7. ( )[ ()→ (x)] º ( ) ()→( ) (x)
8. ( )[ () (x)] º ( ) () ( ) (x) ■
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XIX , - . - . , , , .
{0,1}, 0 1. = ××... × (n ) n, 0 1. , 1= = {0,1}. , 0 1 , , , , - , .
, 4-1.1. . n : 1, 2, . , , n , - = {0,1}; - . , - . , - .
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. , .
1.1. . - . f (x 1, , xn) + 1 . n x 1, , xn, (n + 1)- - f (x 1, , xn) f .
.1. f (x 1, , xn)
x 1 | ...... | xn 1 | xn | f (x 1, , xn 1, xn) |
...... | f (0, , 0, 0) | |||
...... | f (0, , 0, 1) | |||
...... | f (0, , 1, 0) | |||
...... | ..... | |||
...... | f (1, , 1, 1) |
:
(α 1, , αn) (β 1, , βn) ↔ i {1, , n }, , j < i αj = βj αi < βi. (1)
, 1- 0, 2- 1, 3- 2,..., 2 n 1. 2. , , , . . . ( ) , , ; , , , .., , , . , , 5.
2.
x 1 | x 2 | x 3 | f (x 1, x 2, x 3) |
. , 10 1024 . ( = 2, 3, 4) - .
1.2. . - , - . 3. :
3. 1-
x | φ 0 | φ 1 | φ 2 | φ 3 |
x. 4 4 - . φ 0 φ 3 0 1; x. 4-1.1 . φ 1 x: φ 1(x) = x. φ 2(x) x. - Ø, 1-1 1-2 . , x 0, ~ x.
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1-2 , . 0 1, F T , . .
. 16. 4.
4. 2-
x 1 | x 2 | ψ 0 | ψ 1 | ψ 2 | ψ 3 | ψ 4 | ψ 5 | ψ 6 | ψ 7 | ψ 8 | ψ 9 | ψ 10 | ψ 11 | ψ 12 | ψ 13 | ψ 14 | ψ 15 |
: (0, 0), (0, 1), (1, 0), (1, 1), - . 16 16 - : ψi 4 ψi 4- . , -, 1 2, .
16- - . 1 . F T 0 1 6 1-2.1 6 , 4. , .
1. ψ 0(x 1, x 2) = 0 0;
2. ψ 15(x 1, x 2) = 1 1;
3. ψ 3(x 1, x 2) = x 1 , 1- ;
4. ψ 12(x 1, x 2) = Ø x 1 x 1;
5. ψ 5(x 1, x 2) = x 2 , 2- ;
6. ψ 10(x 1, x 2) = Ø x 2 x 2;
7. ψ 1(x 1, x 2) = x 1Ù x 2 x 1 x 2 ( x 1& x 2 x 1 x 2);
8. ψ 7(x 1, x 2) = x 1Ú x 2 x 1 x 2;
9. ψ 13(x 1, x 2) = x 1 → x 2 x 1 x 2 ( 1 2 1 2;
10. ψ 6(x 1, x 2) = x 1 Å x 2 2 (- x 1 + x 2);
11. ψ 9(x 1, x 2) = x 1 x 2 x 1 x 2 ( x 1 x 2 x 2 = 1 , x 1 = 1);
12. ψ 14(x 1, x 2) = x 1 | x 2 ( );
13. ψ 8(x 1, x 2) = x 1 ↓ x 2 ( ).
, 2- , , 1- 2- ( ψ (x 1, x 2) ). ψ 2(x 1, x 2), ψ 4(x 1, x 2), ψ 11(x 1, x 2) .
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1. 4 . , 00, 01, 10 11 . .
a → b º Ø a Ú b (2)
a Å b º (Ø a Ù b) Ú (a Ù Ø b) (3)
a Å 1 º Ø a (4)
a b º (a Ù b) Ú (Ø a Ù Ø b) (5)
a | b º Ø(a Ù b) (6)
a ↓ b º Ø(a Ú b). (7)
x 1, x 2 x , , , ■
, ψ 3(x 1, x 2), ψ 12(x 1, x 2), ψ 5(x 1, x 2), ψ 10(x 1, x 2) , ψ 3(x 1, x 2) ψ 12(x 1, x 2) x 2, ψ 5(x 1, x 2) ψ 1(x 1, x 2) x 1. ψ 0(x 1, x 2) ψ 15(x 1, x 2) 0 1, .. . , .
4 , ψi :
5. 2-
x 1 | x 2 | x 1Ù x 2 | ψ 2 | x 1 | ψ 4 | x 2 | x 1Å x 2 | x 1Ú x 2 | x 1 ↓ x 2 | x 1 x 2 | Ø x 2 | ψ 11 | Ø x 1 | x 1→ x 2 | x 1 | x 2 | ||
, . , f 1 f 2 -, f 2 f 1 ⁄ - . , , - .
, , . sin2 x + cos2 x = 1, , x f (x) = sin2 x + cos2 x .
. ó . B ( ) . - V = { x 1, x 2, }. B V. dep () , , .
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) . xi V c B - -0,.. dep (xi) = dep (c)= 0. . -, , , c {0, 1}.
) . f (x 1, , xm) B, 1, , , = k. = f ( 1, , m) , dep () k + 1, 1, , .
, , . - , , . .
, , (. 2-1). ( ) , , - . . .
2. B, : 0, 1, Ø () Ú ().
: {0, 1, x 1, x 2, }. , 0. , - 1 Ø x 1, Ø x 2, , xi Ú xj (i, j = 1, 2, ) c Ú xi, xi Ú c (i = 1, 2, , c = 0, 1). , 2 Ø xi Ú xj, xi ÚØ xj, Ø xi ÚØ xj, Ø(Ø xi), (xi Ú xj)Ú xk, ..
, , Ø xi Ú xj (xi Ú xj)Ú xk 2. , Ø xi Ú xj 1 = Ø xi 2 = xj. 1 1, 2 0, 1 - = Ø xi Ú xj 1 + 1 = 2. (xi Ú xj)Ú xk 1 = xi Ú xj, 1 = xk, 1 0 , , = (xi Ú xj)Ú xk 2. , Ø xi ÚØ xj 2 ■
, -, . , .. , - , .
. dep () = 0. = xi V = c B. 1- - f (xi) = xi, 2- , c.
. ( ), B - k . (x 1, , xn) k + 1. , = f ( 1, , m), f (x 1, , xm) B = k. , k g 1(x 1, , xn), , gm (x 1, , xn). f (x 1, , xn) = f (g 1, , gm). , x 1, , xn .