Independent finite automata on Cayley graphs |
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Authors: | Ville Salo Ilkka Törmä |
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Affiliation: | 1.Center of Mathematical Modeling,University of Chile,Santiago,Chile;2.Department of Computer Science,Boston University,Boston,USA;3.Department of Mathematics and Statistics,University of Turku,Turku,Finland |
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Abstract: | In the setting of symbolic dynamics on discrete finitely generated infinite groups, we define a model of finite automata with multiple independent heads that walk on Cayley graphs, called group-walking automata, and use it to define subshifts. We characterize the torsion groups (also known as periodic groups) as those on which the group-walking automata are strictly weaker than Turing machines, and those on which the head hierarchy is infinite. |
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