1
GATE CSE 1998
+2
-0.6
Which of the following statements is false?
A
Every finite subset of a non-regular set is regular
B
Every subset of a regular set is regular
C
Every finite subset of a regular set is regular
D
The intersection of two regular sets is regular
2
GATE CSE 1997
+2
-0.6
Which of the following languages over $$\left\{ {a,b,c} \right\}$$ is accepted by Deterministic push down automata?
A
$$\left\{ {w \subset {w^R}\left| {w \in \left\{ {a,b} \right\}{}^ * } \right.} \right\}$$
B
$$\left\{ {w{w^R}\left| {w \in \left\{ {a,b,c} \right\}{}^ * } \right.} \right\}$$
C
$$\left\{ {{a^n}{b^n}{c^n}\left| {n \ge 0} \right.} \right\}$$
D
$$\left\{ {w\left| w \right.} \right.$$ is palindrome over $$\left. {\left\{ {a,b,c} \right\}} \right\}$$
3
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
$${L_1}\, \cup \,{L_2}$$
4
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).

GATE CSE Subjects
EXAM MAP
Medical
NEET