{"docId":2968,"paperId":2968,"url":"https:\/\/dmtcs.episciences.org\/2968","doi":"10.46298\/dmtcs.2968","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":261,"name":"DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems"}],"section":[{"sid":66,"title":"Proceedings","description":[]}],"repositoryName":"Hal","repositoryIdentifier":"hal-01196135","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-01196135v1","dateSubmitted":"2017-01-31 10:21:25","dateAccepted":null,"datePublished":"2011-01-01 00:00:00","titles":{"en":"Conservation Laws and Invariant Measures in Surjective Cellular Automata"},"authors":["Kari, Jarkko","Taati, Siamak"],"abstracts":{"en":"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."},"keywords":[["surjective cellular automata"],["conservation laws"],["invariant measures"],["statistical equilibrium"],"[INFO.INFO-DM] Computer Science [cs]\/Discrete Mathematics [cs.DM]","[MATH.MATH-DS] Mathematics [math]\/Dynamical Systems [math.DS]","[NLIN.NLIN-CG] Nonlinear Sciences [physics]\/Cellular Automata and Lattice Gases [nlin.CG]","[MATH.MATH-CO] Mathematics [math]\/Combinatorics [math.CO]"]}