Title :
On Two-Level Exclusive-or Majority Networks
Author :
Robbins, Woodrow E. ; Rudolph, Luther D.
Author_Institution :
Department of Computer Science, North Carolina State University
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.
Keywords :
Majority gate, restricted-affine-group (RAG) equivalence, threshold logic, two-level EXCLUSIVE-OR majority network, two-level EXCLUSIVE-OR weighted majority network, universal networks.; Boolean functions; Computer science; Dynamic range; Information science; Logic design; Logic devices; Mathematical model; Sequential circuits; Sufficient conditions; Vectors; Majority gate, restricted-affine-group (RAG) equivalence, threshold logic, two-level EXCLUSIVE-OR majority network, two-level EXCLUSIVE-OR weighted majority network, universal networks.;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/T-C.1974.223774
