Normal forms for spiking neural P systems and some of its variants

Spiking Neural P (SN P) systems are membrane computing systems that are abstracted from the behavior of spiking neurons, or brain cells. These systems take advantage of various features, such as the ability of neurons to forget, the ability of neurons to create and remove synapses, and many others. Some variants of SN P systems are (1) SN P systems with Structural Plasticity, which include the ability to create and delete synapses, and (2) SN P systems with Rules on Synapses, which associates rules with synapses instead of with neurons. The main results of this work show that for SN P systems, having only one type of regular expression in the entire system is sufficient for universality. Moreover, for the two variants of SN P systems mentioned above, having a maximum of one rule per neuron and one regular expression in the system is sufficient for universality. For normal forms with such parameters, e.g. number of rules per neuron, types of regular expressions in the system, our universality results are optimal. We also show some optimisations on the types of neurons in a system, involving the removal of some unbounded neurons in favour of simpler and bounded neurons.