As a Continuation to my first question
I have found a way for determining the activity of each parameter.
Activity definition: activity of each parameter is its contribution to get the whole boolean function equal to 1 when itself becomes 1.
e.g.
f = x1; the activity of x1 is 1
f = x1 + x2; the activity of x1 is 1/2
complete example:
f = (x1 v x2') XOR (x1 v x3' x4).
act(x1) = ||f(x1 = 1)|| = ||(x2' XOR x3' x4) XOR (1 XOR 1)|| = || x2' XOR x3' x4|| = ||x2'|| + ||x3' x4|| - 2|| x2' x3' x4|| = 1/2 + 1/4- 2(1/8) = 1/2
act(x2) = ||f(x2 = 1)|| = ||1 XOR (x1 v x3' x4) XOR x1 XOR (x1 v x3' x4)|| = ||x1|| = 1/2
act(x3) = ||f(x3 = 1)|| = ||(x1 v x2') XOR (x1 v x4) XOR (x1 v x2') XOR x1|| = ||(x1 v x4) XOR x1|| = ||x1 v x4|| + ||x1|| -2||x1|| = 3/4 + 1/2 -2(1/2) = 1/4
act(x4) = ||f(x4 = 1)|| = ||(x1 v x2') XOR x1 XOR (x1 v x2') XOR (x1 v x3')|| = ||x1 XOR (x1 v x3')|| =||x1|| + || x1 v x3'|| + 2||x1|| = 1/2 + 3/4 -2(1/2) = 1/4
It seems that the norm and activity are related. However i still cant understand the detail of the calculations could any one explain the general idea for this?
Thanks