Give informal descriptions and state diagrams of pushdown automata for the languages in Exercise 2.4.

Exercise 2.4.

Answer each part for the following context-free grammar G.

R → XRX | S

S → aT b | bT a

T → XTX | X | ε

X → a | b

a. What are the variables of G?

b. What are the terminals of G?

c. Which is the start variable of G?

d. Give three strings in L(G).

e. Give three strings not in L(G).

f. True or False: T ⇒ aba.

g. True or False: T ⇒^* aba.

h. True or False: T ⇒ T .

i. True or False: T ⇒^*T.

j. True or False: XXX ⇒^* aba.

k. True or False: X ⇒^* aba.

l. True or False: T ⇒^* XX.

m. True or False: T ⇒^* XXX.

n. True or False: S ⇒^* ε.

o. Give a description in English of L(G).