  Leader election and arbitrary pattern formation are funda- mental tasks for a
set of autonomous mobile robots. The former consists in distinguishing a unique
robot, called the leader. The latter aims in arranging the robots in the plane
to form any given pattern. The solv- ability of both these tasks turns out to
be necessary in order to achieve more complex tasks. In this paper, we study
the relationship between these two tasks in a model, called CORDA, wherein the
robots are weak in several aspects. In particular, they are fully asynchronous
and they have no direct means of communication. They cannot remember any
previous observation nor computation performed in any previous step. Such
robots are said to be oblivious. The robots are also uniform and anonymous,
i.e, they all have the same program using no global parameter (such as an
identity) allowing to differentiate any of them. Moreover, we assume that none
of them share any kind of common coordinate mechanism or common sense of
direction and we discuss the influence of a common handedness (i.e.,
chirality). In such a system, Flochini et al. proved in [11] that it is
possible to elect a leader for n \geq 3 robots if it is possible to form any
pattern for n \geq 3. In this paper, we show that the converse is true for n
\geq 4 when the robots share a common handedness and for n \geq 5 when they do
not. Thus, we deduce that with chirality (resp. without chirality) both
problems are equivalent for n \geq 4 (resp. n \geq 5) in CORDA.
