Q$1$: $(15$ points$)(25$ minutes$)$ DFA, NFA, and $-$NFA

Consider the alphabet ${\displaystyle \underset{?}{\overset{?}{}}}=\{0,1\},$ and the regular expression $RE=0^{**}+(10{)}^{**}+101.$

Design a DFA that accepts this language.

Design an NFA that accepts this language.

Design an $-$NFA that accepts this language using the rules we covered in our lectures.