Spiking Neural P Systems with Anti-Spikes

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 b(c) -> b' or b(c) -> lambda, where b,b' are spikes or anti-spikes. Therefore, the regular expressions which control the spiking are the simplest possible, 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.