1

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

+2

-0.6

Which of the following languages is/are regular?

$${L_1}:\left\{ {wx{w^R}|w,x\, \in \left\{ {a,b} \right\}{}^ * } \right.$$ and $$\left. {\left| w \right|,\left| x \right| > 0} \right\},\,{w^R}$$ is the reverse of string $$w$$

$${L_2}:\left\{ {{a^n}{b^m}\left| {m \ne n} \right.} \right.$$ and $$m,n \ge \left. 0 \right\}$$

$${L_3}:\left\{ {{a^p}{b^q}{c^r}\left| {p,q,r \ge 0} \right.} \right\}$$

2

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 $${X_0}$$?

3

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 ____

4

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?

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

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