Geodesic
On traversing labyrinths by automata in $n$-dimensional space
Diskretnaya Matematika, Tome 12 (2000) no. 4, pp. 121-137

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The problem of traversing spatial labyrinths by automata is considered. It is proved that there exists an automaton that makes one unremovable mark (colour) on vertices of a labyrinth and traverses an arbitrary $n$-dimensional rectangular labyrinth. 
@article{DM_2000_12_4_a9,
     author = {A. Z. Nasyrov},
     title = {On traversing labyrinths by automata in $n$-dimensional space},
     journal = {Diskretnaya Matematika},
     pages = {121--137},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2000_12_4_a9/}
}
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A. Z. Nasyrov. On traversing labyrinths by automata in $n$-dimensional space. Diskretnaya Matematika, Tome 12 (2000) no. 4, pp. 121-137. http://geodesic.mathdoc.fr/item/DM_2000_12_4_a9/