1
GATE CSE 2021 Set 1
Numerical
+2
-0.67

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

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}.

The number of strings of length 100 accepted by the above pushdown automaton is ______

2
GATE CSE 2021 Set 1
+2
-0.67
Let $$\left\langle M \right\rangle$$ denote an encoding of an automation M. Suppose that ∑ = {0, 1}. Which of the following languages is/are NOT recursive?
A
L = { $$\left\langle M \right\rangle$$ | M is a PDA such that L(M) = ∑*}
B
L = { $$\left\langle M \right\rangle$$ | M is a DFA such that L(M) = Φ}
C
L = { $$\left\langle M \right\rangle$$ | M is a PDA such that L(M) = Φ}
D
L = { $$\left\langle M \right\rangle$$ | M is a DFA such that L(M) = ∑*}
3
GATE CSE 2020
+2
-0.67
Consider the following languages.

L1 = {wxyx | w, x, y ∈ (0 + 1)+}
L2 = {xy | x, y ∈ (a + b)*, |x| = |y|, x ≠ y}

Which one of the following is TRUE?
A
L1 is regular and L2 is context-free.
B
L1 is context-free but not regular and L2 is context-free.
C
Neither L1 nor L2 is context-free.
D
L1 is context-free but L2 is not context-free.
4
GATE CSE 2018
+2
-0.6
Consider the following languages:

$$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m + p = n + q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,\,\,{\rm II}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m = n$$ and $$p=q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,{\rm III}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|m = n = p$$ and $$p \ne q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$
$$\,\,\,\,{\rm IV}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|mn = p + q,$$ where $$\left. {m,n,p,q \ge 0} \right\}$$

Which of the languages above are context-free?

A
$${\rm I}$$ and $${\rm IV}$$ only
B
$${\rm I}$$ and $${\rm II}$$ only
C
$${\rm II}$$ and $${\rm III}$$ only
D
$${\rm II}$$ and $${\rm IV}$$ only
GATE CSE Subjects
EXAM MAP
Medical
NEET