  We study the Rendezvous problem for 2 autonomous mobile robots in
asynchronous settings with persistent memory called light. It is well known
that Rendezvous is impossible in a basic model when robots have no lights, even
if the system is semi-synchronous. On the other hand, Rendezvous is possible if
robots have lights of various types with a constant number of colors. If robots
can observe not only their own lights but also other robots' lights, their
lights are called full-light. If robots can only observe the state of other
robots' lights, the lights are called external-light.
  In this paper, we focus on robots with external-lights in asynchronous
settings and a particular class of algorithms (called L-algorithms), where an
L-algorithm computes a destination based only on the current colors of
observable lights. When considering L-algorithms, Rendezvous can be solved by
robots with full-lights and 3 colors in general asynchronous settings (called
ASYNC) and the number of colors is optimal under these assumptions. In
contrast, there exists no L-algorithms in ASYNC with external-lights regardless
of the number of colors. In this paper, we consider a fairly large subclass of
ASYNC in which Rendezvous can be solved by L-algorithms using external-lights
with a finite number of colors, and we show that the algorithms are optimal in
the number of colors they use.
