On Two-Level Exclusive-or Majority Networks | IEEE Journals & Magazine | IEEE Xplore

On Two-Level Exclusive-or Majority Networks


Abstract:

It is shown that not all Boolean functions can be realized by a two-level EXCLUSIVE-OR majority network. However, if repeats at the first level are allowed, then it is sh...Show More

Abstract:

It is shown that not all Boolean functions can be realized by a two-level EXCLUSIVE-OR majority network. However, if repeats at the first level are allowed, then it is shown that such a network is universal. A minimal weight vector with respect to this latter network is defined. By using the restricted-affine-group (RAG) equivalence of Boolean functions, it is shown that if two functions are in the same RAG class, then they are realized by the same minimal weight vector to within permutations and/or sign changes.
Published in: IEEE Transactions on Computers ( Volume: C-23, Issue: 1, January 1974)
Page(s): 34 - 41
Date of Publication: 14 August 2006

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