Spiking Neural P Systems: A Tutorial

We brie y present (basic ideas, some examples, classes of spiking neural P systems, some results concerning their power, research topics) a recently initiated branch of membrane computing with motivation from neural computing. Further details can be found at the web page of membrane computing, from http://psystems.disco.unimib.it. 1 The General Framework The most intuitive way to introduce spiking neural P systems (in short, SN P systems) is by watching the movie available at http://www.igi.tugraz. at/tnatschl/spike_trains_eng.html, in the web page of Wofgang Maass, Graz, Austria: neurons are sending to each others spikes, electrical impulses of identical shape (duration, voltage, etc.), with the information encoded in the frequency of these impulses, hence in the time passes between consecutive spikes. For neurologists, this is nothing new, related drawings already appears in papers by Ramón y Cajal, a pioneer of neuroscience at the beginning of the last century, but in the recent years computing by spiking is a vivid research area, with the hope to lead to a neural computing of the third generation see [12], [21], etc. For membrane computing it is somehow natural to incorporate the idea of spiking neurons (already neural-like P systems exist, based on di erent ingredients see [23], e orts to compute with a small number of objects were recently made in several papers see, e.g., [2], using the time as a support of information, for instance, taking the time between two events as the result of a computation, was also considered see [3]), but still important di erences exist between the general way of working with multisets of objects in the compartments of a cell-like membrane structure as in membrane computing and the way the neurons communicate by spikes. A way to answer this challenge was proposed in [18]: neurons as single membranes, placed in the nodes of a graph corresponding to synapses, only one type of objects present