Consider the following PDA:

:$+$ pda PDA$1$

title Example PDA

Q$=\{$qs$,$q$1,$q$2,$qf$\}$

S$=\{$a$,$b$\}$

T$=\{$a$,$b$,$$$\}$

q$0=$qs

F$=\{$qf$\}$

qs$->$q$1$:$\backslash$e$,\backslash$e$->$$

q$1$:a$,\backslash$e$->$a

q$1->$q$2$:$\backslash$e$,\backslash$e$->\backslash$e

q$2$:b$,$a$->\backslash$e

q$2->$qf:$\backslash$e$,$$$->\backslash$e

done.

This is the default PDA constructed in grafstate.

$($a$)10$ points Using grafstate, show the accepting computation of the

string aabb in this machine.

$($b$)7$ points What is the language of this PDA?

$($c$)6$ points Modify the machine so the number of a$$s can be $>=$ the

number of b$$s in the accepted strings.