On the number of bipolar Boolean functions

نویسندگان

  • Ringo Baumann
  • Hannes Strass
چکیده

A Boolean function is bipolar iff it is monotone or antimonotone in each of its arguments. We investigate the number b(n) of n-ary bipolar Boolean functions. We present an (almost) closed-form expression for b(n) that uses the number a(n) of antichain covers of an n-element set. This is closely related to Dedekind’s problem, which can be rephrased as determining the number d(n) of Boolean functions that are monotone in all arguments. Indeed, a closed-form solution of a(n) would directly yield a closed-form solution of d(n), suggesting that determining a(n) is a non-trivial problem of itself. §

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عنوان ژورنال:
  • J. Log. Comput.

دوره 27  شماره 

صفحات  -

تاریخ انتشار 2017