$1.$ First, design a $`$pda$2`$ on line $131$ for the language of $\_$well formed parenthetical expressions$\_$; this language is defined as follows: $E$\backslash$rightarrow EE$|($E$)|\backslash$varepsilon$$.$ So for example, $$()()(())$$ is a well formed parenthetical expression, but $$)($$ is not.

$2.$ Second, design the function $`$PDAdet$`$ for running deterministic PDAs without $$\backslash$varepsilon$ on line $86.$ Note that the determinism and lack of $$\backslash$varepsilon$ makes the design and coding of the function much easier.