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Conservation Laws and Invariant Measures in Surjective Cellular Automata
Abstract : 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.
https://hal.inria.fr/hal-01196135
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, September 9, 2015 - 11:14:54 AM
Last modification on : Wednesday, August 29, 2018 - 11:02:02 AM
Long-term archiving on: : Monday, December 28, 2015 - 11:01:13 PM
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, September 9, 2015 - 11:14:54 AM
Last modification on : Wednesday, August 29, 2018 - 11:02:02 AM
Long-term archiving on: : Monday, December 28, 2015 - 11:01:13 PM
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