  We study a Rendezvous problem for 2 autonomous mobile robots in asynchronous
settings with persistent memory called light. It is well known that Rendezvous
is impossible when robots have no lights in basic common models, even if the
system is semi-synchronous. On the other hand, Rendezvous is possible if robots
have lights with a constant number of colors in several types lights. In
asynchronous settings, Rendezvous can be solved by robots with 4 colors of
lights in non-rigid movement, if robots can use not only own light but also
other robot's light (full-light), where non-rigid movement means robots may be
stopped before reaching the computed destination but can move a minimum
distance \delta > 0 and rigid movement means robots can reach the computed
destination. In semi-synchronous settings, Rendezvous can be solved with 2
colors of full-lights in non-rigid movement.
  In this paper, we show that in asynchronous settings, Rendezvous can be
solved with 2 colors of full-lights in rigid movement and in non-rigid movement
if robots know the value of the minimum distance \delta. We also show that
Rendezvous can be solved with 2 colors of full-lights in general non-rigid
movement if we consider some reasonable restricted class of asynchronous
settings.
