A mouse moves along a tiled corridor with 2m tiles, where

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A mouse moves along a tiled corridor with 2m tiles, where m > 1. From each tile i l' 1, 2m. it moves to either tile i - l or i + 1 with equal probability. From tile 1 or tile 2m, it moves to tile 2 or 2m - 1, respectively, with probability 1. Each time the mouse moves to a tile i $ m or i > m, an electronic device outputs a signal L or R, respectively. Can the generated sequence of signals L and R be described as a Markov chain with states L and R?

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