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Directional movement of a collective of compassless automata on square lattice of width 2 | | Sergey Sapunov
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1 Sep 2023 | | Abstract: | We study the following problem: Can a collective of finite automata maintain
directed movement on a two-dimensional integer lattice of width 2, where the
elements (vertices) are anonymous? The automata do not distinguish between
vertices based on their coordinates of direction (that means each automaton has
no compass). We considered collectives consisting of an automaton and some
pebbles, which are automata of the simplest form, whose positions are entirely
determined by the automaton. We demonstrate that a collective of one automaton
and a maximum of three pebbles cannot maintain a direction of movement on the
lattice. However, a collective of one automaton and four pebbles can do so. | | Source: | arXiv, 2309.00292 | | Services: | Forum | Review | PDF | Favorites | |
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