A4 Refereed article in a conference publication
Conservation Laws and Invariant Measures in Surjective Cellular Automata
Authors: Kari J, Taati S
Editors: Nazim Fatès, Eric Goles, Alejandro Maass, Iván Rapaport
Publisher: DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE
Publication year: 2012
Journal: Discrete Mathematics and Theoretical Computer Science
Book title : Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
Journal name in source: DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
Journal acronym: DISCRETE MATH THEOR
Series title: Discrete Mathematics and Theoretical Computer Science
First page : 113
Last page: 122
Number of pages: 10
ISSN: 1462-7264
Web address : https://inria.hal.science/hal-00654706
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.
