GATE CSE 2016 Set 1 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Which of the following languages is generated by the given grammar? $$$S \to aS|bS|\varepsilon $$$

$$\left\{ {{a^n}{b^m}|n,m \ge 0} \right\}$$

$$\left\{ {w \in \left\{ {a,b} \right\}{}^ * |w} \right.$$ has equal number of $$a’s$$ and $$\left. {b's} \right\}$$

$$\left\{ {{a^n}|n \ge 0} \right\} \cup \left\{ {{b^n}|n \ge 0} \right\} \cup \left\{ {{a^n}{b^n}|n \ge 0} \right\}$$

$${\left\{ {a,b} \right\}^ * }$$

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Which of the following decision problems are undecidable?

$$\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ Given $$NFAs$$ $${N_1}$$ and $${N_2},$$ is $$L\left( {{N_1}} \right) \cap L\left( {{N_2}} \right) = \Phi ?$$
$$\,\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,\,\,\,$$Given a $$CFG\,G = \left( {N,\sum {\,,P} ,S} \right)$$ and string $$x \in \sum {^ * } ,$$ does
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$x \in L\left( G \right)?$$
$$\,\,\,\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ Given $$CFGs\,\,{G_1}$$ and $${G_2},$$ is $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)?$$
$$\,\,\,\,\,\,{\rm I}V.\,\,\,\,\,\,\,\,\,\,$$ Given a $$TM$$ $$M,$$ is $$L\left( M \right) = \Phi ?$$

$${\rm I}$$ and $${\rm IV}$$ only

$${\rm II}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ only

$${\rm I}$$$${\rm I}$$$${\rm I}$$ and $${\rm IV}$$ only

$${\rm II}$$ and $${\rm IV}$$ only

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.3

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive $$0s$$ and two consecutive $$1s?$$

$$\left( {0 + 1} \right){}^ * 0011\left( {0 + 1} \right){}^ * + \left( {0 + 1} \right){}^ * 1100\left( {0 + 1} \right){}^ * $$

$$\left( {0 + 1} \right){}^ * \left( {00\left( {0 + 1} \right){}^ * 11 + 11\left( {0 + 1} \right){}^ * \left. {00} \right)} \right.\left( {0 + 1} \right){}^ * $$

$$\left( {0 + 1} \right){}^ * 00\left( {0 + 1} \right){}^ * + \left( {0 + 1} \right){}^ * 11\left( {0 + 1} \right){}^ * $$

$$00\left( {0 + 1} \right){}^ * 11 + 11\left( {0 + 1} \right){}^ * 00$$

GATE CSE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

Consider the transition diagram of a $$PDA$$ given below with input alphabet $$\sum {\, = \left\{ {a,b} \right\}} $$ and stack alphabet $$\Gamma = \left\{ {X,Z} \right\}.$$ $$Z$$ is the initial stack symbol. Let $$L$$ denote the language accepted by the $$PDA.$$ GATE CSE 2016 Set 1 Theory of Computation - Finite Automata and Regular Language Question 29 English

GATE CSE 2016 Set 1 Theory of Computation - Finite Automata and Regular Language Question 29 English

Which one of the following is TRUE?

$$L = \left\{ {{a^n}{b^n}|n \ge 0} \right\}$$ and is not accepted by any finite automata

$$L = \left\{ {{a^n}|n \ge 0} \right\} \cup \left\{ {{a^n}{b^n}|n \ge 0} \right\}$$ and is not accepted by any deterministic $$PDA$$

$$L$$ is not accepted by any Turing machine that halts on every input

$$L = \left\{ {{a^n}|n \ge 0} \right\} \cup \left\{ {{a^n}{b^n}|n \ge 0} \right\}$$ and is deterministic context-free

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