1

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

+2

-0.6

Consider the following languages over the alphabet $$\sum { = \left\{ {0,\,1,\,c} \right\}:} $$

$$\eqalign{ & {L_1} = \left\{ {{0^n}\,{1^n}\,\left| {n \ge } \right.0} \right\} \cr & {L_2} = \left\{ {wc{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr & {L_3} = \left\{ {w{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr} $$

$$\eqalign{ & {L_1} = \left\{ {{0^n}\,{1^n}\,\left| {n \ge } \right.0} \right\} \cr & {L_2} = \left\{ {wc{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr & {L_3} = \left\{ {w{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr} $$

Here, $${w^r}$$ is the reverse of the string $$w.$$ Which of these languages are deterministic Context- free languages?

2

GATE CSE 2013

MCQ (Single Correct Answer)

+2

-0.6

Consider the $$DFA$$ $$A$$ given below.

Which of the following are **FALSE?**

$$1.$$ Complement of $$L(A)$$ is context - free.

$$2.$$ $$L(A)$$ $$ = \left( {{{11}^ * }0 + 0} \right)\left( {0 + 1} \right){}^ * {0^ * }\left. {{1^ * }} \right)$$

$$3.$$ For the language accepted by $$A, A$$ is the minimal $$DFA.$$

$$4.$$ $$A$$ accepts all strings over $$\left\{ {0,1} \right\}$$ of length at least $$2.$$

3

GATE CSE 2011

MCQ (Single Correct Answer)

+2

-0.6

Consider the languages $${L_1}$$, $${L_2}$$ and $${L_3}$$ are given below.
$$$\eqalign{
& {L_1} = \left\{ {{0^p}{1^q}\left| {p,q \in N} \right.} \right\} \cr
& {L_2} = \left\{ {{0^p}{1^q}\left| {p,q \in N} \right.\,\,and\,\,p = q} \right\}\,\,and \cr
& {L_3} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r\, \in N\,\,\,and\,\,\,p = q = r} \right.} \right\}. \cr} $$$

Which of the following statements is not TRUE?

4

GATE CSE 2011

MCQ (Single Correct Answer)

+2

-0.6

A deterministic finite automation $$(DFA)$$ $$D$$ with alphabet $$\sum { = \left\{ {a,b} \right\}} $$ is given below

Which of the following finite state machines is a valid minimal $$DFA$$ which accepts the same languages as $$D?$$

Questions Asked from Push Down Automata and Context Free Language (Marks 2)

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