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Self-dual Boolean function

  1. Nov 18, 2012 #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 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.
     
  2. jcsd
  3. Nov 18, 2012 #2

    mfb

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    Staff: Mentor

    For the first part, I would calculate the number of self-dual functions, and the number of functions where f(0, 0, . . . , 0) = f(1, 1, . . . , 1). As all self-dual 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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