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Construction of CFG Part - 1
The context f...
Question
The context free grammar given by
S
→
X
Y
X
X
→
a
X
|
b
X
|
λ
Y
→
b
b
b
Generates the language which is defined by regular expression:
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Solution
Option (c)
S
→
X
Y
X
X
→
a
X
|
b
X
|
λ
i.e.
(
a
+
b
)
∗
Y
→
b
b
b
S
→
(
a
+
b
)
∗
(
b
b
b
)
(
a
+
b
)
∗
So, option (c) is correct.
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Similar questions
Q.
Let L(R) be the language represented by regular expression R. Let L(G) be the language generated by a context free grammar G. Let L(M) be the language accepted by a Turing machine M.
Which of the following decision problems are undecidable?
I. Given a regular expression R and a string w,is
ω
ε
L(R)?
II. Given a context-free grammar G, is L(G)=
ϕ
III. Given a context-free grammar G, is L(G) =
∑
∗
for some alphabet
∑
?
IV. Given a Turing machine M and a string
ω
, is
ω
ε
L(M)?
Q.
Which of the following statements are true?
1. Every left-recursive grammar can be converted to a right-recursive grammar and vice-versa.
2. All
ε
-productions can be removed from any context-free grammar by suitable transformations.
3. The language generated by a context-free grammar all of whose productions are of the form X
→
w
or X
→
w
Y
(where, w is a string of terminals and Y is a non-terminal), is always regular.
4. The derivations trees of strings generated by a context-free grammar in Chomsky Normal Form are always binary trees.
Q.
Which one of the regular expressions given below defines the same language as defined by the regular expression R?
Q.
L
a
n
g
u
a
g
e
L
1
i
s
d
e
f
i
n
e
d
b
y
t
h
e
g
r
a
m
m
a
r
:
S
1
→
a
S
1
b
|
ε
L
a
n
g
u
a
g
e
L
2
i
s
d
e
f
i
n
e
d
b
y
t
h
e
g
r
a
m
m
a
r
:
S
2
→
a
b
S
2
|
ε
C
o
n
s
i
d
e
r
t
h
e
f
o
l
l
o
w
i
n
g
i
s
T
R
U
E
?
P
:
L
1
i
s
r
e
g
u
l
a
r
Q
:
L
2
i
s
r
e
g
u
l
a
r
Which one of the following is TRUE?
Q.
Let P be a regular language and Q be a context-free language such that
Q
⊆
P
. (For example, let P be the language represented by the regular expression
P
∗
q
∗
and Q be
{
p
n
q
n
∣
n
ϵ
N
}
Then which of the following is ALWAYS regular ?
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