$(12$ points$)$ Select those CFGs$/$PDAs that derive$/$recognize $1=\{2|2\}$

a$)$

$$

$|$

$$

b$)$

$$

$$

$|$

c$)$

$$

$$

$|$

d$)$

$$

$|$

$$

e$)$ f$)$

$2.(15$ points$)$

$(12$ points$)$ Design a deterministic PDA for $=\{|+$; $,>0\}.$

$(3$ points$)$ Show an accepting configuration trace for the string $$ in $().$

$3.(15$ points$)$

$(12$ points$)$ Design a deterministic PDA for $=\{|$

$2+$; $>0,0\}.$ The division

follow the integer division $(1)/(2)=0,4/2=2,3/2=1.$

$(3$ points$)$ Show an accepting configuration trace for the string $$ in $().$

$4.(15$ points$)$ Build a deterministic PDA recognizing

$=\{+2()+1|,0\}$

$5.(10)$ points$)$ Construct a non$-$deterministic PDA recognizing $=\{|0$; $2\}$

$6.(15$ points$)$ Consider the following grammar G and answer the questions below:

$$

$|$

$|$

$|$

a$.(2$ pts$)$ What are the variables of G$?$

b$.(2$ pts$)$ What are the terminals of G$?$

c$.(1$ pt$)$ What is the start variable of G$?$