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 2010
MCQ (Single Correct Answer)
+2
-0.6
Consider the languages
$$$\eqalign{
& {L_1} = \left\{ {{0^i}{1^j}\,\left| {i \ne j} \right.} \right\},\,{L_2} = \left\{ {{0^i}{1^j}\,\left| {i = j} \right.} \right\}, \cr
& {L_3} = \left\{ {{0^i}{1^j}\,\left| {i = 2j + 1} \right.} \right\}, \cr
& {L_4} = \left\{ {{0^i}{1^j}\,\left| {i \ne 2j} \right.} \right\}, \cr} $$$
Questions Asked from Push Down Automata and Context Free Language (Marks 2)
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