Abstract. Many potential applications exist for multi-robot systems in various contexts related to safety and security. Terminating exploration is a basic building block for many of these applications. It requires that starting from a configuration where no two robots occupy the same location, every location needs to be visited by at least one robot, with the additional constraint that all robots eventually stop moving. We consider weak autonomous mobile robots, i.e., the are anonymous, oblivious, disoriented, and unable to (directly) communicate together. They are also myopic, i.e., they are cannot see beyond a certain fixed distance φ. We consider strong myopia that is, a robot can only sense robots located at its own and at its immediate neighboring nodes—φ = 1. We prove that within such settings, no deterministic exploration is possible in the semisynchronous model. We then address the synchronous model and show that no deterministic exploration protocol solves the problem with less than five robots when n> 6. We provide optimal (in terms of number of robots) deterministic algorithms in the fully synchronous model for both cases 3 ≤ n ≤ 6 and n> 6.