Spiking Neural P Systems with Anti-Spikes

Abstract

Besides usual spikes employed in spiking neural P systems, we consider “anti-spikes", which participate in spiking and forgetting rules, but also annihilate spikes when meeting in the same neuron. This simple extension of spiking neural P systems is shown to considerably simplify the universality proofs in this area: all rules become of the form bc → b′ or bc → lambda , where b,b′ are spikes or anti-spikes. Therefore, the regular expressions which control the spiking are the simplest possi- ble, identifying only a singleton. A possible variation is not to produce anti-spikes in neurons, but to consider some “inhibitory synapses", which transform the spikes which pass along them into anti-spikes. Also in this case, universality is rather easy to obtain, with rules of the above simple forms.