Question $2$

$(6$ marks$)$

Complete the construction of the following deterministic pushdown automaton that accepts the language

$L=\{0^n{1}^{3n}in\{0,1{\}}^{**}$:$n0\}$

The automaton is given by $M=(Q,,,,q_0),$ where $=\{0,1\},=\{$$$,S\},Q=\{q_0,q_1\}$ and $$ by the following instructions. Complete the ride$-$hand side for each of the given instructions.

$q_{0}0$$$$

$q_{0}0S$

$q_{0}1$$$$

$q_{0}1S$

$q_0$$$$

$q_{0}S$

$q_{1}0$$$$

$q_{1}0S$

$q_{1}1$$$$

$q_{1}1S$

$q_1$$$$

$q_{1}S$