On the computational complexity of spiking neural P systems

TL;DR

This paper proves that standard spiking neural P systems cannot simulate Turing machines efficiently with sub-exponential resources, but introduces a universal system with only 10 neurons that does so in linear time.

Contribution

It establishes lower bounds on the simulation efficiency of standard spiking neural P systems and constructs a minimal universal system with linear-time simulation.

Findings

Standard systems require exponential overheads to simulate Turing machines.

A universal spiking neural P system with 10 neurons achieves linear-time simulation.

The minimal number of neurons for universality is significantly reduced.

Abstract

It is shown that there is no standard spiking neural P system that simulates Turing machines with less than exponential time and space overheads. The spiking neural P systems considered here have a constant number of neurons that is independent of the input length. Following this we construct a universal spiking neural P system with exhaustive use of rules that simulates Turing machines in linear time and has only 10 neurons.