will go to state B
4. Second input is a, so from state B we will go to state C
5. Third input is b, so from state C we will go to state C itself(final state)