Costas Busch - RPI
1
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Costas Busch - RPI
2
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Costas Busch - RPI
3
M
$
M
%
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$
Costas Busch - RPI
4
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M
%
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M
'
Costas Busch - RPI
"
M
5
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%
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Costas Busch - RPI
6
!
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a
b
c
d
1
11
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Costas Busch - RPI
7
"
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q1
q2
q3
q4
1
11
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L
R
1
11
Costas Busch - RPI
8
*
δ (q1, a ) = (q2 , b, L)
*
1 0 1 0 11 0 11 0 1
Costas Busch - RPI
9
*
δ (q1, a ) = (q2 , b, L)
δ (q2 , b) = (q3 , c, R )
*
1 0 1 0 11 0 11 0 1 00 11 0 1 10 111 0 111 0 11
Costas Busch - RPI
10
(
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Costas Busch - RPI
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Costas Busch - RPI
12
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Costas Busch - RPI
13
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Costas Busch - RPI
"
14
$
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Costas Busch - RPI
15
!
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6
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Costas Busch - RPI
16
*
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0, 2, 4, 6,
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1, 2, 3, 4,
7
n +1
2n
Costas Busch - RPI
17
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1 3 7
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Costas Busch - RPI
18
6 8
7
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7
%
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9
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Costas Busch - RPI
2 2 2
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19
:
1
1
1
2
1
3
2
1
2
2
2
3
3
1
3
2
4
1
Costas Busch - RPI
1
4
20
1
1
1
2
1
3
2
1
2
2
2
3
3
1
3
2
4
1
Costas Busch - RPI
1
4
21
1
1
1
2
1
3
2
1
2
2
2
3
3
1
3
2
4
1
Costas Busch - RPI
1
4
22
1
1
1
2
1
3
2
1
2
2
2
3
3
1
3
2
4
1
Costas Busch - RPI
1
4
23
1
1
1
2
1
3
2
1
2
2
2
3
3
1
3
2
4
1
Costas Busch - RPI
1
4
24
1
1
1
2
1
3
2
1
2
2
2
3
3
1
3
2
4
1
Costas Busch - RPI
1
4
25
6
7
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1, 2, 3, 4, 5,
Costas Busch - RPI
26
)
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Costas Busch - RPI
27
%
.
S
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S
S
!
*
Costas Busch - RPI
28
s1, s2 , s3 ,
∈S
*
S
4
5
s1, s2 , s3 ,
t1, t2 , t3 ,
;
Costas Busch - RPI
29
*
,
q0
t1
x1 # s1
qs
Costas Busch - RPI
30
t2
x2 # s2
qs
t3
x3 # s3
qs
Costas Busch - RPI
31
<!
$
1
!
Costas Busch - RPI
32
*
+
{a, b, c}
!
7
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Costas Busch - RPI
33
6
7
a
aa
aaa
aaaa
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%
-
9
b
!
Costas Busch - RPI
34
:
(= 7
(
& =7
&
' =7
'
> =7
>
==========
Costas Busch - RPI
35
a
b
c
7
aa
ab
ac
ba
bb
bc
ca
cb
cc
aaa
aab
aac
......
Costas Busch - RPI
(
&
'
36
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,-
!
(-
;
Costas Busch - RPI
37
(= ?
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9
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Costas Busch - RPI
38
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Costas Busch - RPI
"
39
%
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Costas Busch - RPI
40
.
S
!
!
2
S
Costas Busch - RPI
S
!
41
"
S
! 1
S = {s1 , s2 , s3 , }
S
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Costas Busch - RPI
42
*
{s1, s3}
{s5 , s7 , s9 , s10 }
22
Costas Busch - RPI
43
)
!
,-
(-
*
7
s1
s2
s3
s4
{s1}
1
0
0
0
{s2 , s 3 }
0
1
1
0
{s1 , s 3 , s4 }
1
0
1
1
Costas Busch - RPI
44
.
-
4
5
! =
Costas Busch - RPI
45
7
*
t1
1
0
0
0
0
t2
1
1
0
0
0
t3
1
1
0
1
0
t4
1
1
0
0
1
Costas Busch - RPI
46
9
!
Costas Busch - RPI
47
t1
1
0
0
0
0
t2
1
1
0
0
0
t3
1
1
0
1
0
t4
1
1
0
0
1
0011
6
4!
5
Costas Busch - RPI
48
ti
!
+
1
-
!
ti
ti
!
!
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Costas Busch - RPI
49
"
2
S
Costas Busch - RPI
S
!
50
.
*
!
{a, b}
"
S = {a, b} = {λ , a, b, aa, ab, ba, bb, aaa, aab, }
*
!
Costas Busch - RPI
51
*
{a, b}
!
"
S = {a, b} = {λ , a, b, aa, ab, ba, bb, aaa, aab, }
*
!
!
S
L = {aa, ab, aab}
Costas Busch - RPI
52
*
{a, b}
!
"
S = {a, b} = {λ , a, b, aa, ab, ba, bb, aaa, aab, }
*
!
S
2 = {{λ},{a},{a, b}{aa, ab, aab}, }
S
L1 L2
L3
Costas Busch - RPI
L4
53
.
!
L1
L2
L3
Lk
M1
M2
M3
?
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Costas Busch - RPI
54
!
4
!
!
!
5
Costas Busch - RPI
55
.
!
Lk
.
!
Costas Busch - RPI
56