Asynchronous Spiking Neural P Systems with Anti-Spikes

Spiking neural P systems with anti-spikes (ASN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes and inhibitory spikes. ASN P systems working in the synchronous manner with standard spiking rules have been proved to be Turing completeness, do what Turing machine can do. In this work, we consider the computing power of ASN P systems working in the asynchronous manner with standard rules. As expected, the non-synchronization will decrease the computability of the systems. Specifically, asynchronous ASN P systems with standard rules can only characterize the semilinear sets of natural numbers. But, by using weighted synapses, asynchronous ASN P systems can achieve the equivalence with Turing machine again. It implies that weighted synapses has some "programming capacity" in the sense of achieving computing power. The obtained results have a nice interpretation: the loss in power entailed by removing the synchronization from ASN P systems can be compensated by using weighted synapses among connected neurons.