1
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-0.3
Which two of the following four regular expressions are equivalent?
(i) $${\left( {00} \right)^ * }\left( {\varepsilon + 0} \right)$$
(ii) $${\left( {00} \right)^ * }$$
(iii) $${0^ * }$$
(iv) $$0\,\,{\left( {00} \right)^ * }$$
A
(i) and (ii)
B
(ii) and (iii)
C
(i) and (iii)
D
(iii) and (vi)
2
GATE CSE 1996
MCQ (Single Correct Answer)
+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
3
GATE CSE 1996
MCQ (Single Correct Answer)
+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).

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