# Minimization of DFA

I have the following question

I have minimized the DFA as the following since the states can only be partitioned to [S0][S1 S2]

EDIT: Is my Minimization correct?

• Do you have a question? – Patrick Stevens Dec 2 '15 at 9:28
• Your minimized DFA is correct; the language in question is the set of non-empty words over the alphabet $\{a,b\}^*$. – Brian M. Scott Dec 2 '15 at 9:28
• @PatrickStevens Please see the update. – techno Dec 2 '15 at 10:58
• @BrianM.Scott Thanks.The rectangular state indicate the start state i think.Plus i think that the steps required to minimize would be writing the transition table.. then saying that only partition possible is [S0][S1 S2] .Hope thats enough.Its a 15 mark question including the general explanation. – techno Dec 2 '15 at 11:01
• @techno: I have to admit that I minimized it by eye. Not knowing exactly what minimization algorithm you’ve been taught, I can’t say how much explanation is really required. The wording suggests that you’re supposed to explain the general procedure for minimizing a DFA, not the details of this particular minimization. – Brian M. Scott Dec 2 '15 at 11:13