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1
CSE303, Spring 2010
Solutions to Homework 1
Section 1.1
3
(c). False.
Counterexample
: Let
A
=
{
ab, cd
}
. Then, we have
A
R
=
{
ba, dc
}
, and
x
=
abdc
∈
(
A
∪
A
R
)
*
. On the other hand, any nonempty string in
A
*
must end
with
b
or
d
, and any nonempty string in (
A
*
)
R
must start with
b
or
d
. Thus
x /
∈
A
*
∪
(
A
*
)
R
.
6
. 0
13
.
Section 1.2
3
(a). (0+1)
*
0(0+1)
4
; or, more formally, (0+1)
*
0(0+1)(0+1)(0+1)(0+1).
3
(c). In general, we divide a string
w
into blocks of 0’s and 1’s like
0
· · ·
01
· · ·
10
· · ·
01
· · ·
1
· · ·
Then, a string
w
in the set under considertation has the property that each
block has length either 1 or 2. So, we may express it by
(0 + 00)(1 + 11)(0 + 00)(1 + 11)
· · ·
In other words, each substring of
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This note was uploaded on 10/20/2011 for the course CSE 303 taught by Professor Ko,k during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Ko,K

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