Abstract
In the setting of symbolic dynamics on discrete finitely generated infinite groups, we define a model of multi-headed finite automata that walk on Cayley graphs, 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.
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Adian, S.I.: The burnside problem on periodic groups and related questions. Proceedings of the Steklov Institute of Mathematics 272(2), 2–12 (2011)
Aubrun, N., Barbieri, S., Sablik, M.: A notion of effectiveness for subshifts on finitely generated groups. ArXiv e-prints, December 2014
Ceccherini-Silberstein, T., Coornaert, M.: Cellular Automata and Groups. Springer Monographs in Mathematics. Springer (2010)
Delorme, M., Mazoyer, J.: Pebble automata. figures families recognition and universality. Fundam. Inf. 52(1–3), 81–132 (2002)
Grigorčuk, R.I.: On Burnside’s problem on periodic groups. Funktsional. Anal. i Prilozhen. 14(1), 53–54 (1980)
Gupta, N., Sidki, S.: On the burnside problem for periodic groups. Mathematische Zeitschrift 182(3), 385–388 (1983)
Jeandel, E.: Some Notes about Subshifts on Groups. ArXiv e-prints, January 2015
Lind, D., Marcus, B.: An introduction to symbolic dynamics and coding. Cambridge University Press, Cambridge (1995)
Salo, V., Törmä, I.: Plane-walking automata. CoRR, abs/1408.6701 (2014)
Schroeppel, R.: A two counter machine cannot calculate \(2^N\) (1972)
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Salo, V., Törmä, I. (2015). Group-Walking Automata. In: Kari, J. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2015. Lecture Notes in Computer Science(), vol 9099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47221-7_17
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DOI: https://doi.org/10.1007/978-3-662-47221-7_17
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