1
GATE CSE 2020
MCQ (Single Correct Answer)
+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?
L1 = {wxyx | w, x, y ∈ (0 + 1)+}
L2 = {xy | x, y ∈ (a + b)*, |x| = |y|, x ≠ y}
Which one of the following is TRUE?
2
GATE CSE 2018
MCQ (Single Correct Answer)
+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?
3
GATE CSE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the following context-free grammars:
$$\eqalign{ & {G_1}:\,\,\,\,\,S \to aS|B,\,\,B \to b|bB \cr & {G_2}:\,\,\,\,\,S \to aA|bB,\,\,A \to aA|B|\varepsilon ,\,\,B \to bB|\varepsilon \cr} $$
$$\eqalign{ & {G_1}:\,\,\,\,\,S \to aS|B,\,\,B \to b|bB \cr & {G_2}:\,\,\,\,\,S \to aA|bB,\,\,A \to aA|B|\varepsilon ,\,\,B \to bB|\varepsilon \cr} $$
Which one of the following pairs of languages is generated by $${G_1}$$ and $${G_2}$$, respectively?
4
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Which of the following languages are context-free?
$$$\eqalign{
& {L_1} = \left\{ {{a^m}{b^n}{a^n}{b^m}|m,n \ge 1} \right\} \cr
& {L_2} = \left\{ {{a^m}{b^n}{a^m}{b^n}|m,n \ge 1} \right\} \cr
& {L_3} = \left\{ {{a^m}{b^n}|m = 2n + 1} \right\} \cr} $$$
Questions Asked from Push Down Automata and Context Free Language (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
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