Abstract
We improve and extend a recent result showing that spiking neural P systems with the same rules in all neurons of the system (homogenous) and working in the max sequential manner are universal. The previous work in this area reported by the group led by Dr. Linqiang Pan did not put any bound on the number of neurons used. We believe this is an important question for any future practical implementation of such systems that deserves investigation, and we provide some results in this direction. Extending the aforementioned construction with the work of Korec on small register machines one could estimate the size of the previous construction at 105 neurons. We are able to improve this result and to show that an SNP system with 83 neurons having homogenous rules and working in the max sequential manner is universal. Several related results with respect to max-pseudo sequentiality mode are also obtained: 83 neurons are necessary for this case, too. When considering the case of systems without weighted synapses, we show that one needs at most 244 homogenous neurons for reaching universality in the max-pseudo sequentiality case.