Question $2(18$ marks$).$ Construct pushdown automata that accept the following languages. You

should give your answers in the form of diagrams, and each transition should only push a single

symbol to the stack, i$.$e$.$ you should not use the shorthand used in the proof of Theorem $5\mathrm{.}6.$

a$)\{w\{a,b{\}}^{**}|w=w^R\},$ where $w^R$ denotes the reverse of $w.$

b$)\{\begin{array}{cc}w\{a,& b{\}}^{**}|w\end{array}$ contains more $\text{'}$a$\text{'}$s than $\text{'}$b$\text{'}$s