This paper poses a question about a simple localization problem. The question is if an oblivious walker on a line-segment can localize the middle point of the line-segment in finite steps observing the direction (i.e., Left or Right) and the distance to the nearest end point. This problem is arisen from self-stabilizing location problems by autonomous mobile robots with limited visibility, that is a widely interested abstract model in distributed computing. Contrary to appearances, it is far

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... m trivial if this simple problem is solvable or not, and unsettled yet. This paper is concerned with three variants of the problem with a minimal relaxation, and presents self-stabilizing algorithms for them. We also show an easy impossibility theorem for bilaterally symmetric algorithms.