Lower Bounds of Computational Power of a Synaptic Calculus *

The majority of neural net models presented in the literature focus mainly in the neural structure of nets, leaving aside many details about synapses and dendrites. This can be very reductionist if we want to approach our model to real neural nets. These structures tend to be very elaborate, and are able to process information in very complex ways (see [Mel 94] for details). We will introduce a new model, the S-Net (Synaptic-Net), in order to represent neural nets with special emphasis on synaptic and dendritic transmission. First, we present the supporting mathematical structure of S-Nets, initially inspired on Petri-Net formalism, adding a transition to transition connection type. There are two main components of S-Nets, neurones and synaptic/dendritic units (s/d units). All activation values are integers. Neurones are similar to McCulloch-Pitts neurones, and s/d units will process information within certain class of functions. S-Nets are able to represent spatial nets representations in a very natural way. We can easily modulate the length of an axon, the connection or branching of two dendrites or synaptic connections. Some examples are shown. Next, the focus will be on what kind of functions are suited to s/d units. We will present thre