# Self-dual Boolean function

• Nov 18th 2012, 05:53 AM
kanezila
Self-dual Boolean function
A Boolean function of n variables is a mapping f : {0, 1}^n to {0, 1}. . Determine the number of Boolean functions f of n variables such that
(i) f is not self-dual and f(0, 0, . . . , 0) = f(1, 1, . . . , 1),
(ii) f is self-dual and f(0, 0, . . . , 0) = 1.
I think for the first part, i need to find the number of functions that is not self-dual, then find the number of functions i need from it? For the second part,i absolutely have no clue, please help me with this question.
• Nov 18th 2012, 04:14 PM
chiro
Re: Self-dual Boolean function
Hey kanezila.

I'm sorry but I forget what the notion of a dual is for boolean functions. For those like myself can you remind me?
• Nov 18th 2012, 04:30 PM
Plato
Re: Self-dual Boolean function
Quote:

Originally Posted by chiro
Hey kanezila.
I'm sorry but I forget what the notion of a dual is for boolean functions. For those like myself can you remind me?

In any bit-string change a 1 to zero and a zero to a 1.
• Nov 18th 2012, 05:29 PM
chiro
Re: Self-dual Boolean function
Thanks for that Plato: makes a lot of sense (there are just a lot of different definitions of dual in mathematics).