Instructions:

For each automaton, draw the state diagrams clearly.

Write out the formal definitions $($ Q : set of states, $$ : input alphabet, $$ : transition function, $q_0$ :

start state, F : set of accept states$).$

For conversions $($NFA to DFA, $-$NFA to DFA$),$ show the intermediate steps clearly.

For DFA minimization, show the partitioning process step$-$by$-$step.

Submit your work in a neat, organized manner, including all required tables and diagrams.

Part $1.$ NFA $($Non$-$deterministic Finite Automaton$)$

$($a$)$ Construct an NFA for the following language over the alphabet

starts and ends with $\text{'}1\text{'}$

$($b$)$Design an NFA to accept the language of strings where the second$-$to$-$last character is $1.$

$($c$)$ Design an NFA for the following language starts with $\text{'}$ a $\text{'}$ and ends with $\text{'}$ b $\text{'}$ over

the alphabet $=\{a,b\}.$

Please answer the following questions as soon as possible by showing all the processes

and strictly following the instructions.