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.
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© 2000 Springer Science+Business Media Dordrecht
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Aizenberg, I.N., Aizenberg, N.N., Vandewalle, J. (2000). P-Realizable Boolean Functions and Universal Binary Neurons. In: Multi-Valued and Universal Binary Neurons. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3115-6_3
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DOI: https://doi.org/10.1007/978-1-4757-3115-6_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4978-3
Online ISBN: 978-1-4757-3115-6
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