What is the minimal number of states for the DFA? Let the regular expression $R = ((a^*\cup \emptyset \cup \varepsilon^*)^*b)^*$ above $\Sigma = \{a,b,c,d\}$. What is the minimal number of states for a DFA accepting this regex?



$1$
$2$
$4$
$5$ or more


So for my understanding, this regex is equivalent to $(a^*b)^*$. I was able to build the following DFA, nevertheless, I know the answer is $2$. How is it possible?
Your $\Sigma=\{a,b,c,d\}$ so you have to add at least one dead state. The DFA is: