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CS 341 Automata Theory
Elaine Rich
Homework 5
Due: Thursday, February 15, 2007
This assignment covers Chapters 8 and 9.
1)
For each of the following languages
L
, state whether or not
L
is regular.
Prove your answer:
a)
{
a
i
b
j
:
i, j
≥ 0 and
i
+
j
= 5}.
b)
{
a
i
b
j
:
i, j
≥ 0 and
i

j
= 5}.
c)
{
w
=
xy
:
x
,
y
∈
{
a
,
b
}* and 
x
 = 
y
 and #
a
(
x
)
≥
#
a
(
y
)}.
d)
{
w
=
xyzy
R
x
:
x
,
y
,
z
∈
{
a
,
b
}*}.
e)
{
w
=
xyzy
:
x
,
y
,
z
∈
{
0
,
1
}
+
}.
f)
{
w
∈
{0, 1}* : #
0
(
w
)
≠
#
1
(
w
)}.
g)
{
w
∈
{
a
,
b
}* :
5
x
∈
{
a
,
b
}
+
(
w
=
x x
R
x
)}.
h)
{
w
∈
{
a
,
b
}* : the number of occurrences of the substring
ab
equals the number of occurrences of the
substring
ba
}.
i)
{
w
:
w
∈
{
a
–
z
}* and the letters of
w
appear in reverse alphabetical order}.
For example,
spoonfeed
∈
L
.
j)
L
0
*, where
L
0
= {
ba
i
b
j
a
k
,
j
≥
0, 0
≤
i
≤
k
}.
2)
For each of the following languages
L
, state whether
L
is regular or not and prove your answer:
a)
{
uww
R
v
:
u
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 Fall '08
 Rich

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