Q $4.$Let $L$ be a language over $=\{0,1,2\}$ where each $0$ is followed by a $1$ or $22.$

i$)$ Give a regular grammar that generates $L.$

ii$)$ Convert the regular grammar into an NFA.

iii$)$ Give a regular expression for $L.$

Q $5.$Let $RE=(01+10)((1^{*}0{)}^{*}+(0^{*}1{)}^{*}{)}^{*}.$

i$)$ Convert the above RE to an NFA $M$ using the procedure described in class.

ii$)$ Convert $M$ to a DFA $M^{\text{'}}.$

iii$)$ Minimize $M^{\text{'}}.$

Q $6.$Use generalized transition graphs $($GTG$)$ to convert the following NFAs $($alphabet $=\{a,b\})$ into regular expressions. Show your work, i$.$e$.,$ intermediate GTGs$.$

i$)$

ii$)$