We study the expressive power of positive neural networks. The model uses
positive connection weights and multiple input neurons. Different behaviors can
be expressed by varying the connection weights. We show that in discrete time,
and in absence of noise, the class of positive neural networks captures the
so-called monotone-regular behaviors, that are based on regular languages. A
finer picture emerges if one takes into account the delay by which a
monotone-regular behavior is implemented. Each monotone-regular behavior can be
implemented by a positive neural network with a delay of one time unit. Some
monotone-regular behaviors can be implemented with zero delay. And,
interestingly, some simple monotone-regular behaviors can not be implemented
with zero delay
