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Selfdual Boolean function 
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#1
Nov1812, 09:18 AM

P: 1

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 selfdual and f(0, 0, . . . , 0) = f(1, 1, . . . , 1), (ii) f is selfdual and f(0, 0, . . . , 0) = 1. I think for the first part, i need to find the number of functions that is not selfdual, 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. 


#2
Nov1812, 02:14 PM

Mentor
P: 11,601

For the first part, I would calculate the number of selfdual functions, and the number of functions where f(0, 0, . . . , 0) = f(1, 1, . . . , 1). As all selfdual functions satisfy that condition, both numbers are sufficient to get the answer.
For the second part: Well, you know f(1, 1, . . . , 1) as well. How many independent function values are left which you can choose? 


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