SNQ P Systems with Weights on Synapses

The spiking neural P systems with communication on request (SNQ P systems) are a class of computational models inspired by the information processing of the neurons. We are focusing in this paper especially on the neuron postsynaptic potentials. In the current setting the neuron-neuron communication is abstracted by a request communication pattern which make the SNQ P systems rather limited from the perspective of spike multiplication because spikes are mostly moved from one neuron to another. We introduce a variant of SNQ P systems that have weights on synapses, which influence the number of spikes received by the querying neuron. The computational power of this model is investigated and we show that 5 unbounded neurons are enough to compute all Turing computable sets of number, in generative mode, and that 37 neurons are enough to compute all unary partial recursive functions.