Lecture $04,$ Exercises for Section $2\mathrm{.}3$

Show that the DFA in Figure $2-10$ is minimal.

$,$ igure $2-10$

Minimize the DFA defined by $Q=\{q_0,q_1,q_2,q_3,q_4,q_5,q_6,q_7,q_8,q_9\},$

where the accepting states are $\{q_3,q_4,q_8,q_9\},$ and the transition function, $,$

is defined as follows:

$(q_0,a)=q_1,(q_0,b)=q_9$

$(q_1,a)=q_8,(q_1,b)=q_2$

$(q_2,a)=q_3,(q_2,b)=q_2$

$(q_3,a)=q_2,(q_3,b)=q_4$

$(q_4,a)=q_5,(q_4,b)=q_8$

$(q_5,a)=q_4,(q_5,b)=q_5$

$(q_6,a)=q_7,(q_6,b)=q_5$

$(q_7,a)=q_6,(q_7,b)=q_5$

$(q_8,a)=q_1,(q_8,b)=q_3$

$(q_9,a)=q_7,(q_9,b)=q_8$

Find a minimal DFA for the following NFA. Draw the DFA.