Small universal spiking neural P systems with dendritic/axonal delays and dendritic trunk/feedback

Abstract

In spiking neural P (SN P) systems, neurons are interconnected by means of synapses, and they use spikes to communicate with each other. However, in biology, the complex structure of dendritic tree is also an important part in the communication scheme between neurons since these structures are linked to advanced neural process such as learning and memory formation. In this work, we present a new variant of the SN P systems inspired by diverse dendrite and axon phenomena such as dendritic feedback, dendritic trunk, dendritic delays and axonal delays, respectively. This new variant is referred to as a spiking neural P system with dendritic and axonal computation (DACSN P system). Specifically, we include experimentally proven biological features in the current SN P systems to reduce the computational complexity of the soma by providing it with stable firing patterns through dendritic delays, dendritic feedback and axonal delays. As a consequence, the proposed DACSN P systems use the minimum number of synapses and neurons with simple and homogeneous standard spiking rules. Here, we study the computational capabilities of a DACSN P system. In particular, we prove that DACSN P systems with dendritic and axonal behavior are universal as both number-accepting/generating devices. In addition, we constructed a small universal SN P system using 39 neurons with standard spiking rules to compute any Turing computable function.

Keywords: Axonal delays; Dendritic delays; Dendritic feedback; Dendritic trunk; Spiking neural P systems.