$[4$ marks$]$ Let $M=(Q,,,q_0,F)$ be defined as the following DFA, where

$=\{0,1\},Q=\{q_0,q_1,q_2\},$ with $q_0$ the start state, $F=\{q_2\},$ and transition

function $$ given as a table below.

The language aceepted by $M$ is described by the regular expression $0^{**}{1}^{+}.$

Convert DFA $M$ to a context$-$free grammar that generates the same language.

$[5$ marks$]$ Convert the CFG from Question $2$ to a pushdown automata

given as a state diagram that recognizes the same language.