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This paper presents an analysis of a simple robot model, called Bitbot. The Bitbot has limited capabilities; it can reliably follow walls and sense a contact with a wall. Although the Bitbot does not have a range sensor or a camera, it is able to acquire visibility information from the environment, which is then used to solve a pursuit-evasion task. Our developments are centered on the characterization of the information the Bitbot acquires. At any given moment, due to the sensing uncertainty, the robot does not know the current state. In general, uncertainty in the state is one of the central issues in robotics; the Bitbot model serves as an example of how the notion of information space naturally handles uncertainty. We show that state estimation with the Bitbot is a challenging problem, related to the well-known open problem of characterizing visibility graphs in computational geometry. However, state estimation becomes unnecessary to the achievement of the Bitbot's visibility tasks. We show how pursuit-evasion strategy is derived from a careful manipulation with histories of observations, and present analysis of the algorithm and experimental results.