Section $2\mathrm{.}3$ Deterministic and Nondeterministic Finite Acceptors

$\_($PRACTICE QUESTION$)$ Question $3$:

$**$ Convert the nfa defined by

$(q_0,a)=\{q_0,q_1\}$

$(q_1,b)=\{q_1,q_2\}$

$(q_2,a)=\{q_2\}$

with initial state $q_0$ and final state $q_2$ into an cquivalent dfa.

$\_($PRACTICE QUESTION$)$

Convert the nfa defined by

$(q_0,a)=\{q_0,q_1\}$

$(q_1,b)=\{q_1,q_2\}$

$(q_2,a)=\{q_2\}$

$(q_1,)=\{q_1,q_2\}$

with initial state $q_0$ and final state $q_2$ into an equivalent dfa.

$($GRADED $3$ points$)$ On $=\{0,1\}$

Draw the NFA figure defined by:

$(q0,l)=\{q1\}$

$(q0,)=\{q2\}$

$(q1,l)=\{q2\}$

$(q2,l)=\{q1\}$

$(q2,)=\{q3,q4\}$

$(q4,0)=\{q2\}$

q $0$ is the initial state and q $3$ is the final$($accepting$)$ state

Convert the NFA to a DFA $($show all your work$)$