Exclusive perpetual ring exploration without chirality

In this paper, we study the exclusive perpetual exploration problem with mobile anonymous and oblivious robots in a discrete space. Our results hold for the most generic settings: robots are asynchronous and are not given any sense of direction, so the left and right sense (\emph{i.e.} chirality) is decided by the adversary that schedules robots for execution, and may change between invocations of a particular robots (as robots are oblivious). We investigate both the minimal and the maximal number of robots that are necessary and sufficient to solve the exclusive perpetual exploration problem. On the minimal side, we prove that three deterministic robots are necessary and sufficient, provided that the size $n$ of the ring is at least $10$, and show that no protocol with three robots can exclusively perpetually explore a ring of size less than $10$. On the maximal side, we prove that $k=n-5$ robots are necessary and sufficient to exclusively perpetually explore a ring of size $n$ when $n$ is co-prime with $k$