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 in order to employ them
for such computations.