  We present the results of the most sensitive and comprehensive survey yet
undertaken for radio pulsars and fast transients in the Andromeda galaxy (M31)
and its satellites, using the Westerbork Synthesis Radio Telescope (WSRT) at a
central frequency of 328 MHz. We used the WSRT in a special configuration
called 8gr8 (eight-grate) mode, which provides a large instantaneous
field-of-view, about 5 square degrees per pointing, with good sensitivity, long
dwell times (up to 8 hours per pointing), and good spatial resolution (a few
arc minutes) for locating sources. We have searched for both periodicities and
single pulses in our data, aiming to detect bright, persistent radio pulsars
and rotating radio transients (RRATs) of either Galactic or extragalactic
origin. Our searches did not reveal any confirmed periodic signals or bright
single bursts from (potentially) cosmological distances. However, we do report
the detection of several single pulse events, some repeating at the same
dispersion measure, which could potentially originate from neutron stars in
M31. One in particular was seen multiple times, including a burst of six pulses
in 2000 seconds, at a dispersion measure of 54.7 pc cm^-3, which potentially
places the origin of this source outside of our Galaxy. Our results are
compared to a range of hypothetical populations of pulsars and RRATs in M31 and
allow us to constrain the luminosity function of pulsars in M31. They also show
that, unless the pulsar population in M31 is much dimmer than in our Galaxy,
there is no need to invoke any violation of the inverse square law of the
distance for pulsar fluxes.
