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 AutomataArticle

Authors: Jarkko Kari ORCID1; Siamak Taati ORCID2

  • 1 Departement of Mathematics, University of Turku
  • 2 Department of Mathematics

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]
Funding:
    Source : OpenAIRE Graph
  • Cellular automata and discrete dynamical systems; Funder: Academy of Finland; Code: 131558

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