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P-Realizable Boolean Functions and Universal Binary Neurons

  • Igor N. Aizenberg
  • Naum N. Aizenberg
  • Joos Vandewalle
Chapter

Abstract

The universal binary neurons are a central point of this Chapter. The mathematical models of the universal binary neuron over the field of the complex numbers, the residue class ring and the finite field are considered. A notion of the P-realizable Boolean function, which may be considered as a generalization of a notion of the threshold Boolean function, is introduced. It is shown that the implementation with a single neuron the input/output mapping described by non-threshold Boolean functions is possible, if weights are complex, and activation function of the neuron is a function of the argument of the weighted sum (similar to multi-valued neuron). It is also possible to define an activation function on the residue class ring and the finite field in such a way that the implementation of non-threshold Boolean functions will be possible on the single neuron with weights from these sets. P-realization of multiple-valued function over finite algebras and residue class ring in particular is also considered. The general features of P-realizable Boolean functions are considered, also as the synthesis of universal binary neuron.

Keywords

Weighting Vector Boolean Function Finite Field Threshold Function Acceptable Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Igor N. Aizenberg
    • 1
  • Naum N. Aizenberg
    • 1
  • Joos Vandewalle
    • 2
  1. 1.Neural Networks Technologies Ltd.Israel
  2. 2.Departement Elektrotechniek, ESAT/SISTAKatholieke Universiteit LeuvenBelgium

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