State diagram of DFA I'm trying to understand how to create state diagram of DFA. I found following example. On the first diagram I dont understand why we need fourth state when third state is final and there is no transitive function from fourth state to another state. And one more question about second diagram. Can't this automata take the word aaaa? 


Yes, the second DFA cannot take a word $aaaa$  as it is the language of words with at least two b's with no restriction on the number of $a$'s. Moreover, the first graph is wrong it accepts the language of exactly two $a$'s.
