Asynchronous spiking neural P systems with rules on synapses

Spiking neural P systems (shortly called SN P systems) are a group of neural-like computing models inspired by the functioning of spiking neurons. Recently, a new variant of SN P systems, called SN P systems with rules on synapses (RSSN P systems for short) were proposed. In such systems, at any moment the synapses with enabled rules should use one of the enabled rules, and all the synapses work in the synchronous manner. In this work, we consider RSSN P systems with a non-synchronized (i.e., asynchronous) use of rules: in any step, the synapses with enabled rules are not obligated to use the enabled rules. It is proved that the non-synchronization does not decrease the computing power in the case of using extended rules (several spikes can be produced for once spiking). We obtain again the equivalence with Turing machines (interpreted as generators of sets of natural numbers). Moreover, we construct a universal asynchronous RSSN P system with 94 neurons, which can compute any Turing computable function.