Affiliations: Research Group on Mathematical Linguistics, Universitat
Rovira i Virgili, Pl. Imperial Tàrraco 1, 43005 Tarragona, Spain.
E-mail: armandmihai.ionescu@urv.net | Institute of Mathematics of the Romanian Academy, PO
Box 1-764, 014700 Bucharest, Romania. E-mails: george.paun@imar.ro, gpaun@us.es | Department of Mathematics, School of Education, Waseda
University, 1-6-1 Nishi-waseda, Shinjuku-ku, Tokyo 169-8050, Japan.
E-mail: yokomori@waseda.jp
Abstract: This paper proposes a way to incorporate the idea of spiking neurons
into the area of membrane computing, and to this aim we introduce a class of
neural-like P systems which we call spiking neural P systems (in short, SN P
systems). In these devices, the time (when the neurons fire and/or spike) plays
an essential role. For instance, the result of a computation is the time
between the moments when a specified neuron spikes. Seen as number computing
devices, SN P systems are shown to be computationally complete (both in the
generating and accepting modes, in the latter case also when restricting to
deterministic systems). If the number of spikes present in the system is
bounded, then the power of SN P systems falls drastically, and we get a
characterization of semilinear sets. A series of research topics and open
problems are formulated.
Keywords: Spiking neurons, membrane computing, Turing computability, semilinear set
