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We consider the problem of exploring an anonymous unoriented ring of size $n$by $k$ identical, oblivious, asynchronous mobile robots, that are unable tocommunicate, yet have the ability to sense their environment and take decisionsbased on their local view. Previous works in this weak scenario prove that $k$must not divide $n$ for a deterministic solution to exist. Also, it is knownthat the minimum number of robots (either deterministic or probabilistic) toexplore a ring of size $n$ is 4. An upper bound of 17 robots holds in thedeterministic case while 4 probabilistic robots are sufficient. In this paper,we close the complexity gap in the deterministic setting, by proving that nodeterministic exploration is feasible with less than five robots whenever thesize of the ring is even, and that five robots are sufficient for any $n$ thatis coprime with five. Our protocol completes exploration in O(n) robot moves,which is also optimal.

Optimal deterministic ring exploration with oblivious asynchronous robots