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Introduction to CFL
Consider the ...
Question
Consider the following language;
L
1
:
{
(
X
Y
)
m
x
m
y
m
|
m
>
0
}
L
2
:
{
X
∗
Y
∗
Z
∗
{
X
m
Y
m
Z
m
|
m
>
0
}
}
L
3
:
{
(
w
ϵ
{
0
,
1
}
∗
|
∃
K
≥
0
and
w
is a binary encoding of K
)
}
The number of the above languages which are CFL is________.
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Solution
L
1
is CSL.
L
2
is CFL.
L
2
=
(
X
m
Y
n
Z
p
|
m
,
n
,
p
≤
0
and
m
≠
p
}
L
3
is regular.
. So
L
3
is also CFL.
L
3
=
0
∗
(
1
+
10
∗
1
)
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0
Similar questions
Q.
Consider the following languages over the alphabet
∑
={0,1,c};
L
1
={
0
n
1
n
|
n
≥
0
}
L
2
={
w
c
w
r
|
w
ϵ
{0,1}*}
L
3
={
w
w
r
|
w
ϵ
{0,1}*}
Here,
w
r
is the reverse of the string w. Which of these languages are deterministic Context-free languages?
Q.
Conisder the following languages :
L
1
:
{
w
w
|
w
ϵ
{
a
}
∗
}
L
2
:
{
w
w
|
w
ϵ
{
a
b
}
∗
}
Which of the above languages in non - regular but CFL ?
Q.
Consider the following languages M and N
Then which of the above languages CFLs?
M
=
{
ω
ω
R
ω
ω
R
|
ω
∈
(
0
,
1
)
∗
}
N
=
{
ω
1
ω
1
R
ω
2
ω
2
R
|
ω
∈
(
0
,
1
)
∗
}
Q.
Which of the following languages is/are regular ?
L
1
:
{
w
x
w
R
∣
w
,
x
ϵ
{
a
,
b
}
∗
a
n
d
∣
w
∣
,
∣
x
∣
>
0
}
w
R
is the reverse of string w
L
2
:
{
a
n
b
m
∣
m
≠
n
a
n
d
m
,
n
≥
0
}
L
3
:
{
a
p
b
q
c
r
∣
p
,
q
,
r
≥
0
}
Q.
Consider the following language
I
.
{
w
R
x
R
w
R
y
R
|
w
,
x
,
y
∈
(
0
,
1
)
∗
}
I
I
.
{
x
w
x
R
|
w
,
x
∈
(
0
,
1
)
∗
}
I
I
I
.
{
w
,
x
R
w
y
R
|
w
,
x
,
y
∈
(
0
,
1
)
∗
}
I
V
.
{
w
x
R
w
R
x
|
w
,
x
,
y
∈
(
0
,
1
)
∗
}
Which languages above are regular ?
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