Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T00:42:24.141Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on subgroups of automorphism groups of full shifts

Published online by Cambridge University Press:  08 November 2016

VILLE SALO Open the ORCID record for VILLE SALO [Opens in a new window]
VILLE SALO*
Affiliation:
Faculty of Mathematics and Natural Sciences, University of Turku, FI-20014 Turun Yliopisto, Finland email [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss the set of subgroups of the automorphism group of a full shift and submonoids of its endomorphism monoid. We prove closure under direct products in the monoid case and free products in the group case. We also show that the automorphism group of a full shift embeds in that of an uncountable sofic shift. Some undecidability results are obtained as corollaries.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 4 , June 2018 , pp. 1588 - 1600
Copyright
© Cambridge University Press, 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boyle, M., Lind, D. and Rudolph, D.. The automorphism group of a shift of finite type. Trans. Amer. Math. Soc. 306(1) (1988), 71–114.CrossRefGoogle Scholar
Hedlund, G. A.. Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3 (1969), 320–375.CrossRefGoogle Scholar
Kari, J. and Ollinger, N.. Periodicity and immortality in reversible computing. Proceedings of the 33rd International Symposium on Mathematical Foundations of Computer Science, MFCS ’08. Springer, Berlin, 2008, pp. 419–430.Google Scholar
Kim, K. H. and Roush, F. W.. On the automorphism groups of subshifts. Pure Math. Appl. 1(4) (1990), 203–230.Google Scholar
Kitchens, B. P.. Symbolic dynamics—One-sided, Two-sided and Countable State Markov Shifts. Universitext. Springer, Berlin, 1998.Google Scholar
Lind, D.. Entropies of automorphisms of a topological Markov shift. Proc. Amer. Math. Soc. 99(3) (1987), 589–595.CrossRefGoogle Scholar
Lind, D. and Marcus, B.. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge, 1995.CrossRefGoogle Scholar
Lothaire, M.. Algebraic Combinatorics on Words (Encyclopedia of Mathematics and its Applications, 90) . Cambridge University Press, Cambridge, 2002.CrossRefGoogle Scholar
Salo, V.. Groups and monoids of cellular automata. Cellular Automata and Discrete Complex Systems (Lecture Notes in Computer Science, 9099) . Ed. Kari, J.. Springer, Berlin, 2015, pp. 17–45.CrossRefGoogle Scholar
Salo, V. and Törmä, I.. Computational aspects of cellular automata on countable sofic shifts. Math. Found. Comput. Sci. 2012 (2012), 777–788.Google Scholar