, . G(Y1,Y2,...,Yk)ÎA Fi(X1,X2,...,Xn)ÎA, i =1,2,..., k. G F:
G[F1(X1,...,Xn),...,Fk(X1,...,Xn)] = H(X1,...,Xn)
H(X1,...,Xn)ÎA, .
, .
1. . : F(0,..,0)=0. , X1X2, X1+X2, X1 Å X2.
, : X1X2, X1~X2, X1/X2. , .
G(0,...,0)=0 Fi(0,...,0)=0. G[F1(X1,...,Xn),...,Fk(X1,...,Xn)] = = G[(0,...,0),...,Fk(0,...,0)]=G(0,...,0)=0, .. H(0,...,0)=0. .
2. . : F(1,...,1)=1.
, X1X2, X1+X2, X1X2.
, : X1 Å X2, X1/X2.
, , , , .
3. . . F(X1,X2,...,Xn). F F*, :
F*(X1,X2,...,Xn)= ( 1, 2,..., n).
, F = X + Y, F*= .
, :
F(X1,X2,...,Xn)= ( 1, 2,..., n).
, :
(X1,X2,...,Xn) = F( 1, 2,..., n).
:
F=X1X2+X1X3+X2X3.
,
.
(Y1,..., Yn) (X1,..., Xn)= ( 1,..., n). G Fi: [F1(X1,..., Xn),..., Fk(X1,..., Xn)] = G[ (X1,..., Xn),..., (X1,..., Xn)] = G[F1( 1,..., n),...,F( 1,..., n)] = H( 1,..., n),
.. (X1,...,Xn) = H( 1,..., n).
4. . .
, , . , 0 ³ 0; 1 ³ 0; 1 ³ 1.
, (1,1,0,1) ³ (0,1,0,1). . , (0,1) (1,0) (0,1,0,1) (1,0,1) .
, . . : XY, X+Y, , : X~Y, XY, XÅY. , .
G(Y1,..., Yn) Fi(X1,..., Xn) - . G F:
|
|
G[F1(X1,..., Xn),..., Fk(X1,..., Xn)] = H(X1,..., Xn)
Fi G X1,..., Xn, . Fi , , . G , , . , , , .. H , .
5. . , , .. F(X1,X2,..., Xn) = A0 Å
Å A1X1 Å A2X2 Å... Å AnXn,
A0, A1,..., An - , .
: X Å Y, X ~Y = 1 Å X Å Y..
, . G(Y1,..., Yk) Fi(X1,..., Xn)- . :
G = A0 Å A1Y1 Å A2Y2 Å... Å AkYk,
Fi = B0i Å B1i Å B2i Å... Å BniXn.
Fi Yi G , Ai . . , H(X1,..., Xn) .
, .
. ; F1=X1ÅX2ÅX3; F2=X2ÅX3; F3=1ÅX3. G Fi:
G=1ÅX1ÅX2ÅX3ÅX2ÅX3Å1ÅX3=X1ÅX3.
3.7.