Computational power of sequential dendrite P systems

Abstract

Dendrite P (DeP) systems are a new variant of neural-like P systems, abstracted by the information processing and feedback mechanisms of dendrites. In the variant, a global block is assumed to synchronize all of neurons, hence, DeP systems work in synchronous mode. This paper investigates sequential version of the variant, that is, sequential dendrite P (SDeP) systems. Based on maximum number of spikes in neurons, two sequential modes are distinguished: max-sequentiality and max-pseudo-sequentiality strategies. SDeP systems have two interesting and recognizable features: (i) it behaves as a firing-storing process; (ii) cooperative firing mechanism. The computational completeness of SDeP systems is discussed. We prove that SDeP systems can be used as Turing universal number generating/accepting devices for max-sequentiality and max-pseudo-sequentiality strategies. We also establish a small universal function computing device of SDeP systems with 91 neurons in max-sequentiality strategy.