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On Two-Level Exclusive-or Majority Networks
January 1974 (vol. 23 no. 1)
pp. 34-41
W.E. Robbins, Department of Computer Science, North Carolina State University
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.
Index Terms:
Majority gate, restricted-affine-group (RAG) equivalence, threshold logic, two-level EXCLUSIVE-OR majority network, two-level EXCLUSIVE-OR weighted majority network, universal networks.
W.E. Robbins, L.D. Rudolph, "On Two-Level Exclusive-or Majority Networks," IEEE Transactions on Computers, vol. 23, no. 1, pp. 34-41, Jan. 1974, doi:10.1109/T-C.1974.223774
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