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CS 341 Automata Theory
Elaine Rich
Homework 4
Due Thursday, Sept. 28 at 11:00
1)
Write regular expressions for the following languages:
a)
The set of binary representations, without leading 0’s, of integers that are divisible by 4.
b)
The set of binary representations, without leading 0’s, of integers that are powers of 4.
c)
The set of binary strings that have at least one occurrence of the substring 001.
d)
The set of binary strings that have no substring 001.
e)
The set of binary strings with at most one pair of consecutive 0’s and at most one pair of
consecutive 1’s. (This one is tricky and there isn’t a
simple
answer.)
f)
The set of all binary strings with the property none of its prefixes ends in 0.
g)
{
x
∈
{0, 1}* :
5
y
∈
{0, 1}* 
xy
 is even}
2)
Let
L
= {
w
∈
{
a
,
b
}* :
w
contains
bba
as a substring}.
Find a regular expression for {
a
,
b
}* 
L
.
3)
Consider the following FSM
M
.
Show a regular expression that describes
L
(
M
).
0
a
1
b
3
b
a
b
2
4)
Let
L
= {
w
∈
{
a
,
b
}* :
w
contains an even number of
a
’s and an odd number of
b’s
}.
Write a
regular grammar for
L
.
5)
Let
L
= {
w
∈
{
a
,
b
}* :
w
contains at least one of
baaba
or
bababb
as a substring}.
a)
Write a regular expression that describes
L
.
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 Fall '08
 Rich

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