How many oblivious robots can explore a line

We consider the problem of exploring an anonymous line by a team of k identical, oblivious, asynchronous deterministic mobile robots that can view the environment but cannot communicate. We completely characterize sizes of teams of robots capable of exploring an n  -node line. For k

► Characterization of numbers k► Robots are identical, oblivious, asynchronous and deterministic.
► Exploration is possible if and only if either k=3k=3, or k>4k>4, or k=4k=4 and n is odd.
► When exploration is possible, we give an exploration algorithm.
► For other values, we prove an impossibility result.