# Lower Bounds for the Computational Power of Networks of Spiking Neurons

### Abstract:

We investigate the computational power of a formal model for networks of
spiking neurons. It is shown that simple operations on phase differences
between spike-trains provide a very powerful computational tool that can in
principle be used to carry out highly complex computations on a small network
of spiking neurons. We construct networks of spiking neurons that simulate
arbitrary threshold circuits, Turing machines, and a certain type of random
access machines with real valued inputs. We also show that relatively weak
basic assumptions about the response and threshold functions of the spiking
neurons are sufficient to employ them for such computations.

**Reference:** W. Maass.
Lower bounds for the computational power of networks of spiking neurons.
*Neural Computation*, 8(1):1-40, 1996.