Gathering Semi-Synchronously Scheduled Two-State Robots

Summary

We study the problem Gathering for n autonomous mobile robots in synchronous settings with a persistent memory called light. It is well known that Gathering is impossible in the basic model (OBLOT) where robots have no lights, even if the system is semi-synchronous (called SSynch). Gathering becomes possible, however, if each robot has a light of some type that can be set to a constant number of colors. In the FCOM model, the robots can only see the lights of other robots. In the FSTA model, each robot can only observe its own light. In the LUMI model, all robots can see all lights. This paper focuses on FSTA robots with 2-colored lights in synchronous settings. We show that 2-color FSTA and FCOM robots cannot solve Gathering in SSynch without additional conditions, even with rigid movement and agreement of chiral ity and the minimum moving distance. We also improve the condition of the previous Gathering algorithm for FSTA robots with 2-color working in SSynch.