Spike Trains in Spiking Neural P Systems

We continue here the study of the recently introduced spiking neural P systems, which mimic the way that neurons communicate with each other by means of short electrical impulses, identical in shape (voltage), but emitted at precise moments of time. The sequence of moments when a neuron emits a spike is called the spike train (of this neuron); by designating one neuron as the output neuron of a spiking neural P system Π, one obtains a spike train of Π. Given a specific way of assigning sets of numbers to spike trains of Π, we obtain sets of numbers computed by Π. In this way, spiking neural P systems become number computing devices. We consider a number of ways to assign (code) sets of numbers to (by) spike trains, and prove then computational completeness: the computed sets of numbers are exactly Turing computable sets. When the number of spikes present in the system is bounded, a characterization of semilinear sets of numbers is obtained. A number of research problems is also formulated.