Distortion in One-Head Machines and Cellular Automata

Abstract : We give two families of examples of automorphisms of subshifts that are range-distorted, that is, the radius of their iterations grows sublinearly. One of these families comes from one-head machines, and allows us to build such automorphisms for the full shift, and to obtain undecidability results. We also give some conditions on the functions that can occur as such growths.
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Alberto Dennunzio; Enrico Formenti; Luca Manzoni; Antonio E. Porreca. 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2017, Milan, Italy. Springer International Publishing, Lecture Notes in Computer Science, LNCS-10248, pp.120-138, 2017, Cellular Automata and Discrete Complex Systems. 〈10.1007/978-3-319-58631-1_10〉
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Pierre Guillon, Ville Salo. Distortion in One-Head Machines and Cellular Automata. Alberto Dennunzio; Enrico Formenti; Luca Manzoni; Antonio E. Porreca. 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2017, Milan, Italy. Springer International Publishing, Lecture Notes in Computer Science, LNCS-10248, pp.120-138, 2017, Cellular Automata and Discrete Complex Systems. 〈10.1007/978-3-319-58631-1_10〉. 〈hal-01656350〉

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