Small Universal Spiking Neural P Systems

In search for small universal computing devices of various types, we consider here the case of spiking neural P systems (SN P systems), in two versions: as devices computing functions and as devices generating sets of numbers. We start with the first case and we produce a universal spiking neural P system with 84 neurons. If a slight generalization of the used rules is adopted, namely, we allow rules for producing simultaneously several spikes, then a considerable improvement, to 49 neurons, is obtained. For SN P systems used as generators of sets of numbers, we find a universal system with restricted rules having 76 neurons, and one with extended rules having 50 neurons

Some Open Problems Collected During 7th BWMC

A few open problems and research topics collected during the 7th Brain- storming Week on Membrane Computing are briefly presented; further details can be found in the papers included in the volume.Junta de Andalucía P08 – TIC 0420

Some Quick Research Topics

Some research topics are suggested, in a preliminary form, in most cases dealing with (somewhat nonstandard) extensions of existing types of P systems

Further Open Problems in Membrane Computing

A series of open problems and research topics in membrane com- puting are pointed out, most of them suggested by recent developments in this area. Many of these problems have several facets and branchings, and further facets and branchings can surely be found after addressing them in a more careful manner

Membrane computing [and graph transformation]

Introduction to membrane computing, with an eye on graph theory issues

P Systems with Anti-Matter

After a short introduction to the area of membrane computing (a branch of natural computing), we introduce the concept of anti-matter in membrane computing. First we consider spiking neural P systems with anti-spikes, and then we show the power of anti-matter in cell-like P systems. As expected, the use of anti-matter objects and especially of matter/anti-matter annihilation rules, turns out to be rather powerful: computational completeness of P systems with anti-matter is obtained immediately, even without using catalysts. Finally, some open problems are formulated, too

New Normal Forms for Spiking Neural P Systems

We consider a natural restriction in the architecture of a spiking neural P system, namely, to have neurons of a small number of types (i.e., using a small number of sets of rules), and we prove that three types of neurons are su±cient in order to generate each recursively enumerable set of numbers as the distance between the first two spikes emitted by the system or as the number of spikes in a specified neuron, in the halting configuration. The case we investigate is that of spiking neural P systems with standard rules, with delays, but without using forgetting rules; similar normal forms remain to be found for other types of systems.Junta de Andalucía P08 – TIC 0420

On Parallel Array P Systems

We further investigate the parallel array P systems recently introduced by K.G. Subramanian, P. Isawasan, I. Venkat, and L. Pan. We rst make explicit several classes of parallel array P systems (with one or more axioms, with total or maximal parallelism, with rules of various types). In this context, some results from the above mentioned paper by Subramanian et al. are improved. A series of open problems are formulated

Notes About Spiking Neural P Systems

Spiking neural P systems (SN P systems, for short) are much investigated in the last years in membrane computing, but still many open problems and research topics are open in this area. Here, we first recall two such problems (both related to neural biology) from. One of them asks to build an SN P system able to store a number, and to provide it to a reader without losing it, so that the number is available for a further reading. We build here such a memory module and we discuss its extension to model/implement more general operations, specific to (simple) data bases. Then, we formulate another research issue, concerning pattern recognition in terms of SN P systems. In the context, we define a recent version of SN P systems, enlarged with rules able to request spikes from the environment; based on this version, so-called SN dP systems were recently introduced, extending to neural P systems the idea of a distributed dP automaton. Some details about such devices are also given, as a further invitation to the reader to this area of research.Junta de Andalucía P08 – TIC 0420