  Redback millisecond pulsars (hereafter redbacks) are a sub-population of
eclipsing millisecond pulsars in close binaries. The formation processes of
these systems are not clear. The three pulsars showing transitions between
rotation- and accretion-powered states belong to both redbacks and transient
low-mass X-ray binaries (LMXBs), suggesting a possible evolutionary link
between the them. Through binary evolution calculations, we show that the
accretion disks in almost all LMXBs are subject to the thermal-viscous
instability during certain evolutionary stages, and the parameter space for the
disk instability covers the distribution of known redbacks in the orbital
period - companion mass plane. We accordingly suggest that the abrupt reduction
of the mass accretion rate during quiescence of transient LMXBs provides a
plausible way to switch on the pulsar activity, leading to the formation of
redbacks, if the neutron star has been spun up to be an energetic millisecond
pulsar. We investigate the evolution of redbacks, taking into account the
evaporation feedback, and discuss its possible influence on the formation of
black widow millisecond pulsars.
