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 .
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