  An oblivious mobile robot is a stateless computational entity located in a
spatial universe, capable of moving in that universe. When activated, the robot
observes the universe and the location of the other robots, chooses a
destination, and moves there. The computation of the destination is made by
executing an algorithm, the same for all robots, whose sole input is the
current observation. No memory of all these actions is retained after the move.
When the universe is a graph, distributed computations by oblivious mobile
robots have been intensively studied focusing on the conditions for feasibility
of basic problems (e.g., gathering, exploration) in specific classes of graphs
under different schedulers. In this paper, we embark on a different, more
general, type of investigation.
  With their movements from vertices to neighboring vertices, the robots make
the system transition from one configuration to another. Viewing this
transition as the computation of an abstract function, we ask which functions
are computed by which systems. Our main interest is on identifying sets of
systems that are "universal", in the sense that they can collectively compute
all finite functions. We are able to identify several such classes of fully
synchronous systems. In particular, among other results, we prove the
universality of the set of all graphs with at least one robot, of any set of
graphs with at least two robots whose quotient graphs contain arbitrarily long
paths, and of any set of graphs with at least three robots and arbitrarily
large finite girths.
  We then focus on the minimum size that a network must have for the robots to
be able to compute all functions on a given finite set. We are able to
approximate the minimum size of such a network up to a factor that tends to 2
as $n$ goes to infinity.
