The most robust design for digital logics of multiple variables based on neurons with complex-valued weights

Neurons with complex-valued weights have stronger capability because of their multi-valued threshold logic. Neurons with such features may be suitable for solution of different kinds of problems including associative memory, image recognition and digital logical mapping. In this paper, robustness or tolerance is introduced and newly defined for this kind of neuron ac-cording to both their mathematical model and the perceptron neuron's definition of robustness. Also, the most robust design for basic digital logics of multiple variables is proposed based on these robust neurons. Our proof procedure shows that, in robust design each weight only takes the value of i or -i, while the value of threshold is with respect to the number of variables. The results demonstrate the validity and simplicity of using robust neurons for realizing arbitrary digital logical functions.