Homogenous spiking neural P systems with anti-spikes

Spiking neural P systems with anti-spikes (ASN P systems, for short) are a class of neural-like computing models in membrane computing, which are inspired by neurons communication through both excitatory and inhibitory impulses (spikes). In this work, we consider a restricted variant of ASN P systems, called homogeneous ASN P systems, where any neuron has the same set of spiking and forgetting rules. As a result, we prove that such systems can achieve Turing completeness. Specifically, it is proved that two categories of pure form of spiking rules (for a spiking rule, if the language corresponding to the regular expression that controls its application is exactly the form of spikes consumed by the rule, then the rule is called pure) are sufficient to compute and accept the family of sets of Turing computable natural numbers.