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 ORCID-iD

    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.


    Volume: DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
    Section: Proceedings
    Published on: January 1, 2011
    Imported on: January 31, 2017
    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]
    Fundings :
      Source : OpenAIRE Research Graph
    • Cellular automata and discrete dynamical systems; Funder: Academy of Finland; Code: 131558

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