1
GATE CSE 1996
+1
-0.3
Let $$L \subseteq \sum {^{^ * }\,}$$ where $$\,\sum { = \,\,\left\{ {a,b} \right\}\,\,}$$ which of the following is true?
A
$$L = \,\,\,\left\{ {\left. x \right|\,\,\,x} \right.$$ has an equal number of $$a's$$ and $$\,\left. {b's} \right\}$$ is regular
B
$$L = \left\{ {{a^n}{b^n}\left| {n \ge 1} \right.} \right\}$$ is regular
C
$$L = \,\,\,\left\{ {\left. x \right|\,\,\,x} \right.\,$$ has more $$a's$$ than $$\left. {b's} \right\}$$ is regular
D
$$L = \left\{ {{a^m}{b^n}\left| {m \ge 1,\,n \ge 1} \right.} \right\}$$ is regular
2
GATE CSE 1996
+2
-0.6
If $${L_1}$$ and $${L_2}$$ are context free languages and $$R$$ a regular set, one of the languages below is not necessarily a context free language. Which one?
A
$${L_1}$$$${L_2}$$
B
$${L_1}\, \cap \,{L_2}$$
C
$${L_1}\, \cap \,R$$
D
$${L_1}\, \cup \,{L_2}$$
3
GATE CSE 1996
Subjective
+2
-0
Let $$G$$ be a context free grammar where $$G = \left( {\left\{ {S,A,.B,C} \right\},\left\{ {a,b,d} \right\},P,S} \right)$$ with productions $$P$$ given below
\eqalign{ & S \to ABAC\,\,\,\,\,\,\,\,\,S \to aA{\mkern 1mu} \left| \varepsilon \right. \cr & S \to bB{\mkern 1mu} \left| \varepsilon \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,C \to d \cr}

($$\varepsilon$$ denotes the null string). Transform the given grammar $$G$$ to an equivalent context- free grammar $${G^1}$$ that has no $$\varepsilon$$ productions ($$A$$ unit production is of the from $$x \to y,\,x$$ and $$y$$ are non terminals).

4
GATE CSE 1996
+1
-0.3
Which of the following statements is false?
A
The halting problem for Turing machine is un-decidable
B
Determining whether ambiguity a context free grammar is un-decidable
C
Given two arbitrary context free grammars $${G_1}$$ and $${G_2}$$ whether $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)$$
D
Given two regular grammars $${{G_1}}$$ and $${{G_2}},$$ it is un-decidable whether $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)$$
GATE CSE Papers
2023
2022
2020
2019
2018
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
EXAM MAP
Medical
NEET