Solving the XOR and parity N problems using a single universal binary neuron
 Igor Aizenberg
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A universal binary neuron (UBN) operates with complexvalued weights and a complexvalued activation function, which is the function of the argument of the weighted sum. The activation function of the UBN separates a whole complex plane onto equal sectors, where the activation function is equal to either 1 or −1 depending on the sector parity (even or odd, respectively). Thus, the UBN output is determined by the argument of the weighted sum. This makes it possible the implementation of the nonlinearly separable (nonthreshold) Boolean functions on a single neuron. Hence, the functionality of UBN is incompatibly higher than the functionality of the traditional perceptron. In this paper, we will consider a new modified learning algorithm for the UBN. We will show that classical nonlinearly separable problems XOR and Parity n can be easily solved using a single UBN, without any network. Finally, it will be considered how some other important nonlinearly separable problems may be solved using a single UBN.
 Title
 Solving the XOR and parity N problems using a single universal binary neuron
 Journal

Soft Computing
Volume 12, Issue 3 , pp 215222
 Cover Date
 200802
 DOI
 10.1007/s0050000702049
 Print ISSN
 14327643
 Online ISSN
 14337479
 Publisher
 SpringerVerlag
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 Authors

 Igor Aizenberg ^{(1)}
 Author Affiliations

 1. Department of Computer and Information Sciences, Texas A&M UniversityTexarkana, P.O. Box 5518, 2600 N. Robison Rd., Texarkana, TX, 75505, USA