  We investigate exploration algorithms for autonomous mobile robots evolving
in uniform ring-shaped networks. Different from the usual Look-Compute-Move
(LCM) model, we consider two characteristics: myopia and luminosity. Myopia
means each robot has a limited visibility. We consider the weakest assumption
for myopia: each robot can only observe its neighboring nodes. Luminosity means
each robot maintains a non-volatile visible light. We consider the weakest
assumption for luminosity: each robot can use only two colors for its light.
The main interest of this paper is to clarify the impact of luminosity on
exploration with myopic robots. As a main contribution, we prove that 1) in the
fully synchronous model, two and three robots are necessary and sufficient to
achieve perpetual and terminating exploration, respectively, and 2) in the
semi-synchronous and asynchronous models, three and four robots are necessary
and sufficient to achieve perpetual and terminating exploration, respectively.
These results clarify the power of lights for myopic robots since, without
lights, five robots are necessary and sufficient to achieve terminating
exploration in the fully synchronous model, and no terminating exploration
algorithm exists in the semi-synchronous and asynchronous models. We also show
that, in the fully synchronous model (resp., the semi-synchronous and
asynchronous models), the proposed perpetual exploration algorithm is
universal, that is, the algorithm solves perpetual exploration from any
solvable initial configuration with two (resp., three) robots and two colors.
On the other hand, we show that, in the fully synchronous model (resp., the
semi-synchronous and asynchronous models), no universal algorithm exists for
terminating exploration, that is, no algorithm may solve terminating
exploration from any solvable initial configuration with three (resp., four)
robots and two colors.
