1

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

+2

-0.6

Consider the alphabet $$\sum { = \left\{ {0,1} \right\},} $$ the null/empty string $$\lambda $$ and the sets of strings $${X_0},\,{X_1},$$ and $${X_2}$$ generated by the corresponding non-terminals of a regular grammar. $${X_0},\,\,{X_1},\,$$ and $${X_2}$$ are related as follows.
$$$\eqalign{
& {X_0} = 1\,X{}_1 \cr
& {X_1} = 0{X_1} + 1\,{X_2} \cr
& {X_2} = 0\,{X_1} + \left\{ \lambda \right\} \cr} $$$

Which one of the following choices precisely represents the strings in $${X_0}$$?

Which one of the following choices precisely represents the strings in $${X_0}$$?

2

GATE CSE 2015 Set 1

Numerical

+2

-0

Consider the DFAs M and N given above. The number of states in a minimal DFA that accepts the language L(M) ∩ L(N) is___________.

Your input ____

3

GATE CSE 2015 Set 1

MCQ (Single Correct Answer)

+2

-0.6

Consider the NPDA $$\left\langle {Q = \left\{ {{q_0},{q_1},{q_2}} \right\}} \right.,$$ $$\Sigma = \left \{ 0, 1 \right \},$$ $$\Gamma = \left \{ 0, 1, \perp \right \},$$ $$\delta, q_{0}, \perp,$$ $$\left. {F = \left\{ {{q_2}} \right\}} \right\rangle $$ , where (as per usual convention) $$Q$$ is the set of states, $$\Sigma$$ is the input alphabet, $$\Gamma$$ is the stack alphabet, $$\delta $$ is the state transition function q

_{0}is the initial state, $$\perp$$ is the initial stack symbol, and F is the set of accepting states. The state transition is as follows:Which one of the following sequences must follow the string 101100 so that the overall string is accepted by the automaton?

4

GATE CSE 2014 Set 2

MCQ (Single Correct Answer)

+2

-0.6

Let $${L_1} = \left\{ {w \in \left\{ {0,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(110)'s$$ as $$(011)'s$$$$\left. \, \right\}$$. Let $${L_2} = \left\{ {w \in \left\{ {0,\,\,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(000)'s$$ as $$(111)'s$$$$\left. \, \right\}$$. Which one of the following is TRUE?

Questions Asked from Finite Automata and Regular Language (Marks 2)

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