Context free languages and Push-down automata (original) (raw)

Consider the following languages.

Which one of the following statements is FALSE?

• L1 intersection L2 is context-free.
• Complement of L2 is recursive.
• Complement of L1 is context-free but not regular.

Which of the following pairs have DIFFERENT expressive power?

• Deterministic finite automata(DFA) and Non-deterministic finite automata(NFA)
• Deterministic push down automata(DPDA)and Non-deterministic push down automata(NPDA)
• Deterministic single-tape Turing machine and Non-deterministic single-tape Turing machine
• Single-tape Turing machine and multi-tape Turing machine

Let P be a regular language and Q be context-free language such that Q ⊆ P. (For example, let P be the language represented by the regular expression p*q* and Q be {pn qn | n ∈ N}). Then which of the following is ALWAYS regular?

(A) P ∩ Q

(B) P - Q

(C) ∑* - P

(D) ∑* - Q

Consider the languages L1, L2 and L3 as given below.

LI= {0P1q |p, q∈N}

L2={0p1q |p, q∈ N and p=q} and

L3= {0P1q0r |p, q, r∈ N and p =q = r}

Which of the following statements is **NOT TRUE?

[GATE | CS | 2011 |]

• Push Down Automata (PDA) can be used to recognize L1 and L2
• All the three languages are context free
• Turing machine can be used to recognize all the three languages

Consider the languages -
L1 = {0i1j | i != j}.
L2 = {0i1j | i = j}.
L3 = {0i1j | i = 2j+1}.
L4 = {0i1j | i != 2j}.

• Only L2 and L3 are context free
• Only L1 and L2 are context free

S -> aSa|bSb|a|b; The language generated by the above grammar over the alphabet {a,b} is the set of

• All odd length palindromes.
• Strings that begin and end with the same symbol
• All even length palindromes

Let L = L1∩L2, where L1 and L2 are languages as defined below:

L1 = {am bm can bn | m, n >= 0}

L2 = {ai bj ck | i, j, k >= 0}

Then L is

• Context free but not regular
• Recursively enumerable but not context free.

Which of following statement(s) is/are not correct? (I) Languages generated by the grammar S→aSa ∣ aa is not regular. (II) Languages generated by the grammar S→aSb ∣ aa is not regular. (III) Languages generated by the grammar S→S1|S3, S1→aS1c |S2|λ, S2→aS2b|λ, S3→aS3b|S4| λ, S4→bS4c|λ is {a^nb^mc^k | k = |n - m|, n≥0, m≥0, k≥0}. (IV) Languages generated by the grammar S→S1S3, S1→aS1c |S2|λ, S2→aS2b|λ, S3→aS3b|S4| λ, S4→bS4c|λ is {a^nb^mc^k | k = |n - m|, n≥0, m≥0, k≥0}.

Consider the following languages.

L1 = {ai bj ck | i = j, k ≥ 1}

L1 = {ai bj | j = 2i, i ≥ 0}

Which of the following is true?

• L1 is not a CFL but L2 is
• L1 ∩ L2 = ∅ and L1 is non-regular
• L1 ∪ L2 is not a CFL but L2 is
• There is a 4-state PDA that accepts L1, but there is no DPDA that accepts L2

Match the following:

There are 94 questions to complete.

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