A-B<==>not(not(A)+B)
not(A) And not(B)<====>not(A OR B)
not(A) Ornot (B)<====>not(A AND B)
P指的是Not or,如P(a,b)=not(a or b);
P(a,b) = ~a & ~b
not(a) = P(a,a)
and(a,b)= P(P(a,a),P(b,b))
or(a,b) = P(P(a,b),P(a,b))
xor(a,b)= P(P(P(a,a),P(b,b)),P(a,b))
证明:
not(a) = ~a = ~a & ~a = P(a,a)
and(a,b) = a & b = ~(~a) & ~(~b) = P(not(a),not(b)) = P(P(a,a),P(b,b))
or(a,b) = a | b = ~(~(a|b)) = ~(~a & ~b) = ~P(a,b) = P(P(a,b),P(a,b))
xor(a,b) = ~a & b | a & ~b = ~(~(~a & b | a & ~b)) = ~(~(~a & b) & ~(a & ~b)) = ~((a | ~b) & (~a | b)) = ~(1 | 1 | a & b | ~a & ~b) = ~(a & b) & ~(~a & ~b) = P(and(a,b),P(a,b)) = P(P(P(a,a),P(b,b)),P(a,b))
Q(a,b) = ~a | ~b
not(a) = Q(a,a) 1
and(a,b) = Q(Q(a,b),Q(a,b)) 2
or(a,b) = Q(Q(a,a),Q(b,b)) 3
xor(a,b) = Q(Q(Q(a,a),b),Q(a,Q(b,b))) 5
记录下s大的分析