4
2015
31
:
.
–
•
–
,
L1
,w 2
h
1
?
(w) = :
,
?
.L1 /L2 = {x 2 ⌃ | 9y 2 L2 .xy 2 L1 }
.
L1 /L2 ,(
.h :
h
1
! ⌃?
.h (L) = {h (w) | w 2 L} ,L ✓
,
,L1 , L2 ✓ ⌃
,⌃
?
1
,
?
,
–
)
•
L2
–
•
h (w) = h (w1 ) · · · h (wn )
.
: ⌃? ! P ( ? )
! ⌃?
Sh :
1
.h (L) = x2L h 1 (x) ,L ✓ ⌃?
–
.{x 2
.
?
| h (x) = w}
•
1
:
NFA
L1
1
0
.h (1) = 01
h (0) = 101
.h
1
(L1 )
h
h (L1 ) ,L1
.L1 = L (01)
?
.1
.h (L1 ) = L (10101)
?
.2
.h
1
(L1 ) = L (1? ) .3
2
L2 = {w 2 ⌃? | #a (w) + #b (w) = #c (w)}
.
1
⌃ = {a, b, c}
:
?
h:⌃!
h (a)
=
0
h (b)
=
0
h (c)
=
1
= {0, 1}
:
?
h (L2 ) = {w 2
| #0 (w) = #1 (w)}
:
L0 = h (L2 ) \ L (0? 1? ) = 0i 1i | i
.
,
L2
0
.
L0
,
3
:
Skip (L) = {
1 3
···
2n 1
|
1 2
···
2n
.
h( ) =
, 2⌃
:
h
, 2⌃
h : ! ⌃?
.L
g:
1
(L) = {
1
···
n
| 81  i  n.
.⌃0 = {
0
0
i}
^
,
|
0}
L
= ⌃ [ ⌃0
.h ( 0 ) =
2 ⌃}
h 1 (L) ,
1
,
L1
! ⌃? ,
2 L, n
L
Skip (L)
2 { i,
i
.⌃
···
n
2 L}
.L1 = h
.
1
(L) \ (⌃⌃0 )
.g ( 0 ) = ✏
1
g (L1 ) = g h
.
(L) \ (⌃⌃0 )
Skip (L)
?
?
g( ) =
= Skip (L)
,
4
,
.⌃
,
L2
L1
L2 \L1 = {y 2 ⌃? | 9x 2 L2 .xy 2 L1 }
.
.L (M ) = L1
N =
M = (Q, ⌃, , q0 , F )
.L (N ) = L2 \L1
:
. 0 (q, ) = { (q, )}
N
2⌃
q2Q
,
2
,
n
L1
(Q, ⌃, 0 , S, F )
.
.S = q 2 Q | 9x 2 L2 . ˆ (q0 , x) = q
.L2
x
L1
0
o
•
•
,
x
.
:
y 2 L (N )
,
.y
(
)
,
9q 2 S. ˆ0 (q, y) \ F 6= ;
9q 2 Q, x 2 L2 . ˆ (q0 , x) = q ^ ˆ (q, y) 2 F
,
9x 2 L2 .xy 2 L1
,
,
9x 2 L2 . ˆ (q0 , xy) 2 F
, y 2 L2 \L1
5
:
A[B
/
.
B
A
.
A[B
` = max {`A , `B }
.
|w| `A
w2A
,|w| `
.
– xy i z 2 A ✓ A [ B
i 0
`B
w 2 A[B
.
|xy|  `A  ` ,|y| > 0
.
.
`A
w = xyz
w2B
6
,
,
.L
L
.
:
Lper
/
.{abc, acb, bca, bac, cab, cba}
,L
abc
L
.
Lper
?
.⌃ = {a, b}
,
.
?
Lper
Lper
L = {ab}
.
?
?
Lper \ {a} {b} ,
?
Lper \ {a} {b}
.
= a i bi | i
0
Lper
3
.