On solutions and representations of spiking neural P systems with rules on synapses

Abstract

Spiking neural P systems, or SN P systems, are parallel and nondeterministic computing models inspired by spike processing of neurons. A variant of SN P systems known as SN P systems with rules on synapses, or RSSN P systems, makes use of the neuroscience idea where synapses or links between neurons perform spike processing instead of neurons. The spike processing in synapses instead of in neurons can allow RSSN P systems to have a smaller complexity due to their richer semantics, as compared to SN P systems. In this work we are first to provide the following: definitions of complexity classes of problems solved by RSSN P systems, depending if the problem has a uniform or nonuniform type of solution; both types of solutions to the NP-complete problem Subsetsum; matrix representation and simulation algorithm for RSSN P systems. Such representation and algorithm can aid in practical use of RSSN P systems. We also provide small computer simulations based on our representation and algorithm. Our simulations show that the nonuniform and uniform solutions to Subsetsum are better suited in the sequential CPU and the parallel GPU computer, respectively. Lastly, we remark several directions for investigations of RSSN P systems.