CS 360 final exam questions from Spring 2007
The following questions appeared on the CS 360 final exam for Spring 2007.
(The usual exam
cover sheet, formatting, and point values have been removed.)
1. Define a language
A
⊆ {
0, 1
}
∗
as follows:
A
=
{
w
∈ {
0, 1
}
∗
:
w
contains the substring 000, but does not contain the substring 0000
}
.
Give the state transition diagram of a DFA that recognizes
A
.
2. Consider the following NFA
N
:
q
1
q
2
1
0
0, 1
(a) Give the state transition diagram of a DFA that recognizes the language
L
(
N
)
.
(b) Give an NFA with
two states
that recognizes
L
(
N
)
.
3. Consider the following language over the alphabet
{
0
}
:
B
=
{
0
n
: either
n
is odd or
n
=
2
k
for some integer
k
≥
1
}
.
Prove that
B
is not regular.
4. Let
C
be the following language:
C
=
{
x
∈ {
0, 1
}
∗
:
x
does not contain either of the substrings 011101 or 1100
}
.
Prove that
C
is a contextfree language.
5. Prove that the following language over the alphabet
{
0, 1, #
}
is contextfree:
braceleftBig
x
#
y
#
z
:
x
,
y
,
z
∈ {
0, 1
}
∗
and
parenleftBig
x
=
y
R
or
y
=
z
R
or
z
=
x
R
parenrightBigbracerightBig
.
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 Spring '08
 JohnWatrous
 Formal language, Formal languages, state transition diagram, following language

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