Context free languages and Push-down automata

Question 11

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Here, w^r is the reverse of the string w. Which of these languages are deterministic Context-free languages?

• None of the languages

• Only L1

• Only L1 and L2

• All the three languages

Question 12

• L1 only
• L3 Only
• L1 and L2
• L2 and L3

Question 13

Consider the following statements about the context free grammar

G = {S → SS, S → ab, S → ba, S → Ε}
I. G is ambiguous
II. G produces all strings with equal number of a’s and b’s
III. G can be accepted by a deterministic PDA.

Which combination below expresses all the true statements about G?

• I only
• I and III only
• II and III only
• I, II and III

Question 14

Which one of the following grammars generates the language L = {aⁱ b^j | i ≠ j}

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• A

• B

• C

• D

Question 15

In the correct grammar of above question, what is the length of the derivation (number of steps starring from S) to generate the string a^lb^m with l ≠ m?

• max(l,m) + 2

• l + m + 2

• l + m + 3

• max(l, m) + 3

Question 16

Consider the languages:

L1 = {anbncm | n, m > 0} 
L2 = {anbmcm | n, m > 0} 

Which one of the following statements is FALSE?

• L1 ∩ L2 is a context-free language

• L1 U L2 is a context-free language

• L1 and L2 are context-free language

• L1 ∩ L2 is a context sensitive language

Question 17

Consider the languages:

L1 = {wwR |w ∈ {0, 1}*}
L2 = {w#wR | w ∈ {0, 1}*}, where # is a special symbol
L3 = {ww |  w ∈  (0, 1}*)

Which one of the following is TRUE?

• L1 is a deterministic CFL

• L2 is a deterministic CFL

• L3 is a CFL, but not a deterministic CFL

• L3 is a deterministic CFL

Question 18

The language {a^m bⁿ C^m+n | m, n ≥ 1} is

• regular

• context-free but not regular

• context sensitive but not context free

• type-0 but not context sensitive

Question 19

If the strings of a language L can be effectively enumerated in lexicographic (i.e., alphabetic) order, which of the following statements is true ?

• L is necessarily finite
• L is regular but not necessarily finite
• L is context free but not necessarily regular
• L is recursive but not necessarily context free

Question 20

Let G = ({S}, {a, b} R, S) be a context free grammar where the rule set R is S → a S b | SS | ε Which of the following statements is true?

• G is not ambiguous

• There exist x, y, ∈ L (G) such that xy ∉ L(G)

• There is a deterministic pushdown automaton that accepts L(G)

• We can find a deterministic finite state automaton that accepts L(G)