  We study the Gathering problem for n autonomous mobile robots in
semi-synchronous settings with persistent memory called light. It is well known
that Gathering is impossible in a basic model when robots have no lights, if
the system is semi-synchronous or even centralized (only one robot is active in
each time). On the other hand, Rendezvous (Gathering when n = 2) is possible if
robots have lights of various types with a constant number of colors. In this
paper, we extend the model of robots with lights so that Gathering algorithms
can be discussed properly. Then we show Gathering algorithms with three types
of lights in the semi-synchronous settings and reveal relationship between the
power of lights and other additional assumptions. The most algorithms shown
here are optimal in the number of colors they use.
