In search for "realistic" bio-inspired computing models, we consider asynchronous spiking neural P systems, in the hope to get a class of computing devices with decidable properties. However, although the non-synchronization is known in general to decrease the computing power, in the case of using extended rules (several spikes can be produced by a rule) we obtain again the equivalence with Turing machines (interpreted as generators of sets of vectors of numbers). The problem remains open for the case of restricted spiking neural P systems, whose rules can only produce one spike. On the other hand, we prove that asynchronous spiking neural P systems, with a specific way of halting, using extended rules and where each neuron is either bounded or unbounded, are equivalent to partially blind counter machines and, therefore, have many decidable properties. © 2008 Springer-Verlag Berlin Heidelberg.
Asynchronous spiking neural P systems: Decidability and undecidability / Cavaliere, M.; Egecioglu, O.; Ibarra, O. H.; Ionescu, M.; Paun, G.; Woodworth, S.. - 4848:(2008), pp. 246-255. (Intervento presentato al convegno 13th International Meeting on DNA Computing, DNA13 tenutosi a Memphis, TN, usa nel 2007) [10.1007/978-3-540-77962-9_26].