Jarkko Kari ; Siamak Taati
-
Conservation Laws and Invariant Measures in Surjective Cellular Automata
dmtcs:2968 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
-
https://doi.org/10.46298/dmtcs.2968
Conservation Laws and Invariant Measures in Surjective Cellular Automata
Authors: Jarkko Kari ; Siamak Taati
NULL##0000-0002-6503-2754
Jarkko Kari;Siamak Taati
We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of one-dimensional surjective cellular automata. We also discuss a generalization of this fact to Markov measures and higher-range conservation laws in arbitrary dimension. As a corollary, we show that the uniform Bernoulli measure is the only shift-invariant, full-support Markov measure that is invariant under a strongly transitive cellular automaton.
Mairesse, Jean; Marcovici, Irène, 2014, Probabilistic Cellular Automata And Random Fields With I.I.D. Directions, Annales De L'Institut Henri Poincaré, Probabilités Et Statistiques, 50, 2, 10.1214/12-aihp530, https://doi.org/10.1214/12-aihp530.