  We consider a Gathering problem for n autonomous mobile robots with
persistent memory called light in an asynchronous scheduler (ASYNC). It is well
known that Gathering is impossible when robots have no lights in basic common
models, if the system is semi-synchronous (SSYNC) or even centralized (only one
robot is active in each time). It is known that Gathering can be solved by
robots with 10 colors of lights in ASYNC. This result is obtained by combining
the following results. (1) The simulation of SSYNC robots with k colors by
ASYNC robots with 5k colors, and (2) Gathering is solved by SSYNC robots with 2
colors.
  In this paper, we improve the result by reducing the number of colors and
show that Gathering can be solved by ASYNC robots with 3 colors of lights. We
also show that we can construct a simulation algorithm of any unfair SSYNC
algorithm using k colors by ASYNC robots with 3k colors, where unfairness does
not guarantee that every robot is activated infinitely often. Combining this
simulation and the Gathering algorithm by SSYNC robots with 2 colors, we obtain
a Gathering algorithm by ASYNC robots with 6 colors. Our main result can be
obtained by reducing the number of colors from 6 to 3.
