1
GATE CSE 2022
MCQ (More than One Correct Answer)
+2
-0

Consider the following languages:

L1 = {an wan | w $$\in$$ {a, b}*}

L2 = {wxwR | w, x $$\in$$ {a, b}*, | w | , | x | > 0}

Note that wR is the reversal of the string w. Which of the following is/are TRUE?

A
L1 and L2 are regular.
B
L1 and L2 are context-free
C
L1 is regular and L2 is context-free.
D
L1 and L2 are context-free but not regular.
2
GATE CSE 2022
MCQ (More than One Correct Answer)
+2
-0

Consider the following languages:

$$\eqalign{ & {L_1} = \{ ww|w \in \{ a,b\} *\} \cr & {L_2} = \{ {a^n}{b^n}{c^m}|m,\,n \ge 0\} \cr & {L_3} = \{ {a^m}{b^n}{c^n}|m,\,n \ge 0\} \cr} $$

Which of the following statements is/are FALSE?

A
L1 is not context-free but L2 and L2 are deterministic context-free.
B
Neither L1 nor L2 is context-free.
C
L2, L3 and L2 $$\cap$$ L3 all are context-free.
D
Neither L1 nor its complement is context-free.
3
GATE CSE 2021 Set 2
MCQ (More than One Correct Answer)
+2
-0

For a string w, we define wR to be the reverse of w. For example, if w = 01101 then wR = 10110.

Which of the following languages is/are context-free?

A
{wxwRxR | w, x ∈ {0, 1}*}
B
{wwRxxR | w, x ∈ {0, 1}*}
C
{wxwR | w, x ∈ {0, 1}*}
D
{wxxRwR | w, x ∈ {0, 1}*}
4
GATE CSE 2021 Set 1
Numerical
+2
-0

In a pushdown automaton P = (Q, ∑, Γ, δ, q0, F), a transition of the form,

GATE CSE 2021 Set 1 Theory of Computation - Push Down Automata and Context Free Language Question 16 English 1

where p, q ∈ Q, a ∈ Σ ∪ {ϵ}, and X, Y ∈ Γ ∪ {ϵ}, represents

(q, Y) ∈ δ(p, a, X).

Consider the following pushdown automaton over the input alphabet ∑ = {a, b} and stack alphabet Γ = {#, A}.

GATE CSE 2021 Set 1 Theory of Computation - Push Down Automata and Context Free Language Question 16 English 2
The number of strings of length 100 accepted by the above pushdown automaton is ______

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