Preface

Spiking neural P systems (in short, SN P systems) form a branch of membrane computing inspired from the way the neurons cooperate in the brain by exchanging spikes, electrical impulses of identical shapes. In short, neurons are placed in the nodes of a directed graph whose arcs correspond to axons and synapses; each neuron contains a number of spikes (in terms of membrane computing, identical ‘‘objects’’, identified by a fixed symbol) and rules for evolving the spikes; basically, two types of rules were considered, spiking and forgetting rules. A rule of the former type consumes a certain number of spikes and produces a spike which is sent to all neurons linked by a synapse starting in the spiking neuron (the spike is replicated in the case of multiple destinations); the produced spike leaves the neuron with a specified time delay. Spiking rules are applied under the control of an associated regular expression (over the one-letter alphabet): the rule is applied only if the neuron contains a number of spikes which belongs to the (unary) language described by the regular expression. A forgetting rule just removes spikes from neurons. The rules are chosen non-deterministically, one in each neuron, but the neurons evolve synchronously. The sequence of spikes along each axon defines a spike train. In particular, we can consider spike trains entering specified input neurons or emitted by specified output neurons. In this way we obtain a computing device, which can work in the accepting mode, in the generating mode, or in the transducing mode. The processed data can be the spike trains themselves (hence strings or infinite sequence), numbers (e.g., the time elapsed between the first two spikes of a spike train), or vectors of numbers (in the case of considering several input or output neurons).