automaton has three states:

the starting state $s,$

the working state $w,$ and

the final state $f.$

In the stack, in addition to the bottom symbol $$,$ we have:

either one or several Cs $--$ indicating how many more Cs than Ls we have,

or one or several Ls $--$ indicating how many more Ls than Cs we have.

The transitions are as follows:

From $s$ to $w,$ the transition is $,$$$.$

From $w$ to $f,$ the transition is: $,.$

From $f$ to $f,$ we have two transitions: $,C$ and $,$$$.$

From w to w$,$ we have the following transitions:

If we see the symbol $L$ and $C$ is on top of the stack, we delete the top $C,$ i$.$e$.,$ we have transition $L,C.$

If we see the symbol $C$ and $L$ is on top of the stack, we delete the top $L$ from the stack, i$.$e$.,$ we have transition $C,L.$

$($Due February $7)$ Show, step by step, how the following grammar describing sequences of simple assignment statements will generate the expression

$a=2$;$b=a$;

In this grammar, D stands for digit, $L$ stands for letter, $S$ stands for statement. The rules are:

$D0$

$..$

$D9$

$La$

$...$

$Lz$

$SL=D$;

$SL=L$;

$SSS$